UBC Theses and Dissertations

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UBC Theses and Dissertations

Testing a heuristic that determines customer service level in a two-echelon inventory system Hofmann, Nadine Elisabeth 1985

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T E S T I N G A H E U R I S T I C T H A T DETERMINES "CUSTOMER S E R V I C E L E V E L IN A TWO-ECHELON INVENTORY SYSTEM by NADINE E L I S A B E T H HOFMANN B . S c . ( M a t h e m a t i c s ) , U n i v e r s i t y o f M o n t r e a l , 1970 D i p l o m a o f E d u c a t i o n , M c G i l l U n i v e r s i t y , 1971 A T H E S I S SUBMITTED IN P A R T I A L F U L F I L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SC IENCE (BUSINESS ADMINISTRATION) i n THE FACULTY OF GRADUATE STUDIES F a c u l t y o f Commerce a n d B u s i n e s s A d m i n i s t r a t i o n We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF B R I T I S H COLUMBIA S e p t e m b e r , 1985 © N a d i n e E l i s a b e t h H o f m a n n , 1985 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e The U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my D e p a r t m e n t o r by h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . F a c u l t y o f Commerce and B u s i n e s s A d m i n i s t r a t i o n The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5 D a t e : S e p t e m b e r , 1985 ABSTRACT The p u r p o s e o f t h i s t h e s i s i s t o t e s t , v i a a GPSS s i m u l a t i o n , a h e u r i s t i c d e v e l o p e d by B.A. Rosenbaum. The h e u r i s t i c d e t e r m i n e s t h e l e v e l o f s e r v i c e a c u s t o m e r r e c e i v e s i n a m u l t i - e c h e l o n i n v e n t o r y s y s t e m . The s y s t e m c o n s i s t s o f one c e n t r a l D i s t r i b u t i o n C e n t r e (DC) w h i c h i s t h e s o u r c e o f s u p p l y f o r e i g h t R e g i o n a l D i s t r i b u t i o n C e n t r e s ( R D C ' s ) , w h i c h t h e m s e l v e s a r e t h e s o u r c e o f s u p p l y f o r c u s t o m e r demand. S e r v i c e i s d e f i n e d t o be t h e f r a c t i o n o f demand met f r o m o n-hand s t o c k a t t h e l o c a t i o n where t h e o r d e r i s p l a c e d . Two d i s t i n c t s e t s o f t e s t s on t h e h e u r i s t i c a r e ' p e r f o r m e d i n t h i s t h e s i s . F i r s t , a w i d e r a n g e o f p a r a m e t e r v a l u e s a r e u s e d i n t h e s i m u l a t i o n s t o t e s t t h e s e n s i t i v i t y o f t h e a s s u m p t i o n s e s s e n t i a l i n t h e d e v e l o p m e n t o f t h e h e u r i s t i c . S e c o n d , t h e r o b u s t n e s s o f t h e h e u r i s t i c i s e x a m i n e d when d i f f e r e n t a s s u m p t i o n s a r e s u b s t i t u t e d i n t h e i n v e n t o r y s y s t e m a n a l y s e d . The a n a l y s i s i n d i c a t e s t h e h e u r i s t i c p e r f o r m s f a i r l y w e l l u n d e r v a r i o u s c o n d i t i o n s . I n p a r t i c u l a r , i n c r e a s i n g t h e o r d e r s i z e o r r e d u c i n g t h e number o f w a r e h o u s e s i n t h e s y s t e m y i e l d c a l c u l a t e d v a l u e s p r e d i c t i v e o f t h e s i m u l a t e d r e s u l t s . i i T a b l e of C o n t e n t s 1. INTRODUCTION 1 2. THE STRUCTURE OF THE INVENTORY SYSTEM 3 2.1 D e f i n i n g the System Under Study 3 3. THE HEURISTIC . . 8 3.1 D e f i n i t i o n of a H e u r i s t i c 8 3.2 The Assumptions of the H e u r i s t i c 8 3.3 E s t i m a t i n g Customer S e r v i c e L e v e l 10 3.4 Overview of the H e u r i s t i c 10 4. THE GPSS SIMULATION MODEL 16 4.1 D e f i n i n g the I n v e n t o r y System ....16 4.2 E v a l u a t i n g the Parameters of Demand 17 4.3 D i v e r g e n c e from Rosenbaum's S i m u l a t i o n Model ....18 4.4 D e f i n i n g the GPSS Model *' 19 4.5 V a l i d a t i n g the GPSS Model 21 5. TESTING THE ASSUMPTIONS 24 5. 1 Base Run 24 5.2 V a r y i n g the number of RDC'S i n the system .......27 5.3 I n c r e a s i n g the EOQ s i z e s 29 .6. TESTING THE ROBUSTNESS OF THE HEURISTIC 42 6.1 D e f i n i n g the U n i f o r m D i s t r i b u t i o n 42 6.2 Base Run w i t h Lowered DSL Va l u e 43 6.3 U n i f o r m D i s t r i b u t i o n of Lead Time 44 6.4 T r u n c a t i n g the D i s t r i b u t i o n of Demand 46 7. CONCLUSIONS 61 REFERENCES 63 APPENDIX A 65 i i i APPENDIX B GLOSSARY APPENDIX C L I S T OF TABLES TABLE Page 1 B a r b a r a A. Rosenbaum's S i m u l a t i o n R e s u l t s 31 2 I n p u t s t o a n d R e s u l t s f r o m S i m u l a t i o n s I a n d I I S e t t i n g a R e f e r e n c e P o i n t 32 3 R e s u l t s f r o m S i m u l a t i o n s I I I - V I - I n v e n t o r y S y s t e m w i t h V a r y i n g Numbers o f RDC's 35 4 R e s u l t s f r o m S i m u l a t i o n s V I I - I X - I n c r e a s i n g EOQ S i z e s 36 5 R e s u l t s f r o m S i m u l a t i o n s X a n d XI - D i s t r i b u t i o n o f Demand i s N o r m a l a n d N o r m a l T r u n c a t e d a t Z e r o 50 6 R e s u l t s f r o m S i m u l a t i o n s X I I - X I V - U n i f o r m L e a d Time D i s t r i b u t i o n 52 7 R e s u l t s f r o m S i m u l a t i o n s I I , XV a n d XVI - N o r m a l D i s t r i b u t i o n o f Demand T r u n c a t e d a t Z e r o . . . 55 8 R e s u l t s f r o m S i m u l a t i o n s X V I I - X I X - N o r m a l D i s t r i b u t i o n o f Demand T r u n c a t e d a t - M / 2 . . . . 57 9 R e s u l t s f r o m S i m u l a t i o n s X X - X X I I - N o r m a l D i s t r i b u t i o n o f Demand T r u n c a t e d a t M 59 v L I S T OF FIGURES F I G Page 1 A T w o - E c h e l o n I n v e n t o r y S y s t e m 4 2 The A v e r a g e Number o f O r d e r s O u t s t a n d i n g a t any one Time a t t h e RDC's when t h e Demand D i s t r i b u t i o n i s N o r m a l o r N o r m a l T r u n c a t e d a t Z e r o w i t h DSL=80% a n d RSL=98% 33 3 The Minimum and Maximum Number o f O r d e r s P e r Y e a r a t e a c h RDC when t h e Demand D i s t r i b u t i o n i s N o r m a l w i t h DSL=80% a n d RSL=98% 34 4 The Minimum and Maximum Number o f O r d e r s P e r Y e a r a t e a c h RDC when t h e Demand D i s t r i b u t i o n i s N o r m a l T r u n c a t e d a t Z e r o w i t h DSL=75% and RSL=98% 37 5 The Minimum and Maximum Number o f O r d e r s P e r Y e a r a t e a c h RDC when t h e Demand D i s t r i b u t i o n i s N o r m a l T r u n c a t e d a t Z e r o a nd EOQ i s D o u b l e d w i t h DSL=75% and RSL=98% 38 6 The Minimum and Maximum Number o f O r d e r s P e r Y e a r a t e a c h RDC when t h e Demand D i s t r i b u t i o n i s N o r m a l T r u n c a t e d a t Z e r o a nd EOQ i s T r i p l e d w i t h DSL=75% and RSL=98% 39 7 The Minimum and Maximum Number o f O r d e r s P e r Y e a r a t e a c h RDC when t h e Demand D i s t r i b u t i o n i s N o r m a l T r u n c a t e d a t Z e r o a nd EOQ i s M u l t i p l i e d by E i g h t w i t h DSL=75% a n d RSL=98% 40 8 The A v e r a g e Number o f O r d e r s O u t s t a n d i n g a t any one Time a t t h e RDC's when t h e Demand D i s t r i b u t i o n i s N o r m a l T r u n c a t e d a t Z e r o and EOQ i s M u l t i p l i e d by One,Two,Three a n d E i g h t w i t h DSL=75% and RSL=98% 41 9 The A v e r a g e Number Of O r d e r s O u t s t a n d i n g a t any one Time a t t h e RDC's when t h e Demand D i s t r i b u t i o n i s N o r m a l T r u n c a t e d a t Z e r o w i t h RSL=98% and DSL=70% a n d 80% 51 10 The A v e r a g e Number o f O r d e r s O u t s t a n d i n g a t any one Time a t t h e RDC's when t h e Demand D i s t r i b u t i o n i s N o r m a l T r u n c a t e d a t Z e r o , t h e L e a d Time D i s t r i b u t i o n i s U n i f o r m a t t h e DC, RDC's and B o t h t h e DC a n d t h e RDC's w i t h DSL=70% and RSL=98% 53 v i L I S T OF FIGURES (CONT'D)  F I G Page 11 The C o e f f i c i e n t s o f V a r i a t i o n o f t h e N o r m a l D i s t r i b u t i o n T r u n c a t e d a t Z e r o , M e a n / 2 , a n d t h e Mean P l o t t e d a s F u n c t i o n s o f t h e C o e f f i c i e n t o f V a r i a t i o n o f t h e S t a n d a r d N o r m a l D i s t r i b u t i o n 54 12 The A v e r a g e Number o f O r d e r s O u t s t a n d i n g a t any one Time a t t h e RDC's when t h e Demand D i s t r i b u t i o n i s N o r m a l T r u n c a t e d a t Z e r o , t h e C o e f f i c i e n t s o f V a r i a t i o n Range f r o m .21 t o 6.0, a n d DSL=80% and RSL=98% 56 13 The A v e r a g e Number o f O r d e r s O u t s t a n d i n g a t any one Time a t t h e RDC's when t h e Demand D i s t r i b u t i o n i s N o r m a l T r u n c a t e d a t Mean/2 w i t h t h e C o e f f i c i e n t s o f V a r i a t i o n R a n g i n g f r o m .21 t o 6.0, a n d DSL=80% and RSL=98%... 58 14 The A v e r a g e Number of o r d e r s O u t s t a n d i n g a t any one Time a t t h e RDC's when t h e Demand D i s t r i b u t i o n i s N o r m a l T r u n c a t e d a t t h e Mean w i t h C o e f f i c i e n t s o f V a r i a t i o n R a n g i n g f r o m .21 t o 6.0, a n d DSL=80% a n d RSL=98%... 60 v i i A c k n o w l e d g e m e n t I w o u l d l i k e t o t h a n k t h e members o f my c o m m i t t e e P r o f e s s o r s M a u r i c e Q u e y r a n n e , Dean Uyeno a n d e s p e c i a l l y P r o f e s s o r D e r e k A t k i n s , t h e C h a i r m a n who o r i g i n a l l y s u g g e s t e d t h e t o p i c t o me and g ave me c o n s t a n t s u p p o r t a n d e n c o u r a g e m e n t t h r o u g h o u t t h e e n t i r e p r o j e c t . My d e e p e s t a p p r e c i a t i o n g o e s t o my v e r y good f r i e n d s B a r b , B e r n a r d , L a u r a , M i c h a e l a n d R u t h f o r t h e i r w i l l i n g n e s s t o l i s t e n t o i n - d e p t h d i s c u s s i o n s o f my t o p i c , t h u s e n a b l i n g me t o c l a r i f y my t h o u g h t s , a n d f o r t h e i r s u p p o r t when my e n t h u s i a s m and e n e r g y were l a g g i n g . The p r o c e s s o f c o m p l e t i n g my t h e s i s w o u l d have been a much h a r d e r one w i t h o u t t h e s e t r u l y f i n e - f r i e n d s a r o u n d me. L a s t , b u t n o t l e a s t , I w o u l d l i k e t o t h a n k my c h i l d r e n , C l a u d i n e a n d D a v i d Lam, f o r s h a r i n g f u l l y i n t h i s e x p e r i e n c e a n d f o r t h e i r u n d e r s t a n d i n g when I was n o t a v a i l a b l e t o them. v i i i C h a p t e r 1 INTRODUCTION T r y i n g t o d e t e r m i n e t h e p e r c e n t a g e o f s e r v i c e a v a i l a b l e t o c u s t o m e r s i n an i n v e n t o r y s y s t e m i s i m p o r t a n t t o most f i r m s . T h i s s e r v i c e l e v e l , h o w e v e r , i s d i f f i c u l t t o a s s e s s s i n c e i t d e p e n d s on s e v e r a l p a r a m e t e r s i n h e r e n t t o i n v e n t o r y s y s t e m s . The most common of t h e s e p a r a m e t e r s a r e t h e t y p e o f demand a n d t h e amount o f s t o c k a v a i l a b l e a t e a c h l o c a t i o n i n t h e s y s t e m , t h e t i m e r e q u i r e d b e t w e e n o r d e r p l a c e m e n t a n d o r d e r r e c e i p t , t h e t y p e o f r e v i e w s y s t e m u s e d , i . e . , c o n t i n u o u s v s p e r i o d i c , a n d w h e t h e r b a c k o r d e r s a r e a c c u m u l a t e d o r must be c o n s i d e r e d a s l o s t s a l e s . The d i f f i c u l t y i s m u l t i p l i e d when t h e s y s t e m c o n s i s t s o f more t h a n one l e v e l o f w a r e h o u s e s o r c e n t r e s , i . e . , i s a m u l t i - e c h e l o n i n v e n t o r y s y s t e m . T h e r e i s a l o n g h i s t o r y o f a n a l y s i s r e l a t e d t o m u l t i - e c h e l o n p r o b l e m s i n t h e l i t e r a t u r e . A c o m p r e h e n s i v e summary h a s been w r i t t e n by C l a r k [ 2 ] and i n c l u d e s t h e m a j o r p a p e r s r e l a t i n g t o t h i s t o p i c w h i c h were p u b l i s h e d b e f o r e 1974. A l a r g e number o f p a p e r s h a v e c o n s i d e r e d d e t e r m i n i s t i c s y s t e m s b o t h w i t h c o n s t a n t a n d d y n a m i c demand. T h i s p a p e r h o w e v e r , c o n s i d e r s t h e s t o c h a s t i c m u l t i - e c h e l o n s y s t e m . Some work h a s a l s o been done i n t h i s a r e a i n t h e f o r m o f o p t i m a l p o l i c i e s . H o w e v e r , v e r y l i t t l e work on s y s t e m s e r v i c e l e v e l s h a s been done f o r m u l t i - e c h e l o n s y s t e m s w i t h f a i r l y r e a l i s t i c s e t s o f a s s u m p t i o n s . The o n l y p a p e r s on t h i s p a r t i c u l a r t o p i c t h a t c o u l d be i d e n t i f i e d a s m a k i n g a 1 2 s u b s t a n t i a l c o n t r i b u t i o n a r e t h o s e by Rosenbaum [ 8 ] , [ 9 ] , and S a n d [ 1 0 ] . Rosenbaum s t u d i e d a s y s t e m where demand a n d l e a d t i m e s a r e s t o c h a s t i c a n d t h e o r d e r i n g p o l i c y i s p e r i o d i c a t t h e d i s t r i b u t i o n c e n t r e b u t f o l l o w s a d a i l y r e v i e w p o l i c y a t t h e p r i m a r y e c h e l o n . T h i s p a r t i c u l a r t y p e o f i n v e n t o r y s y s t e m i s o f i n t e r e s t s i n c e i t r e f l e c t s more a c c u r a t e l y t h e s i t u a t i o n f a c e d by most f i r m s t o d a y . C h a p t e r 2 THE STRUCTURE OF THE INVENTORY SYSTEM 2 . 1 D E F I N I N G THE SYSTEM UNDER STUDY The i n v e n t o r y s y s t e m m o d e l e d i s a m u l t i - e c h e l o n s y s t e m w i t h s t o c h a s t i c demand a n d l e a d t i m e s . The m u l t i - e c h e l o n i n v e n t o r y s y s t e m c o n s i d e r e d h e r e i s one i n w h i c h a number o f R e g i o n a l D i s t r i b u t i o n C e n t r e s , ( R D C ' s ) , s a t i s f y c u s t o m e r demand f o r g o o d s w h i l e a c t i n g a s c u s t o m e r s o f a h i g h e r l e v e l D i s t r i b u t i o n C e n t r e , ( D C ) . T h e D i s t r i b u t i o n C e n t r e i n t u r n o r d e r s d i r e c t l y f r o m an o u t s i d e m a n u f a c t u r e r o r f a c t o r y . F i g u r e 1 i l l u s t r a t e s t h e t w o - l e v e l i n v e n t o r y s y s t e m t o be a n a l y s e d . O t h e r c h a r a c t e r i s t i c s o f t h e s y s t e m a r e a s f o l l o w s : 1. A t e a c h RDC, demand i n n o n - o v e r l a p p i n g e q u a l t i m e i n t e r v a l s i s i n d e p e n d e n t a n d f o l l o w s a n o r m a l d i s t r i b u t i o n w i t h n e g l i g i b l e p r o b a b i l i t y t h a t demand i s l e s s t h a n z e r o . 2 . C u s t o m e r demand o c c u r s o n l y a t t h e R D C ' s . 3 . No t r a n s s h i p m e n t s a r e p e r m i t t e d t o o c c u r b e t w e e n t h e R D C ' s . 4 . DC l e a d t i m e s a n d t h o s e RDC l e a d t i m e s when t h e DC h a s s t o c k f o l l o w a s t a t i o n a r y n o r m a l d i s t r i b u t i o n a t e a c h l o c a t i o n a n d a r e i n d e p e n d e n t . R e p l e n i s h m e n t o r d e r s a r r i v e i n t h e o r d e r i n w h i c h t h e y were p l a c e d . 5 . No o r d e r c a n be e x p e d i t e d . 6 . The i n v e n t o r y s y s t e m i s a s s u m e d t o be i n a s t e a d y s t a t e 3 4 FIGURE 1: A T w o - E c h e l o n I n v e n t o r y S y s t e m , FACTORY D ISTRIBUT ION CENTRE REGIONAL D ISTRIBUT ION CENTRE T REGIONAL D ISTRIBUT ION CENTRE J REGIONAL DISTRIBUTION CENTRE T CUSTOMERS 5 c o n d i t i o n . 7 . No p a r t o r d e r s f r o m t h e f a c t o r y t o t h e DC a r e a l l o w e d . 8 . B a c k o r d e r s a r e a c c u m u l a t e d a t a l l l o c a t i o n s a n d a r e f i l l e d when a r e p l e n i s h m e n t o r d e r a r r i v e s . In a d d i t i o n , p e r i o d i c r e v i e w i s i n e f f e c t a t t h e DC w h i c h u s e s an ' o r d e r up t o ' p o l i c y . A p e r i o d i c r e v i e w i s one w h i c h a l l o w s a f i x e d number o f d a y s , L , t o e l a p s e b e t w e e n o r d e r p l a c e m e n t s . The o r d e r s i z e i s e q u a l t o t h e d i f f e r e n c e b e t w e e n S , t h e ' o r d e r up t o ' q u a n t i t y , a n d t h e i n v e n t o r y p o s i t i o n a t t h e t i m e o f o r d e r i n g where t h e i n v e n t o r y p o s i t i o n , I P , i s ( o n - h a n d s t o c k + o u t s t a n d i n g o r d e r s -b a c k o r d e r s ) . The R D C ' s u s e a d a i l y r e v i e w EOQ/ROP, ( Q , R ) , s y s t e m . EOQ o r Q i s t h e e c o n o m i c o r d e r q u a n t i t y c a l c u l a t e d f r o m a n d d e p e n d e n t upon t h e u n i t c o s t , h o l d i n g c o s t a n d y e a r l y demand o f a p a r t i c u l a r i t e m . ROP o r R i s t h e r e o r d e r p o i n t a t e a c h RDC. When t h e i n v e n t o r y p o s i t i o n , I P , r e a c h e s t h i s p o i n t , an o r d e r f o r EOQ u n i t s i s s e n t t o t h e D C . The o r d e r up t o q u a n t i t y , S , i s c o m p u t e d b a s e d on t h e d i s t r i b u t i o n o f demand a t t h e DC o v e r i t s s c h e d u l i n g i n t e r v a l ( p r o d u c t i o n l e a d t i m e + L ) , a n d t h e s e r v i c e l e v e l D S L . S p e c i f i c a l l y S i s t h e s o l u t i o n t o : (1) E f D e m a n d o v e r L ] where f , ( a ) i s t h e p r o b a b i l i t y d e n s i t y f u n c t i o n o f A , t h e demand on t h e DC o v e r I. 6 A t e a c h R D C i r EOQ^ w i t h t h e p r o b a b i l i t y d e n s i t y f u n c t i o n o f B^, c u s t o m e r demand o v e r t h e RDCN l e a d t i m e ( L T . ) , a n d t h e RDC- i n p u t s e r v i c e l e v e l (RSL.) a r e u s e d t o 1 1 r l c a l c u l a t e t h e r e o r d e r p o i n t R^. S p e c i f i c a l l y , R^ i s t h e s o l u t i o n t o : \ D (b - R . ) f n ( b ) d b 1 - RSL = 1 B i (2) EOQ i where f - (b) i s t h e p r o b a b i l i t y d e n s i t y f u n c t i o n o f B.. I We must n o t e w i t h p a r t i c u l a r a t t e n t i o n t h a t LT^ r e p r e s e n t s t h e l e a d t i m e f r o m o r d e r p l a c e m e n t t o o r d e r r e c e i p t when t h e DC h a s s t o c k a v a i l a b l e when t h e o r d e r a r r i v e s f r o m t h e RDC^. LT^ r e p r e s e n t s t h e sum o f o r d e r p r o c e s s i n g a n d t r a n s i t t i m e a t any l o c a t i o n . RSL^ c a n t h u s be d e f i n e d t o be t h e f r a c t i o n o f c u s t o m e r demand s a t i s f i e d f r o m o n-hand i n v e n t o r y a t RDC^ i f t h e DC a l w a y s h a s s t o c k a v a i l a b l e , i . e . , i f DSL i s 100%. The c u s t o m e r s e r v i c e l e v e l CSL^ i s t h e f r a c t i o n o f c u s t o m e r demand t h a t c a n a c t u a l l y . b e f i l l e d f r o m o n - h a n d s t o c k a t any RDC^ a n d i s s e e n t o be d e p e n d e n t on DSL and RSL^. I n f a c t , RSL^ i s t h e u p p e r bound on CSL^, s i n c e i f t h e DC a l w a y s h a s s t o c k a v a i l a b l e t o f i l l t h e o r d e r s f o r EOQ^ f r o m RDC^, t h e c u s t o m e r s e r v i c e l e v e l ( CSL^) e q u a l s t h e i n p u t s e r v i c e l e v e l a t RDC^ ( R S L ^ ) . When t h e DC e x p e r i e n c e s s t o c k - o u t we s e e t h a t t h e RDC^ c a n n o t o b t a i n s t o c k a n d t h e s e r v i c e p r o v i d e d t o i t s c u s t o m e r s w i l l d r o p b e l o w t h e i n p u t 7 RSL i . I t i s o b v i o u s from e q u a t i o n s 1 and 2 t h a t DSL and RSL^ determine the amount of s t o c k kept a t each l o c a t i o n i n the system. T h i s on-hand s t o c k i n t u r n a f f e c t s the customer s e r v i c e l e v e l a c t u a l l y d e l i v e r e d a t each l o c a t i o n . C h a p t e r 3 THE HEURISTIC 3.1 D E F I N I T I O N OF A HEURISTIC I n t h e p r e s e n t c o n t e x t a h e u r i s t i c i s a m a t h e m a t i c a l m o d e l w h i c h makes u s e o f a p p r o x i m a t i o n s t o r e d u c e t h e c o m p l e x i t y o f t h e c o m p u t a t i o n s n e e d e d t o a r r i v e a t a s o l u t i o n . 3.2 THE ASSUMPTIONS OF THE HEURISTIC B a r b a r a A. Rosenbaum d e v e l o p e d a h e u r i s t i c f o r an i n v e n t o r y s y s t e m s i m i l a r t o t h e one d e s c r i b e d i n t h e p r e v i o u s c h a p t e r . T h i s h e u r i s t i c d e t e r m i n e s t h e a c t u a l c u s t o m e r s e r v i c e l e v e l g i v e n a n y c o m b i n a t i o n o f DSL a n d RSL. F o r c o m p u t a t i o n a l e a s e , t h e f o l l o w i n g a s s u m p t i o n s r e g a r d i n g t h e b e h a v i o u r o f t h e s y s t e m a r e made: 1. C u s t o m e r demand i s n o r m a l l y d i s t r i b u t e d o v e r RDC^ l e a d t i m e s b e g i n n i n g when t h e DC e x p e r i e n c e s a z e r o - s t o c k s i t u a t i o n . T h i s a s s u m p t i o n d e p e n d s on t h e f a c t t h a t t h e c u s t o m e r demand a t t h e RDC's i s d e f i n e d t o be n o r m a l l y d i s t r i b u t e d . 2. Demand on t h e DC i s n o r m a l l y d i s t r i b u t e d o v e r i t s s c h e d u l i n g i n t e r v a l ( l e a d t i m e + r e v i e w p e r i o d ) w i t h n e g l i g i b l e p r o b a b i l i t y t h a t demand i s l e s s t h a n z e r o . The v a l i d i t y o f t h i s a s s u m p t i o n d e p e n d s on t h e a r r i v a l o f a s u f f i c i e n t number o f o r d e r s a t t h e DC o v e r t h e s c h e d u l i n g i n t e r v a l t o a p p r o x i m a t e a n o r m a l 8 9 d i s t r i b u t i o n . T h r e e e s s e n t i a l f a c t o r s c o n t r i b u t e i n a c h i e v i n g t h i s a . t h e l e n g t h o f t h e t i m e p e r i o d b . t h e number o f R D C ' s o r d e r i n g f r o m t h e DC a n d c . t h e f r e q u e n c y o f o r d e r i n g a t e a c h r e g i o n a l l o c a t i o n , i . e . , t h e EOQ s i z e . A l e n g t h y s c h e d u l i n g i n t e r v a l , n u m e r o u s R D C ' s a n d s m a l l EOQ q u a n t i t i e s w o u l d l i k e l y r e s u l t i n a p p r o x i m a t i n g a n o r m a l d i s t r i b u t i o n . 3 . When a r e p l e n i s h m e n t o r d e r a r r i v e s a t a n y l o c a t i o n i t i s o f a d e q u a t e s i z e t o f i l l a l l o u t s t a n d i n g b a c k o r d e r s . A l l o u t s t a n d i n g o r d e r s t o a n y RDC a r e b a t c h e d a n d s h i p p e d t o g e t h e r when t h e DC i s r e p l e n i s h e d . 4 . When t h e DC o n - h a n d i n v e n t o r y , OH , i s l e s s t h a n an i n c o m i n g o r d e r f o r EOQ^ , i t i s a s s u m e d t h a t OH i s u n i f o r m l y d i s t r i b u t e d o v e r t h e i n t e r v a l [ 0 , E O Q ^ ] . The RDC^ i s s h i p p e d t h e OH u n i t s a n d o r d e r s a s u b s e q u e n t EOQ^ - OH u n i t s t h e n e x t t i m e t h e i n v e n t o r y p o s i t i o n r e a c h e s R^, t h e r e o r d e r p o i n t . T h i s a s s u m p t i o n i s n e c e s s a r y t o a l l o w t h e l e a d t i m e s o f r e p l e n i s h m e n t when t h e DC h a s s t o c k t o be u n a f f e c t e d by t h e o c c u r r e n c e o f s t o c k o u t s , w h i l e t h e b a c k o r d e r e d u n i t s w i l l h a v e l e a d t i m e s w h i c h a r e a f f e c t e d by a z e r o s t o c k s i t u a t i o n . The two p o r t i o n s o f t h e o r d e r a r e t r e a t e d a s two i n d e p e n d e n t o r d e r s e a c h w i t h i t s own l e a d t i m e . 5 . A t t h e t i m e t h e DC e x p e r i e n c e s a s t o c k o u t , t h o s e R D C ' s w h i c h d i d not p l a c e t h e o r d e r c a u s i n g t h e s i t u a t i o n a r e 10 assumed t o h a v e an i n v e n t o r y p o s i t i o n w h i c h i s u n i f o r m l y d i s t r i b u t e d o v e r [ R i , R i + E O Q i ] . 3.3 ESTIMATING CUSTOMER SERVICE L E V E L The h e u r i s t i c c a l c u l a t e s t h e c u s t o m e r s e r v i c e l e v e l , C SL, g i v e n any i n p u t s e r v i c e l e v e l , R SL^, a t RDC^ and any i n p u t s e r v i c e l e v e l DSL a t t h e DC. S i n c e no a s s u m p t i o n s a r e made r e g a r d i n g i d e n t i c a l p a r a m e t e r v a l u e s a t t h e RDC's, ( i . e . , EOQ, demand a n d l e a d t i m e d i s t r i b u t i o n s ) , t h e same v a l u e o f DSL and RSL a t two d i f f e r e n t l o c a t i o n s may y i e l d d i f f e r e n t CSL^ v a l u e s . F o r t h i s r e a s o n t h e h e u r i s t i c c a l c u l a t i o n s must be r e p e a t e d f o r e a c h RDC l o c a t i o n . F o r e a s e o f n o t a t i o n , s i n c e we a r e d e a l i n g w i t h t h e DC and a g i v e n RDC, l o c a t i o n s u b s c r i p t w i l l no l o n g e r a p p e a r . Time s u b s c r i p t s a r e n o t n e e d e d s i n c e t h e s y s t e m i s assumed t o h a v e r e a c h e d s t e a d y s t a t e . O n l y t h o s e s e c t i o n s o f t h e h e u r i s t i c w h i c h a r e r e l e v a n t t o t h e a n a l y s i s p e r f o r m e d i n l a t e r c h a p t e r s a r e d i s c u s s e d h e r e . F o r f u r t h e r d e t a i l s s e e Rosenbaum [ 8 ] . 3.4 OVERVIEW OF THE HEURISTIC CSL i s d e f i n e d t o be t h e s t e a d y s t a t e a v e r a g e v a l u e o f t h e a n n u a l f i l l r a t e o f an i t e m a t a p a r t i c u l a r RDC a n d i s c a l c u l a t e d t o be CSL = 1 - E [ G ] / M a d (3) where E [ G ] = t h e e x p e c t e d number o f u n i t s b a c k o r d e r e d p e r y e a r 11 a t t h e RDC, a n d mean o f a n n u a l demand on t h e RDC. AD When c a l c u l a t i n g E [ G ] , two s i t u a t i o n s a r e c o n s i d e r e d : t h e s i t u a t i o n when RDC o r d e r s a n d DC h a s s t o c k a n d t h e s i t u a t i o n when RDC o r d e r s a n d DC h a s no s t o c k a v a i l a b l e . We t h e r e f o r e h a v e t h a t E [ G ] = E[G|N>0]-Pr(N>0) + E[G|N=0]•Pr(N=0) (4) where N = o n - h a n d i n v e n t o r y a t t h e DC. By d e f i n i t i o n , t h e e x p e c t e d number of u n i t s b a c k o r d e r e d p e r y e a r a t RDC i s 1-RSL m u l t i p l i e d by t h e e x p e c t e d y e a r l y demand, i . e . , E[G|N>0] = ( 1 - R S L ) • , a n d t h e p r o b a b i l i t y t h a t t h e DC h a s s t o c k i s DSL, ( P r ( N > 0 ) = D S L ) . The s e c o n d t e r m o f t h e sum i n e q u a t i o n (4) r e p r e s e n t s t h e e x p e c t e d number o f b a c k o r d e r e d u n i t s a t t h e RDC o c c u r r i n g e a c h y e a r d u r i n g l e a d t i m e s b e g i n n i n g when t h e DC has no s t o c k . A l l l e a d t i m e s b e g i n n i n g d u r i n g a z e r o - s t o c k s i t u a t i o n a t t h e DC w i l l end a t t h e same t i m e s i n c e i t i s assumed t h a t when t h e DC r e c e i v e s a r e p l e n i s h m e n t o r d e r i t i s s u f f i c i e n t t o f i l l a l l b a c k o r d e r s . I t i s a l s o assumed t h a t a l l o u t s t a n d i n g o r d e r s t o an RDC a r e b a t c h e d a n d s h i p p e d t o g e t h e r ( A s s u m p t i o n 3 ) . I t i s t h e r e f o r e n e c e s s a r y o n l y t o d e a l w i t h t h e f i r s t l e a d t i m e o c c u r r i n g a f t e r t h e DC d e p l e t e s i t s s t o c k , L T ' , t o c o m p u t e E[G|N=0]. A l l o t h e r l e a d t i m e s b e g i n n i n g d u r i n g t h e s t o c k o u t w i l l be c o m p l e t e l y c o n t a i n e d by LT'. 1 2 The DC p l a c e s o r d e r s on t h e f a c t o r y e v e r y L d a y s , a n d a s s u m i n g 260 w o r k i n g d a y s i n one y e a r , p o t e n t i a l s t o c k o u t s c a n t a k e p l a c e 2 6 0 / L t i m e s e a c h y e a r , w i t h a maximum of 2 6 0 / L o c c u r r e n c e s o f L T ' p e r y e a r . To c a l c u l a t e t h e e x p e c t e d number o f o c c u r r e n c e s o f L T ' p e r y e a r , t h e p r o b a b i l i t y t h a t DC e x p e r i e n c e s a s t o c k o u t a n d an o r d e r f o r EOQ i s p l a c e d by an RDC i s r e q u i r e d . T h i s i s d e f i n e d a s P r ( Y < T ) , where Y = number o f d a y s a f t e r t h e DC d e p l e t e s i t s s t o c k t h a t an RDC p l a c e s i t s f i r s t o r d e r on t h e D C . T = number o f d a y s t h e DC i s i n z e r o - s t o c k s i t u a t i o n d u r i n g a s c h e d u l i n g i n t e r v a l i n w h i c h DC d e p l e t e s i t s s t o c k . W i t h 0 ( x ) d x = U n i t N o r m a l D e n s i t y f u n c t i o n , a n d t h e p r o b a b i l i t y t h a t t h e DC d e p l e t e s i t s s t o c k d u r i n g t h e DC i s a s s u m e d t o be n o r m a l l y d i s t r i b u t e d o v e r I ( A s s u m p t i o n The s e c o n d t e r m o f t h e sum i n e q u a t i o n (4) c a n now be w r i t t e n a s s c h e d u l i n g i n t e r v a l I i s $( (S-y.^)/o^) s i n c e demand on t h e 2 ) . E [ G | N = 0 ] - P r ( N = 0 ) = 2 6 0 - P r ( Y < T ) L | S M A J - E [ C | N = 0 ] (5) By a s s u m p t i o n 1, t h e demand o v e r L T ' a t t h e RDC i s n o r m a l l y d i s t r i b u t e d a n d t h e r e f o r e , 1 3 E[C|N=0] = j R ( z - R ) 1 <t> lZ M B'\dz ° B ' I V / (6) where t h e mean i s MTJT-I • E [ L T ' ] a n d a - a. * + V a r [ L T ' ] . M * RD* L T ' i s d e f i n e d t o be t h e l e a d t i m e o f r e p l e n i s h m e n t a t t h e RDC b e g i n n i n g when t h e DC e x p e r i e n c e s s t o c k o u t . I t i s t h e sum o f L T , o r d e r p r o c e s s i n g + t r a n s i t t i m e , a n d t h e number o f d a y s t h e RDC o r d e r must w a i t f o r r e p l e n i s h m e n t t o a r r i v e a t t h e D C , i . e . , T - Y | Y < T . The mean a n d v a r i a n c e o f L T ' c a n now be w r i t t e n a s The n e e d t o c o m p u t e E [ T - Y | Y < T ] , V a r [ T - Y | Y < T ] a n d P r ( Y < T ) l e a d s B . A . Rosenbaum t o make s e v e r a l a p p r o x i m a t i o n s a t t h i s p o i n t b e c a u s e o f t h e c o m p l e x i n t e r a c t i o n o f T a n d Y . U , t h e i n v e n t o r y p o s i t i o n a t t h e RDC when t h e DC e x p e r i e n c e s s t o c k o u t i s f o u n d t o be a p p r o x i m a t e l y u n i f o r m b e t w e e n R a n d R + EOQ. By A s s u m p t i o n 6 , t h i s i s t r u e f o r a l l R D C ' s w h i c h d i d n o t c a u s e t h e z e r o s t o c k s i t u a t i o n t o o c c u r a t t h e D C . H o w e v e r , t h e RDC w h i c h c a u s e s t h e s t o c k o u t r e c e i v e s OH u n i t s w h i c h a r e u n i f o r m l y d i s t r i b u t e d b e t w e e n 0 E [ L T ' ] = E [ L T ] + E [ T - Y | Y < T ] a n d (7) V a r t L T ' ] = V a r [ L T ] + V a r [ T - Y | Y < T ] 1 4 a n d EOQ ( A s s u m p t i o n 5 ) . The i n v e n t o r y p o s i t i o n a t t h e RDC i s now R + OH w h i c h i s u n i f o r m l y d i s t r i b u t e d b e t w e e n R and R + EOQ. The p r o b a b i l i t y d e n s i t y f u n c t i o n o f Y i s t h e n e s t i m a t e d a n d i s f o u n d t o be a p p r o x i m a t e l y u n i f o r m b e t w e e n 0 a n d E [ TB ] , t h e number o f d a y s i t t a k e s t o d e p l e t e EOQ a t t h e RDC. A t t h e t i m e t h e DC e x p e r i e n c e s s t o c k o u t , t h e i n v e n t o r y p o s i t i o n a t t h e RDC i s a p p r o x i m a t e l y u n i f o r m l y d i s t r i b u t e d b e t w e e n R a n d R + EOQ ( A s s u m p t i o n 6 ) . B e c a u s e t h e RDC o r d e r s when R i s r e a c h e d a n d demand i s i d e n t i c a l l y d i s t r i b u t e d e a c h d a y , t h e n Y must be a p p r o x i m a t e l y u n i f o r m o v e r [ 0 , E [ T B ] ] . The f o l l o w i n g a p p r o x i m a t i o n s a r e t h u s made: G i v e n Y < E [ T B ] , f y ( y ) = 1 , a n d E [ TB ] G i v e n Y > E [ T B ] , f y ( y ) = 0 (8) As t h e v a r i a n c e i n demand a t t h e RDC i n c r e a s e s , t h e u n i f o r m d i s t r i b u t i o n o f Y b e t w e e n 0 a n d E [ T B ] b e g i n s t o b r e a k down and t h i s a p p r o x i m a t i o n may c a u s e d e v i a t i o n s b e t w e e n s i m u l a t e d a n d c a l c u l a t e d CSL v a l u e s . The i n p u t p a r a m e t e r s r e q u i r e d t o c a l c u l a t e CSL f r o m t h e h e u r i s t i c a r e t h e mean a n d s t a n d a r d d e v i a t i o n o f demand a t t h e RDC's, ^RD' aRD^' t * i e m e a n a n c ^ s t a n d a r d d e v i a t i o n o f l e a d t i m e , ( E [ L T ] , S . D . f L T ] ) , EOQ, t h e r e g i o n a l s e r v i c e l e v e l RSL, t h e d i s t r i b u t i o n c e n t r e s e r v i c e l e v e l DSL, t h e r e v i e w p e r i o d L, a n d t h e mean a n d s t a n d a r d d e v i a t i o n o f t h e 15 s c h e d u l i n g i n t e r v a l , ( E [ I ] , S . D . [ I ] ) . The h e u r i s t i c c a l c u l a t i o n s a r e done i n t h e f o l l o w i n g o r d e r : E[T-Y|Y<T] a r e c a l c u l a t e d a n d u s e d t o o b t a i n t h e mean an d v a r i a n c e of LT' w h i c h a r e r e q u i r e d t o o b t a i n a v a l u e f o r E [ C | N = 0 ] . E[C|N=0] i s u s e d w i t h P r ( Y < T ) i n e q u a t i o n 5 t o o b t a i n t h e s e c o n d t e r m o f e q u a t i o n 4. E q u a t i o n 4 t h e n y i e l d s E [ G ] , t h e number of u n i t s b a c k o r d e r e d a t t h e RDC a n d CSL c a n be e s t i m a t e d . A p r o g r a m w r i t t e n i n B a s i c i s u s e d t o c a l c u l a t e a l l h e u r i s t i c a l l y - e s t i m a t e d CSL v a l u e s a n d c a n be f o u n d i n A p p e n d i x B. A v e r y good a p p r o x i m a t i o n f o r t h e c u m u l a t i v e n o r m a l f u n c t i o n d i s c u s s e d by Page [ 7 ] i s u s e d i n t h e B a s i c p r o g r a m s i n c e a t a b l e l o o k - u p method c a n be t i m e c o n s u m i n g and c o s t l y . C h a p t e r 4 THE GPSS SIMULATION MODEL 4.1 DEFINING THE INVENTORY SYSTEM I n o r d e r t o t e s t t h e v a r i o u s a s s u m p t i o n s u s e d i n d e v e l o p i n g t h e h e u r i s t i c d e s c r i b e d i n C h a p t e r 3, a s i m u l a t i o n p r o g r a m was w r i t t e n t o compare t h e r e s u l t s o f t h e h e u r i s t i c w i t h s i m u l a t e d d a t a . The s i m u l a t i o n was w r i t t e n i n GPSS and f o l l o w s t h e d e s c r i p t i o n o f t h e i n v e n t o r y p r e s e n t e d i n C h a p t e r 2 w h i l e h a v i n g t h e f o l l o w i n g a d d i t i o n a l c h a r a c t e r i s t i c s : 1. C u s t o m e r demand a t e a c h RDC i s r a n d o m l y s a m p l e d f r o m a s t a n d a r d n o r m a l d i s t r i b u t i o n . The mean a n d s t a n d a r d d e v i a t i o n o f t h e d a i l y c u s t o m e r demand a t e a c h RDC a r e i n p u t t o t h e s i m u l a t i o n p r o g r a m . 2. E a c h RDC p l a c e s an o r d e r f o r EOQ on t h e DC w h e n e v e r t h e i n v e n t o r y p o s i t i o n i s e q u a l t o o r l e s s t h a n R, t h e r e o r d e r p o i n t c a l c u l a t e d b a s e d on a g i v e n RSL a n d d a i l y demand d i s t r i b u t i o n . Whenever t h e DC o n - h a n d s t o c k , OH, i s l e s s t h a n an i n c o m i n g RDC o r d e r f o r EOQ , OH u n i t s a r e s h i p p e d t o t h e RDC a n d t h e n e x t t i m e t h e r e o r d e r p o i n t i s r e a c h e d (EOQ - OH) u n i t s a r e o r d e r e d . 3. The l e a d t i m e o f r e p l e n i s h m e n t a t t h e RDC's , i . e . t h e t i m e b e t w e e n p l a c e m e n t o f t h e o r d e r and t h e r e c e i v i n g , i s s a m p l e d f r o m a s t a n d a r d n o r m a l d i s t r i b u t i o n w i t h mean an d s t a n d a r d d e v i a t i o n i n p u t t o t h e m o d e l f o r e a c h RDC. 4. The DC p l a c e s an o r d e r on t h e f a c t o r y e a c h 20 d a y s ( o r 16 17 e v e r y 4 w e e k s ) . The q u a n t i t y o f t h e o r d e r i s (S - I P ) , where I P i s t h e i n v e n t o r y p o s i t i o n a t t h e DC a t t h e t i m e o f o r d e r i n g a n d S i s t h e o r d e r - u p - t o q u a n t i t y c a l c u l a t e d t o y i e l d a p r e d e t e r m i n e d CSL. I P i s d e f i n e d a s t h e o n - h a n d u n i t s + t h e u n i t s o u t s t a n d i n g - an y b a c k o r d e r s . The l e a d t i m e o f r e p l e n i s h m e n t a t t h e DC i s s a m p l e d f r o m t h e s t a n d a r d n o r m a l d i s t r i b u t i o n w i t h mean 20 a n d s t a n d a r d d e v i a t i o n 5. 4.2 EVALUATING THE PARAMETERS OF DEMAND A t t h e DC, t h e mean and s t a n d a r d d e v i a t i o n o f demand o v e r t h e s c h e d u l i n g i n t e r v a l , M a and o^, a r e e v a l u a t e d u s i n g t h e t o t a l c u s t o m e r demand on t h e RDC's: "A " E [ l ] ' i i / R D o A = Ml]. . I ^ + V a r t l ] . ( i l / R o ) 2 C u s t o m e r demand and t h e l e a d t i m e o f r e p l e n i s h m e n t a t e a c h RDC i s u s e d t o a r r i v e a t t h e mean a n d s t a n d a r d d e v i a t i o n o f demand o v e r LT^ and c a l c u l a t e d a s f o l l o w s : 0 „ . = / E [ L T . ] « a 2 . + S . D . [ L T . ] 2 • u * .. B i l J R D l l J R D l 18 4 . 3 DIVERGENCE FROM ROSENBAUM'S SIMULATION MODEL No u p d a t e s a r e made d u r i n g t h e s i m u l a t i o n s i n t h e t h e s i s . The o b j e c t i v e i s t o c o m p a r e t h e C S L c a l c u l a t e d u s i n g t h e h e u r i s t i c w i t h C S L r e s u l t i n g f r o m t h e s i m u l a t e d s y s t e m when all input values common to both are identical. P a r t i c u l a r a t t e n t i o n s h o u l d be p a i d t o t h e f a c t t h a t all p a r a m e t e r v a l u e s i n p u t t o t h e s i m u l a t i o n s i n t h i s t h e s i s a r e exogenous t o t h e s y s t e m b e i n g a n a l y s e d . In c o n t r a s t , R o s e n b a u m ' s s i m u l a t i o n s make u s e of e x p o n e n t i a l s m o o t h i n g t e c h n i q u e s t o f o r e c a s t t h e mean a n d s t a n d a r d d e v i a t i o n o f c u s t o m e r demand o v e r l e a d t i m e a t e a c h r e g i o n a l c e n t r e . A t t h e D C , t h e e x p r e s s i o n s f o r t h e mean a n d s t a n d a r d d e v i a t i o n , M a , a r e c a l c u l a t e d t a k i n g i n t o a c c o u n t t h e i n v e n t o r y p o s i t i o n , I P , a t e a c h r e g i o n a l c e n t r e a n d t h e f a c t t h a t demand o c c u r s i n lumpy EOQ q u a n t i t i e s . In a d d i t i o n , a t e a c h RDC, R^ a n d EOQ^ a r e r e c a l c u l a t e d w e e k l y b a s e d on t h e l a t e s t e x p o n e n t i a l l y - s m o o t h e d v a l u e s . A t t h e D C , t h e o r d e r up t o q u a n t i t y S i s r e c a l c u l a t e d b e f o r e e a c h o r d e r i s p l a c e d a t t h e e n d o f t h e r e v i e w p e r i o d o f 20 d a y s . In summary , M R D, O R D , uk, <>A, R ^ E O Q i a n d S a r e a l l endogenous t o t h e i n v e n t o r y s y s t e m s i m u l a t e d by R o s e n b a u m . T h e r e i s no i n d i c a t i o n i n h e r p a p e r t h a t t h e C S L v a l u e o b t a i n e d f r o m t h e h e u r i s t i c i s an a v e r a g e . I t i s t h e r e f o r e a s s u m e d t h a t t h e d y n a m i c s i m u l a t i o n r e s u l t s a r e c o m p a r e d t o a s t a t i c e x o g e n o u s h e u r i s t i c r e s u l t . The t h e s i s h o w e v e r , c o m p a r e s two s t a t i c s y s t e m s whose i n p u t p a r a m e t e r v a l u e s a r e i d e n t i c a l . 19 A second d i s t i n c t i o n has been made i n the s i m u l a t i o n model used i n the t h e s i s . A f t e r a s t o c k o u t s i t u a t i o n , when the DC r e c e i v e s a r e p l e n i s h m e n t o r d e r , o u t s t a n d i n g o r d e r s t o an RDC a r e not batched and s h i p p e d t o g e t h e r but a r e d e a l t w i t h s e p a r a t e l y . Each l e a d time i s randomly sampled from a s t a t i o n a r y normal d i s t r i b u t i o n a t the time the o r d e r i s sent out t o the DC. When a z e r o s t o c k s i t u a t i o n i s e n c o u n t e r e d a t the DC, each l e a d time i s l e n g t h e n e d by the number of days i t must w a i t f o r r e p l e n i s h m e n t t o a r r i v e a t the DC. C a r e f u l a n a l y s i s of the consequences of t h i s change r e v e a l s t h a t the o u t s t a n d i n g o r d e r s a r r i v e w i t h i n one or two days of one a n o t h e r and cannot a f f e c t the customer s e r v i c e l e v e l s i n c e no EOQ q u a n t i t y i n p u t t o the model i s d e p l e t e d i n so s h o r t a t i m e . 4.4 DEFINING THE GPSS MODEL Each s i m u l a t i o n model run i n v o l v e s one p r o d u c t s t o c k e d a t the D i s t r i b u t i o n C e n t r e and 8 R e g i o n a l D i s t r i b u t i o n C e n t r e s , so t h a t e i g h t i t e m - l o c a t i o n s are b e i n g c o n s i d e r e d . Parameters a t a l l RDC's are not i d e n t i c a l but are c l o s e l y r e l a t e d . T h i s i s done t o h e l p d e t e r m i n e which assumptions i n the h e u r i s t i c a r e s e n s i t i v e t o v a r i a t i o n and which assumptions a r e f a i r l y r o b u s t . The s t e p s f o l l o w e d p r i o r t o d a t a c o l l e c t i o n from the s i m u l a t i o n model are as f o l l o w s : 1. S, the o r d e r - u p - t o q u a n t i t y a t the DC i s i n p u t t o the model t o be used t o c a l c u l a t e the o r d e r q u a n t i t y when the r e v i e w p e r i o d of 20 days has e l a p s e d . S i s based on 20 a s e t DSL and t h e mean a n d s t a n d a r d d e v i a t i o n o f demand a t t h e DC. R, t h e r e o r d e r - p o i n t a t t h e RDC's i s i n p u t t o t h e m o d e l t o t r i g g e r o r d e r s f r o m t h e RDC's t o t h e DC. R i s c a l c u l a t e d b a s e d on a s e t RSL and t h e mean a n d s t a n d a r d d e v i a t i o n o f demand o v e r t h e l e a d t i m e . EOQ, t h e r e o r d e r q u a n t i t y a t e a c h RDC i s i n p u t t o t h e s i m u l a t i o n and i s d e r i v e d f r o m t h e mean o f t h e demand m u l t i p l i e d by E [ T B ] , t h e a v e r a g e number o f d a y s r e q u i r e d t o d e p l e t e EOQ. T h i s i s done s i n c e no EOQ v a l u e s a r e l i s t e d by Rosenbaum and t h e s i m u l a t i o n s i n t h i s t h e s i s a t t e m p t t o p a r a l l e l h e r a n a l y s i s f o r r e a s o n s o f c o m p a r i s o n . The i n i t i a l v a l u e f o r on-hand i n v e n t o r y a t e a c h RDC i s s e t a t (R + EOQ/2) w h i l e b a c k o r d e r s a n d i n - p r o c e s s i n v e n t o r y a r e s e t t o z e r o . A t t h e DC t h e i n i t i a l o n - hand i n v e n t o r y i s s e t t o S, w h i c h h a s been c a l c u l a t e d u s i n g a s e t DSL a n d t h e mean and s t a n d a r d d e v i a t i o n v a l u e s o f t h e l e a d t i m e a n d d a i l y demand d i s t r i b u t i o n . The i n i t i a l v a l u e f o r t h e i n v e n t o r y i n t r a n s i t f r o m t h e f a c t o r y i s s e t a t 0. When a r e p l e n i s h m e n t o r d e r a n d demand o c c u r s i m u l t a n e o u s l y i n t h e s i m u l a t i o n , p r i o r i t y i s g i v e n t o t h e r e p l e n i s h m e n t . The s y s t e m i s r u n f o r an i n i t i a l i z a t i o n p e r i o d o f 160 d a y s t o a l l o w s t e a d y s t a t e t o be r e a c h e d . No d a t a i s c o l l e c t e d d u r i n g t h i s p h a s e . D a t a was c o l l e c t e d a f t e r 21 f i v e day s n a p i n t e r v a l s o v e r a one y e a r p e r i o d . T h i s was r e p e a t e d s e v e r a l t i m e s w i t h d i f f e r e n t p a r a m e t e r v a l u e s a n d t h e r e s u l t s a n a l y s e d . A f t e r 160 d a y s no v a l u e a p p e a r e d w h i c h was t h e minimum o r t h e maximum o f t h e p r e v i o u s o b s e r v a t i o n s . T h i s c r i t e r i a f o r r e a c h i n g s t e a d y s t a t e i s d e s c r i b e d by S c h r i b e r [ 1 1 ] . 8. The s y s t e m i s t h e n r u n f o r a f u r t h e r 260 d a y s (1 y e a r ) and d a t a on demand a n d b a c k o r d e r s i s c o l l e c t e d a t e a c h RDC. A t t h e end o f t h e y e a r , CSL a t e a c h RDC i s c a l c u l a t e d a s : 1 _ # u n i t s b a c k o r d e r e d a t RDC # u n i t s demanded a t t h e RDC 9. The s y s t e m i s c l e a r e d o f a l l v a l u e s . 10. S t e p s 1-9 a r e r e p e a t e d 20 t i m e s , e a c h t i m e u s i n g t h e same i n i t i a l c o n d i t i o n s b u t u s i n g a d i f f e r e n t s e e d f o r t h e s e l e c t i o n o f random n u m b e r s . T h i s p r o c e s s g e n e r a t e s 20 i n d e p e n d e n t o b s e r v a t i o n s o f CSL a t e a c h R e g i o n a l D i s t r i b u t i o n C e n t r e . 4.5 VALIDATING THE GPSS MODEL T h e r e a r e two a r e a s t o l o o k a t t o v a l i d a t e a s i m u l a t i o n m o d e l . F i r s t i s t h e v a l i d a t i o n o f t h e d a t a s t r e a m o u t p u t o f t h e m o d e l a l s o c a l l e d o u t p u t v a l i d i t y . S e c o n d i s t h e v a l i d a t i o n o f t h e d a t a s t r e a m o u t p u t o f t h e m o d e l known a s d e s i g n v a l i d i t y . D e s i g n v a l i d i t y i s u s u a l l y a s sumed t o be c o r r e c t i f t h e d a t a o u t p u t b e h a v e s a s e x p e c t e d , s i n c e i t i s v e r y d i f f i c u l t t o a s s e s s t h e e x a c t p r o c e s s e s o f t h e m o d e l . 22 The f o l l o w i n g t e s t s a r e r u n t o v a l i d a t e t h e r e s u l t s o b t a i n e d f r o m t h e GPSS m o d e l : 1. The s y s t e m was r u n u s i n g f i x e d c u s t o m e r demand a t t h e R D C ' s a n d f i x e d l e a d t i m e b e t w e e n t h e R D C ' s a n d t h e D C . The d a t a o u t p u t f o r c u s t o m e r demand a n d l e a d t i m e f r o m t h e s i m u l a t i o n was i d e n t i c a l t o t h e d a t a i n p u t a s e x p e c t e d . 2. D a i l y d a t a on i n v e n t o r y p o s i t i o n , o n - h a n d s t o c k a n d s e q u e n c e o f o r d e r a r r i v a l a t t h e R D C ' s was c o l l e c t e d f o r 100 d a y s a n d c o m p a r e d e x a c t l y w i t h d e s k c a l c u l a t i o n s . The v a l u e s s a m p l e d r a n d o m l y f o r demand a n d l e a d t i m e s were w i t h i n t h e e x p e c t e d r a n g e . T h e s e r e s u l t s show t h e u n d e r l y i n g p r o c e s s e s a r e p e r f o r m i n g a s d e s i g n e d . 3. The o r d e r - u p - t o q u a n t i t y S , a t t h e DC was s e t t o g i v e a s e r v i c e l e v e l o f 100%. The C S L c a l c u l a t e d f r o m t h e r e s u l t s o f t h e s i m u l a t i o n e q u a l l e d t h e i n p u t RSL a s e x p e c t e d . 4 . C o n f i d e n c e i n t e r v a l s were c a l c u l a t e d a t 95% c o n f i d e n c e w h i c h c o n f i r m e d t h a t t h e r e s u l t s f r o m t h e s i m u l a t i o n were c o m p a r a b l e t o r e s u l t s o b t a i n e d f r o m t h e h e u r i s t i c . 5. S i n c e t h e s i m u l a t i o n m o d e l was n o t w r i t t e n t o s i m u l a t e a r e a l l i f e s i t u a t i o n , no c o m p a r i s o n c a n be made w i t h t h e a c t u a l o u t c o m e o f t h e s y s t e m . H o w e v e r , t h e n e x t b e s t t h i n g was done w h i c h was t o r u n t h e s i m u l a t i o n u s i n g a s e t o f p a r a m e t e r s w i t h v a l u e s c o m p a r a b l e t o t h o s e u s e d by B a r b a r a A . R o s e n b a u m . The o u t c o m e o f t h e s i m u l a t i o n r u n c o m p a r e d f a v o r a b l y w i t h t h e r e s u l t s o b t a i n e d by B . A . Rosenbaum a n d i s f u l l y d i s c u s s e d i n C h a p t e r C h a p t e r 5 TESTING THE ASSUMPTIONS 5.1 BASE RUN To e s t a b l i s h a b a s e o f r e f e r e n c e , a GPSS s i m u l a t i o n m o d e l i s r u n w i t h p a r a m e t e r s e t t i n g s t h a t a r e most l i k e l y t o s u p p o r t t h e a s s u m p t i o n s u s e d i n d e v e l o p i n g t h e h e u r i s t i c d e s c r i b e d e a r l i e r . I n p a r t i c u l a r , demand a t e a c h RDC i s n o r m a l l y d i s t r i b u t e d , t h e EOQ s i z e s a t t h e RDC's a r e r e l a t i v e l y s m a l l c o m p a r e d t o t h e l e a d t i m e s , a n d t h e r e a r e e i g h t RDC's i n t h e s y s t e m . T h e s e t h r e e c o n d i t i o n s a l l e n c o u r a g e n o r m a l i t y o f demand a t t h e DC o v e r t h e s c h e d u l i n g i n t e r v a l o f 40 d a y s . I n a d d i t i o n , demand a t t h e RDC's i s n o r m a l l y d i s t r i b u t e d w i t h c o e f f i c i e n t s o f v a r i a t i o n r a n g i n g f r o m .21 t o .3, and l e a d t i m e s o f r e p l e n i s h m e n t a t t h e DC a n d t h e RDC's f o l l o w n o r m a l d i s t r i b u t i o n s i n d i v i d u a l l y d e f i n e d . T a b l e 1 i s a r e p r o d u c t i o n o f t h e r e s u l t s o b t a i n e d by Rosenbaum (1981) a nd f o l l o w i n g a r e h e r comments. "The s i m u l a t i o n m o d e l was r u n f o u r t i m e s u s i n g a v a r i e t y o f p a r a m e t e r v a l u e s f o r ° ^ £ ) / ^ ^ r E [ T B ] , DSL, E [ L T ] AND S.D.[LT] i n o r d e r t o d e t e r m i n e t h e a c c u r a c y o f t h e h e u r i s t i c i n r e p r e s e n t i n g t h e p r o b l e m u n d e r s t u d y . Demand v a r i a b i l i t y , i . e . , a R D / M R D , i s p r o b a b l y t h e p a r a m e t e r w i t h the. most i m p a c t on t h e e f f e c t i v e n e s s o f t h e h e u r i s t i c T h e r e f o r e , we f i r s t s i m u l a t e d 24 s i t u a t i o n s w i t h ^ T J / ^ R D C^ear^-Y w i t h i n t h e a c c e p t a b l e l i m i t s a n d v a r i e d t h e v a l u e s f o r E [ T B ] , E [ L T ] , S . D . [ L T ] and DSL. F o l l o w i n g t h a t , we v a r i e d 0 R D / M r d i n o r d e r t o d i s c e r n a t what l e v e l o f a R r j / J U R D t h e h e u r i s t i c r e s u l t s become u n a c c e p t a b l e . S i m u l a t i o n s I , I I , a n d I I I m a i n t a i n a l o w v a l u e o f o R T j / M R T J and c o n s i d e r a v a r i e t y o f v a l u e s f o r t h e o t h e r p a r a m e t e r s . The v a l u e o f CSL c a l c u l a t e d u s i n g t h e h e u r i s t i c f a l l s i n t o a 98% c o n f i d e n c e i n t e r v a l o f t h e s i m u l a t e d v a l u e o f CSL i n a l l c a s e s e x c e p t i n S i m u l a t i o n I I a t RDC's 1, 3 a n d 4. I n t h e s e c a s e s , t h e s i m u l a t e d v a l u e o f CSL i s h i g h e r t h a n p r e d i c t e d by t h e h e u r i s t i c . We h y p o t h e s i z e t h a t t h i s s i t u a t i o n o c c u r s due t o t h e p r o b l e m o f o v e r l a p p i n g l e a d t i m e s t h e h e u r i s t i c i s d e v e l o p e d u n d e r t h e a s s u m p t i o n of n o n - o v e r l a p p i n g l e a d t i m e s , w h e r e a s i n S i m u l a t i o n I I a t RDC's 1, 3 and 4, we have a h i g h p r o b a b i l i t y o f o v e r l a p p i n g l e a d t i m e s due t o t h e s h o r t amount o f t i m e b e t w e e n o r d e r p l a c e m e n t . I n S i m u l a t i o n I V , a r a n g e o f a R j j / ^ R D ^ R O M ^-5 t o 2.0 was t e s t e d i n o r d e r t o d e t e r m i n e a t what l e v e l o f demand v a r i a b i l i t y t h e h e u r i s t i c i s no l o n g e r e f f e c t i v e i n m o d e l i n g t h e p r o b l e m u n d e r s t u d y . From t h i s s i m u l a t i o n a n a l y s i s , i t a p p e a r s t h a t t h e h e u r i s t i c l o s e s i t s e f f e c t i v e n e s s a t some p o i n t b e t w e e n ^ R D / ^ R D = 1 « ° a n d aRD / / / xRD = 1 , 5 ( p . 9 3 5 - 9 3 6 ) " 26 T a b l e 2, S i m u l a t i o n I shows t h e r e s u l t s o b t a i n e d when p a r a m e t e r v a l u e s s i m i l a r t o Rosenbaum's S i m u l a t i o n I were u s e d . 1 The s i m u l a t i o n r e s u l t s c l e a r l y show t h a t a l l o f t h e c a l c u l a t e d CSL v a l u e s f a l l w i t h i n a 9 5 % c o n f i d e n c e i n t e r v a l f o r t h i s p a r t i c u l a r s e t o f p a r a m e t e r s . The r e s u l t s a l s o e s t a b l i s h t h e a c c u r a c y o f t h e h e u r i s t i c i n d e t e r m i n i n g CSL when t h e i n v e n t o r y s y s t e m u n d e r s t u d y d o e s n o t v i o l a t e any o f t h e a s s u m p t i o n s on w h i c h t h e h e u r i s t i c i s b a s e d . The d i s t r i b u t i o n o f demand b e i n g n o r m a l , some n e g a t i v e demand i s o c c u r r i n g a t t h e RDC's. T h i s i s o f c o u r s e e a s i l y i n t e r p r e t e d a s r e t u r n s o f m e r c h a n d i s e . However, a s y s t e m where no r e t u r n s a r e a l l o w e d i s o f i n t e r e s t a n d S i m u l a t i o n I I i s r u n w i t h a n o r m a l d i s t r i b u t i o n o f demand t r u n c a t e d a t z e r o t h u s e l i m i n a t i n g n e g a t i v e demand a t t h e RDC's. R e s u l t s ( T a b l e 2, S i m u l a t i o n I I ) show t h a t a l l o f t h e c a l c u l a t e d CSL v a l u e s a r e i n c l u d e d i n t h e 9 5 % c o n f i d e n c e i n t e r v a l . T h i s i n d i c a t e s t h a t a l t h o u g h t h e h e u r i s t i c t a k e s i n t o a c c o u n t t h e o c c u r r e n c e o f n e g a t i v e demand, i t i s a l s o u s e f u l i n d e t e r m i n i n g CSL v a l u e s f o r a s y s t e m w i t h o u t n e g a t i v e demand when t h i s p a r t i c u l a r s e t o f p a r a m e t e r v a l u e s i s u s e d . An i n t e r e s t i n g o b s e r v a t i o n t o be made when a n a l y s i n g t h e r e s u l t s o f S i m u l a t i o n s I and I I i s t h e number of o u t s t a n d i n g o r d e r s a t e a c h RDC a t a n y one t i m e . Due t o t h e r e l a t i v e l y s m a l l EOQ s i z e s a n d t h e l o n g l e a d t i m e s e a c h RDC 1 O t h e r i n p u t v a l u e s t o t h e GPSS p r o g r a m , i . e . , R. t h e r e o r d e r p o i n t a t e a c h RDC, a n d S t h e o r d e r - u p - t o q u a n t i t y a t t h e DC, a r e l i s t e d i n A p p e n d i x A T a b l e A 1 . 27 a l w a y s h a s a t l e a s t one o r d e r f o r EOQ o u t s t a n d i n g ( F i g u r e 2 ) . T h i s i s a d i r e c t r e s u l t o f h a v i n g 29 t o 55 o r d e r s p e r RDC p e r y e a r ( F i g u r e 3 ) , o r an o r d e r g o i n g o u t e v e r y 4 t o 8 d a y s . W i t h e i g h t RDC's i n t h e s y s t e m , t h e DC i s n o t l i k e l y t o e x p e r i e n c e d a y s w i t h z e r o demand. T h i s e n s u r e s t h a t t h e a s s u m p t i o n o f n o r m a l demand a t t h e DC o v e r i t s s c h e d u l i n g i n t e r v a l i s p r e s e r v e d ( A s s u m p t i o n 2 ) . 5.2 VARYING THE NUMBER OF RDC'S IN THE SYSTEM The a s s u m p t i o n t h a t demand a t t h e DC i s n o r m a l o v e r t h e s c h e d u l i n g i n t e r v a l i s d e p e n d e n t i n p a r t on t h e number o f RDC's o r d e r i n g f r o m t h e DC. S i m u l a t i o n s I a n d I I showed t h a t e i g h t RDC's seemed t o be an a d e q u a t e number o f RDC's i n an i n v e n t o r y s y s t e m where a l l o t h e r a s s u m p t i o n s were a s d e s c r i b e d i n t h e d e v e l o p m e n t o f t h e h e u r i s t i c . S i m u l a t i o n s I I I t o VI ( T a b l e 3) m o d e l i n v e n t o r y s y s t e m s w i t h e i g h t t o t h r e e RDC's where t h e DSL h a s been l o w e r e d t o 75% w h i l e t h e RSL r e m a i n s a t 9 8 % . 2 S i m u l a t i o n I I I and I V e s t a b l i s h t h e d i f f e r e n c e i n r e s u l t s when u s i n g t h e n o r m a l v e r s u s t h e n o r m a l t r u n c a t e d a t z e r o a s d i s t r i b u t i o n o f demand a t t h e RDC's. I n S i m u l a t i o n I I I we o b s e r v e t h a t RDC4 h a s a c a l c u l a t e d CSL v a l u e w h i c h d o e s n o t f a l l w i t h i n t h e b o u n d s o f t h e 95% c o n f i d e n c e i n t e r v a l o b t a i n e d f r o m t h e s i m u l a t i o n a n a l y s i s . T h i s c o u l d i n d i c a t e t h a t d e c r e a s i n g t h e p e r c e n t a g e o f 2 A 1 1 i n p u t v a l u e s t o S i m u l a t i o n s I I I t o VI a r e t o be f o u n d i n A p p e n d i x A, T a b l e A2. 28 s e r v i c e l e v e l a t t h e DC a f f e c t s t h e v a l i d i t y o f t h e h e u r i s t i c r e s u l t s s i n c e a l l p a r a m e t e r v a l u e s o t h e r t h a n t h e DSL a r e i d e n t i c a l t o t h o s e u s e d i n S i m u l a t i o n I . H o w e v e r , t h i s c o u l d a l s o be a r e s u l t o f r a n d o m n e s s a n d f u r t h e r a n a l y s i s w i l l n e e d t o be done t o e s t a b l i s h i f d e c r e a s i n g t h e DSL a f f e c t s t h e r e l i a b i l i t y o f CSL a s c a l c u l a t e d by t h e h e u r i s t i c . . I n S i m u l a t i o n I V , a l l c a l c u l a t e d v a l u e s o f CSL a r e w i t h i n t h e i r r e s p e c t i v e 9 5 % c o n f i d e n c e i n t e r v a l e v e n t h o u g h t h e d i s t r i b u t i o n o f demand a t t h e RDC's i s a n o r m a l d i s t r i b u t i o n o f demand t r u n c a t e d a t z e r o . When an i n v e n t o r y s y s t e m w i t h f i v e RDC's i s m o d e l l e d , S i m u l a t i o n V, t h e c a l c u l a t e d v a l u e o f CSL a t RDC4 i s n o t c o n t a i n e d by t h e 95% c o n f i d e n c e i n t e r v a l . I t a p p e a r s t h a t l o w e r i n g t h e number o f RDC's t o f i v e i s b e g i n n i n g t o a f f e c t t h e r e s u l t s o b t a i n e d f r o m t h e h e u r i s t i c . S i m u l a t i n g a s y s t e m w i t h o n l y t h r e e RDC's r e s u l t s i n RDC's 1 a n d 2 h a v i n g c a l c u l a t e d CSL v a l u e s o u t s i d e t h e i r r e s p e c t i v e 9 5 % c o n f i d e n c e i n t e r v a l s ( S i m u l a t i o n V I ) . T h e s e c a l c u l a t e d v a l u e s a r e l o w e r t h a n t h e s i m u l a t i o n r e s u l t s b u t v e r y c l o s e t o t h e e d g e s o f t h e i n t e r v a l s a s i s i n d i c a t e d by t h e i r p - v a l u e s o f .047 and .049 r e s p e c t i v e l y . A l t h o u g h a s s u m p t i o n 2b h a s been v i o l a t e d a n d t h e r e a r e f e w e r RDC's o r d e r i n g f r o m t h e DC, t h e h e u r i s t i c r e s u l t s a r e f a i r l y c l o s e t o t h e s i m u l a t e d r e s u l t s l e a d i n g t o t h e c o n c l u s i o n t h a t t h e h e u r i s t i c r e m a i n s a good p r e d i c t o r o f CSL u n d e r t h e s e p a r t i c u l a r c o n d i t i o n s . 29 5.3 INCREASING THE EOQ S I Z E S I t i s common i n an i n v e n t o r y s y s t e m f o r RDC's t o e x p e r i e n c e p e r i o d s when no o r d e r s f o r EOQ a r e o u t s t a n d i n g . T h i s i s a r e s u l t o f h a v i n g l a r g e r EOQ s i z e s a n d l e s s f r e q u e n t o r d e r i n g . The EOQ q u a n t i t y u s e d i n S i m u l a t i o n I V i s m u l t i p l i e d by t w o , t h r e e , a n d e i g h t t o d e t e r m i n e t h e d e g r e e o f s e n s i t i v i t y o f t h e h e u r i s t i c t o t h i s p a r a m e t e r . The d i s t r i b u t i o n o f demand a t e a c h RDC i s n o r m a l t r u n c a t e d a t z e r o t o e l i m i n a t e t h e o c c u r r e n c e o f n e g a t i v e demand. 3 When EOQ i s d o u b l e d o r t r i p l e d a l l CSL v a l u e s o b t a i n e d by u s i n g t h e h e u r i s t i c f a l l w i t h i n t h e i r 9 5 % c o n f i d e n c e i n t e r v a l e x c e p t a t RDC7 i n S i m u l a t i o n V I I a n d a t RDC3 i n S i m u l a t i o n V I I I ( T a b l e 4 ) . The p - v a l u e s a s s o c i a t e d w i t h t h e s e RDC's a r e q u i t e s m a l l , .003 a n d l e s s t h a n .001 r e s p e c t i v e l y , l e a d i n g t o t h e c o n c l u s i o n t h a t i n c r e a s i n g t h e EOQ s i z e seems t o c o n t r i b u t e t o t h e d e t e r i o r a t i o n o f t h e h e u r i s t i c . T h i s i s due t o t h e v i o l a t i o n o f t h e a s s u m p t i o n o f n o r m a l i t y o f demand a t t h e DC w h i c h d e p e n d s i n p a r t on EOQ s i z e ( A s s u m p t i o n 2 c ) . To f u r t h e r t e s t t h e s e n s i t i v i t y o f t h e h e u r i s t i c t o EOQ s i z e , t h e EOQ s i z e o f S i m u l a t i o n I V i s m u l t i p l i e d by e i g h t . RDC's 1,3 5, a n d 6 a r e s e e n t o have c a l c u l a t e d v a l u e s o f CSL o u t s i d e t h e i r r e s p e c t i v e 9 5 % c o n f i d e n c e i n t e r v a l w i t h p - v a l u e s r a n g i n g f r o m l e s s t h a n .001 t o .018 ( T a b l e 4, S i m u l a t i o n I X ) . 3 I n p u t v a l u e s t o S i m u l a t i o n s V I I - I X a r e l i s t e d i n A p p e n d i x A T a b l e A 3 . 30 F i g u r e s 5, 6, and 7 i l l u s t r a t e t h e minimum and maximum number o f o r d e r s p e r y e a r a t e a c h RDC a s t h e EOQ s i z e i s m u l t i p l i e d by two, t h r e e a n d e i g h t r e s p e c t i v e l y . When EOQ i s d o u b l e d , t h e RDC's o r d e r 15 t o 29 t i m e s p e r y e a r . T h e s e f i g u r e s d r o p t o 10 t o 21 t i m e s when EOQ i s t r i p l e d a n d t o 4 t o 10 t i m e s when EOQ i s m u l t i p l i e d by e i g h t . F i g u r e 8 p o r t r a y s t h e a v e r a g e number o f o r d e r s o u t s t a n d i n g a t any one t i m e a t e a c h RDC a s EOQ s i z e i s i n c r e a s e d . We o b s e r v e t h a t d o u b l i n g t h e EOQ s i z e r e d u c e s t h e o c c u r r e n c e o f o u t s t a n d i n g o r d e r s t o a b o u t 60 t o 70 p e r c e n t o f t h e t i m e . T r i p l i n g EOQ s i z e r e s u l t s i n o r d e r s b e i n g o u t s t a n d i n g 40 t o 50 p e r c e n t o f t h e t i m e w h i l e m u l t i p l y i n g t h e EOQ s i z e by e i g h t f i n d s t h e RDC's e x p e r i e n c i n g o u t s t a n d i n g o r d e r s f o r EOQ o n l y 13 t o 23 p e r c e n t o f t h e t i m e . As EOQ s i z e i s i n c r e a s e d t h e DC e x p e r i e n c e s z e r o demand p e r i o d s more f r e q u e n t l y a n d t h e a s s u m p t i o n o f n o r m a l i t y o f demand a t t h e DC i s no l o n g e r v a l i d ( A s s u m p t i o n 2 ) . TABLE 1 : B a r b a r a A . R o s e n b a u m ' s S i m u l a t i o n R e s u l t s D S L = 8 1 . 3 % , 8 2 . 3 % , 6 7 . 6 % , 7 6 . 8 % [ l ] = 4 0 d a y s RSL=98% a t e a c h RDC S . D . [ l ] = 5 d a y s °RD E[TB] E[LT] S.D.[LT] H S 98% C.I. *i (days) (days) (days) (%) (%) for S Sim u l a t i o n I RDC 1 0 .26 6 .0 7, .0 1 , .6 93 .9 94. 5 [92. 90,96. 10] RDC 2 0 . 32 12 .7 6. .0 1 , . 7 95 .8 95. 4 [94. 30,96. 50] RDC 3 0 .21 6 . 5 8. .6 1 . ,6 94 . 1 94. 5 [93. 20,95. 80] RDC 4 0 . 24 e . 6 1 1 , . 5 2, .5 95 .9 95. 5 [94. 20,96. 80] RDC 5 0 .22 6 . 4 12 , .5 2, . 5 95 .4 96. 3 [95. 40,97. 20] RDC 6 0 .25 6 .6 S. . 5 2, . 1 95 .4 94. 2 [93. 00,95. 40] RDC 7 0 .27 5 .4 7 , .5 1 , .9 94 .0 94. 2 [92. 80,95. 60] Simuiat ior, : i RDC 1 0 .26 3 . 1 7 .0 1 . 6 92 c 94 . 7 [93. 30,96. .101 RDC 2 0 . 32 5 . 3 6 .0 1 . 7 94 . 1 94. 2 [92. 90,95, .50] RDC 3 0 .21 2 .6 e . 6 1 . 6 92 .3 94. 9 [93. 50,96, .30] RDC 4 0 .24 4 . 4 11 . 5 2 . 5 94 .8 96. 9 [95. 90,97, . 90 ] RDC 5 0 . 2 2 5 . 1 12 £ 2 . 5 94 .6 95. 6 [94. 60,96, .60] RDC 6 0 . 25 5 . 7 9 2 . 1 94 . 7 94. 6 [ 91 . 30,96, .00] RDC 7 0 . 27 3 . 1 7 c 1 _ 0 92 . 7 94 . 0 [ 92. 50,95 , .50] Simulat ion 111 RDC 1 0, .26 6. 5 7 . , 0 1 . 6 86 . 5 86. 5 [83. 90,89 .10] RDC 2 0. . 32 5. 3 6. , 0 1 . 7 85 . 9 86. 0 [83. 50,86 .50] RDC 3 0. .21 6. 5 8. .6 1 .6 86 . 5 86. 1 [83. 90,86 .30] RDC4 0. .24 6. 6 1 1 . c 2, . 5 89 .7 90. 1 [88. 30 , 91 .90] RDC5 0. . 22 7 . 7 12. 5 2, . 5 90 .6 90. 2 [87. 90,92 .50] RDC 6 c. .25 5. 8 9. 5 2, . 1 67 .8 86. 7 [63. 70,89 .70] RDC 7 0. .27 6. 3 7 . 5 1 , .9 86 .8 86. 3 [ 83. ,80,88 .80] S i m u l a t i o n IV RDC 1 RDC 2 0. 1. . 5 ,0 6. 8. 7 4 7 . 12. 0 5 1 . 2 . 6 5 91 95 .8 . 6 92. 94. 1 6 [90. [92. 40,93. 60,96. ,60] , 60 ] RDC 3 1 . , 0 6. 0 6. 0 1 . 7 93 . 5 92. 6 [ 9 1 . 30,93. . 90 ] RDC 4 1. , 5 6. 2 8. 6 1 . 6 96 .2 91 . 9 [90. 20,93. .60] RDC 5 1 . . 5 7. 5 9. 5 2. 1 96 .2 93. 2 [ 9 1 . 30,95. ,10] RDC 6 2. 0 9. 6 1 1 . 5 2. 5 97 .2 94. 3 [92. 30,96. ,30] RDC 7 2. 0 9. 4 7. 5 1 . 9 96 .8 92. 9 [ 9 1 . 30,94. ,50] H = c a l c u l a t e d CSL S = average simulated CSL * i n d i c a t e s the c a l c u l a t e d CSL, H, i s outsi d e the Confidence I n t e r v a l 32 TABLE 2: I n p u t s t o and R e s u l t s f r o m S i m u l a t i o n s I and I I  S e t t i n g a R e f e r e n c e P o i n t DSL=80% E [ I ] = 4 0 d a y s RSL=98% a t e a c h RDC S . D . [ l ] = 5 d a y s °RD EtTB] E[LT] S.D.[LT] H S 95% C.I. P-VALUE * i R n (days) ( d a y s ) , (days) (%) (%) for S S i m u l a t i o n I RDC 1 0, . 2 1 6. . 5 7 . 5 1 , . 8 93. . 1 5 91 . 9 1 [89. 72,94. .10] .246 RDC 2 0, .24 7 . . 4 6. .0 1 , . 9 93, .81 92 .85 [ 9 1 . 04,94 , .65] . 140 RDC 3 0, . 22 5, . 2 6. .0 1 , . 5 91 . 68 90 . 5 3 [86. 49,92. .56] .252 RDC 4 0. .27 e! ,0 10. .0 2, .0 94. .29 94 .93 [93. 5 3 ,96. .32] .349 RDC 5 0. . 30 6. ,6 7 , 0 1 , . 5 92, .81 91 . 22 [89. 33,93. .10] .094 RDC6 0, . 32 6. . 5 9, . 5 2 . 2 9 4 . .77 95 . 19 [93. 89,96. . 46 ] .252 RDC 7 0. .22 0 _ ,0 1 l . . 0 2, .5 95, , 15 94 .89 [93. 21,96. .57] .760 RDC 6 0. . 26 e! .2 10, . 5 2 . 3 94 , .73 94 .38 [ 92. 64,95, .92] .637 S imulat i on 11 RDCl 0. 21 6. 5 7 . 5 1 . 6 93, . 1 5 92 .73 [ 91 . 09,94. . 38] .602 RDC 2 0. .24 7 . , 4 6 . 0 1 . g 93, . 81 94 .40 [93. 23,95, .57] .306 RDC 3 0. .22 5. .2 6. ,0 1 . 5 91 , .66 91 .26 [ 89. 76,92. .76] .569 RDC 4 c, .27 6 . . 0 l G . . 0 2 . 0 94, .29 94 .69 [93. 30,96. .08] . 555 RDC 5 0. .30 6. .6 7 . 0 1 . ,5 92, .81 91 .23 [89. 32,93. .15] .051 RDC 6 0 , .32. 6 . . 5 9 _ , 5 2. ,2 94, . 77 95 .39 [94. 33,96, ,46] .237 RDC 7 0. .22 9. .0 l 1 . , 0 2. , 5 95, . 1 5 94 .57 [92. 83,96. .30] .492 RDC 8 0. . 26 8, . 2 10. . 5 2. . 3 94, .73 95 .30 [94. 16,96. ,44] . 153 H <= c a l c u l a t e d CSL S = average simulated CSL 33 FIGURE 2: The A v e r a g e Number of O r d e r s O u t s t a n d i n g a t any one Time a t t h e RDC's when t h e Demand D i s t r i b u t i o n i s N o r m a l o r N o r m a l T r u n c a t e d a t Z e r o w i t h DSL=80% and RSL=98%. 1.35-1 34 FIGURE 3: The Minimum and Maximum Number o f O r d e r s P e r Year a t e a c h RDC when t h e Demand D i s t r i b u t i o n i s N o r m a l w i t h DSL=80% a n d RSL=98%. 6 0 n 5 5 -50 < Ld >-or: 4-5 LxJ O O LJ 35 m 30 2 5 -20 m I m Legend ^ MINIMUM NUMBER OF ORDERS »ER YEAR E3 MAXIMUM NUMBER Or ORDERS PER YEAR y 0 i ^>° N 9SP- ^ $P $f>* 35 T A B L E 3 : R e s u l t s f r o m S i m u l a t i o n s I I I - V I - I n v e n t o r y S y s t e m  w i t h V a r y i n g Numbers o f R D C ' s DSL=75% E [ I ] = 4 0 d a y s RSL=98% a t e a c h RDC S . D . [ I ] = 5 d a y s H S 95% C . I . P - V A L U E (%) (%) f o r S S i m u l a t i o n I I I RDC 1 9 0 . 9 6 9 0 . 6 0 [ 8 8 . 6 5 , 9 2 . 5 5 ] . 7 0 1 RDC 2 91 . 8 7 91 . 2 7 [ 8 9 . 5 7 , 9 2 . 9 7 ] . 4 6 8 RDC 3 8 9 . 0 3 8 7 . 2 3 [ 8 4 . 5 9 , 8 9 . 8 7 ] . 1 72 RDC 4 9 2 . 5 4 9 2 . 8 6 [ 9 1 . 0 5 , 9 4 . 6 5 ] . 7 1 5 RDC 5 9 0 . 5 3 8 8 . 9 6 [ 8 7 . 5 2 , 9 0 . 4 0 ] * . 0 3 4 RDC 6 9 3 . 2 1 9 2 . 8 0 [ 9 0 . 9 8 , 9 4 . 6 2 ] . 6 4 4 RDC 7 9 3 . 7 4 9 4 . 7 2 [ 9 3 . 2 4 , 9 6 . 2 0 ] . 1 8 1 RDC 8 9 3 . 1 4 9 3 . 5 2 [ 9 1 . 5 5 , 9 5 . 4 9 ] . 6 9 4 S i m u l a t i o n IV RDC 1 9 0 . 96 91 . 0 2 [ 8 9 . 4 4 , 9 2 . 5 9 ] . 9 3 7 RDC 2 91 . 8 7 9 2 . 3 3 [ 9 0 . 4 4 , 9 4 . 2 2 ] . 6 1 6 RDC 3 8 9 . 0 3 . 8 7 . 2 8 • [ 8 4 . 5 8 , 8 9 . 9 9 ] . 1 93 RDC 4 9 2 . 5 4 9 3 . 0 0 [ 9 1 . 6 2 , 9 4 . 3 8 ] . 4 9 2 RDC 5 9 0 . 5 3 9 0 . 4 9 [ 8 8 . 6 4 , 9 2 . 3 4 ] . 9 6 1 RDC 6 9 3 . 2 1 9 2 . 3 9 [ 9 0 . 8 9 , 9 3 . 8 9 ] . 2 6 8 RDC 7 9 3 . 7 4 9 3 . 2 5 [ 9 2 . 1 5 , 9 4 . 3 5 ] . 3 6 4 RDC 8 9 3 . 14 9 3 . 7 6 [ 9 2 . 2 9 , 9 5 . 2 3 ] . 3 9 0 S i m u l a t i o n V RDC 1 9 0 . 9 0 91 . 6 0 [ 8 9 . 8 3 , 9 3 . 3 6 ] . 4 1 7 RDC 2 91 . 8 2 9 2 . 8 0 [ 9 0 . 9 7 , 9 4 . 6 3 ] . 2 7 7 RDC 3 8 8 . 9 6 8 8 . 9 4 [ 8 6 . 3 7 , 9 1 . 5 1 ] . 9 8 4 RDC 4 9 2 . 4 9 9 4 . 5 7 [ 9 2 . 8 5 , 9 6 . 3 0 ] * . 0 2 1 RDC 5 9 0 . 4 7 9 0 . 7 0 [ 8 8 . 1 7 , 9 3 . 2 2 ] . 8 5 1 S i m u l a t i o n VI RDC 1 9 0 . 9 5 9 3 . 0 9 [ 9 0 . 9 7 , 9 5 . 3 2 ] * . 0 4 9 RDC 2 91 . 8 6 9 3 . 5 5 [ 9 1 . 8 9 , 9 5 . 2 1 ] * . 0 4 7 RDC 3 8 9 . 0 2 8 8 . 1 3 [ 8 6 . 1 1 , 9 0 . 1 4 ] . 3 6 9 N o t e : S i m u l a t i o n I I I u s e s a N o r m a l d i s t r i b u t i o n o f demand a t t h e R D C ' s , w h e r e a s S i m u l a t i o n s IV t o VI u s e a N o r m a l d i s t r i b u t i o n o f demand t r u n c a t e d a t z e r o H = c a l c u l a t e d CSL S = a v e r a g e s i m u l a t e d C S L * i n d i c a t e s t h e c a l c u l a t e d C S L , H , i s o u t s i d e t h e C o n f i d e n c e I n t e r v a l 36 T A B L E 4 : R e s u l t s f r o m S i m u l a t i o n V I I - I X - I n c r e a s i n g EOQ  S i z e s DSL=75% E [ I ] = 4 0 d a y s RSL=98% a t e a c h RDC S . D . [ l ] = 5 d a y s H S 95% C . I . P - V A L U E (%) (%) f o r S S i m u l a t i o n V I I : 2 EOQ RDC 1 9 3 . 8 7 9 4 . 5 7 [ 9 3 . 2 6 , 9 5 . 8 8 ] . 2 7 7 RDC 2 9 4 . 2 5 9 3 . 18 [ 9 1 . 4 7 , 9 4 . 8 9 ] . 2 0 6 RDC 3 9 2 . 5 2 9 2 . 6 2 [ 9 1 . 0 2 , 9 4 . 2 2 ] . 8 9 7 RDC 4 9 4 . 7 8 9 4 . 3 4 [ 9 2 . 4 4 , 9 6 . 2 4 ] . 6 3 0 RDC 5 9 3 . 6 6 9 3 . 0 8 [ 9 1 . 2 4 , 9 4 . 9 2 ] . 5 1 7 RDC 6 9 5 . 14 9 5 . 14 [ 9 3 . 4 1 , 9 6 . 8 6 ] 1 . 0 0 0 RDC 7 9 5 . 4 1 9 6 . 4 8 [ 9 5 . 8 2 , 9 7 . 1 3 ] * . 0 0 3 RDC 8 9 5 . 1 1 9 4 . 7 5 [ 9 3 . 2 5 , 9 6 . 2 4 ] . 6 2 3 S i m u l a t i o n V I 1 1 : 3 EOQ RDC 1 9 5 . 0 0 9 4 . 0 3 [ 9 1 . 5 2 , 9 6 . 5 3 ] . 4 2 8 RDC 2 9 5 . 3 8 9 4 . 2 9 [ 9 2 . 5 8 , 9 6 . 0 0 ] . 1 9 9 RDC 3 9 4 . 1 1 8 9 . 2 9 [ 8 6 . 7 8 , 9 1 . 7 9 ] * < . 0 0 1 RDC 4 9 5 . 6 3 9 6 . 12 [ 9 5 . 0 3 , 9 7 . 2 1 ] . 2 8 5 RDC 5 9 4 . 8 7 9 3 . 3 2 [ 9 1 . 3 6 , 9 5 . 2 8 ] . 1 1 3 RDC 6 9 5 . 8 7 9 4 . 7 5 [ 9 3 . 3 4 , 9 6 . 1 7 ] . 1 1 5 RDC 7 9 6 . 0 5 9 5 . 6 3 [ 9 4 . 3 5 , 9 6 . 9 0 ] . 4 9 8 RDC 8 9 5 . 8 3 9 4 . 6 0 [ 9 2 . 9 2 , 9 6 . 2 9 ] . 143 S i m u l a t i o n I X : 8 EOQ RDC 1 9 6 . 6 5 9 4 . 14 [ 9 2 . 3 3 , 9 5 . 9 5 ] * . 0 0 9 RDC 2 9 6 . 8 1 9 7 . 0 3 [ 9 6 . 2 2 , 9 7 . 8 4 ] . 3 3 9 RDC 3 9 6 . 2 8 9 2 . 2 5 [ 9 0 . 4 4 , 9 4 . 0 5 ] * < . 0 0 1 RDC 4 9 6 . 9 1 9 6 . 2 0 [ 9 4 . 2 8 , 9 8 . 1 2 ] . 4 4 5 RDC 5 9 6 . 6 3 91 . 6 5 [ 8 9 . 3 3 , 9 3 . 9 7 ] * < . 0 0 1 RDC 6 9 6 . 9 9 9 4 . 8 0 [ 9 2 . 9 7 , 9 5 . 6 3 ] * . 0 1 8 RDC 7 9 7 . 0 6 9 7 . 5 5 [ 9 6 . 4 7 , 9 8 . 6 3 ] . 3 5 4 RDC 8 9 6 . 9 7 9 6 . 4 2 [ 9 4 . 9 7 , 9 7 . 8 6 ] . 4 3 4 H = c a l c u l a t e d CSL S = a v e r a g e s i m u l a t e d C S L * i n d i c a t e s t h e c a l c u l a t e d C S L , H , i s o u t s i d e t h e C o n f i d e n c e I n t e r v a l 37 FIGURE 4: The Minimum a nd Maximum Number o f O r d e r s P e r Y e a r a t e a c h RDC when t h e Demand D i s t r i b u t i o n i s N o r m a l T r u n c a t e d a t Z e r o w i t h DSL=75% and RSL=98%. Legend ^ MINIMUM NUMBER Or ORDERS PER YEAR • MAXIMUM NUMBER OF ORDERS PER YEAR 8 $P tf>tf 38 39 FIGURE 6: The Minimum and Maximum Number o f O r d e r s P e r Y e a r a t e a c h RDC when t h e Demand D i s t r i b u t i o n i s N o r m a l T r u n c a t e d a t Z e r o and EOQ i s T r i p l e d w i t h DSL=75% and RSL=98%. 24- i 22 2 0 -18-1 6 -Li_ 1 4 -12 1 0 -8 -Y Y Y\ y Y 1 I w. Legend ^ MINIMUM NUMBER OF ORDERS E J MAXIMUM NUMBER OF ORDERS Yi YJ Yy Yy $f> <$f> 40 FIGURE 7: The Minimum a n d Maximum Number o f O r d e r s P e r Y e a r a t e a c h RDC when t h e Demand D i s t r i b u t i o n i s N o r m a l T r u n c a t e d a t Z e r o and EOQ i s M u l t i p l i e d by E i g h t w i t h DSL=75% and RSL=98%. or: < LU >-or: CO or: LxJ Q or O o or: U J m Legend ^ MINIMUM NUMBER OF ORDERS E3 MAXIMUM NUMBER OF ORDERS ^f> 41 FIGURE 8: 1.6 The A v e r a g e Number o f O r d e r s O u t s t a n d i n g a t any one Time a t t h e RDC's when t h e Demand D i s t r i b u t i o n i s N o r m a l T r u n c a t e d a t Z e r o a n d EOQ i s M u l t i p l i e d by One, Two, T h r e e and E i g h t w i t h DSL=75% and RSL=98%. Legend ^ SINGLE E00 C Z DOUBLE EOQ W TRIPLE E00 \ZZ\ EOQ TIMES EIGHT tf><* $f*> C h a p t e r 6 TESTING THE ROBUSTNESS OF THE HEURISTIC The f o l l o w i n g two s e t s o f s i m u l a t i o n m o d e l r u n s a t t e m p t t o t e s t t h e r o b u s t n e s s o f t h e h e u r i s t i c by s u b s t i t u t i n g s l i g h t l y d i f f e r e n t a s s u m p t i o n s a s c o m p o n e n t s o f t h e i n v e n t o r y s y s t e m u n d e r s t u d y . The f i r s t s e t i n v e s t i g a t e s r e p l a c i n g t h e n o r m a l d i s t r i b u t i o n o f l e a d t i m e o f r e p l e n i s h m e n t by a u n i f o r m d i s t r i b u t i o n . The s e c o n d s e t o f t e s t s t r u n c a t e s t h e n o r m a l d i s t r i b u t i o n o f demand a t t h e RDC's a t v a r i o u s p o i n t s w h i l e i n c r e a s i n g t h e c o e f f i c i e n t s o f v a r i a t i o n . 6.1 DEFINING THE UNIFORM DISTRIBUTION A u n i f o r m d i s t r i b u t i o n o f l e a d t i m e o f r e p l e n i s h m e n t i s s u b s t i t u t e d a t v a r i o u s l o c a t i o n s i n t h e i n v e n t o r y s y s t e m . The mean and s t a n d a r d d e v i a t i o n o f t h e u n i f o r m d i s t r i b u t i o n a t a p a r t i c u l a r l o c a t i o n a r e i d e n t i c a l t o t h e p a r a m e t e r s o f t h e n o r m a l d i s t r i b u t i o n p r e v i o u s l y i n e f f e c t a t t h a t l o c a t i o n . To a c h i e v e t h i s , we u s e t h e f o l l o w i n g c a l c u l a t i o n s t o show t h e r e l a t i o n s h i p b e t w e e n t h e end p o i n t s o f t h e u n i f o r m d i s t r i b u t i o n t o t h e mean and s t a n d a r d d e v i a t i o n o f t h e d i s t r i b u t i o n . b a2 = / ( X - M ) 2 _ J _ dx (9) a b-a w h i c h r e s u l t s i n a 2 = ( b - a ) 2 (10) 12 42 43 S i m p l i f i c a t i o n y i e l d s o/T2 = b-a ( 1 1 ) By d e f i n i t i o n , t h e mean o f t h e u n i f o r m d i s t r i b u t i o n i s n = b+a (12) 2 S o l v i n g e q u a t i o n s (3) a n d (4) s i m u l t a n e o u s l y , we o b t a i n t h e two p o i n t s d e f i n i n g t h e i n t e r v a l o f t h e u n i f o r m d i s t r i b u t i o n : a = -a/3 + M ( 1 3 ) b = +o/3 + ju ( 1 4 ) 6.2 BASE RUN WITH LOWERED DSL VALUE The u n i f o r m d i s t r i b u t i o n o f l e a d t i m e o f r e p l e n i s h m e n t i s u s e d i n s i m u l a t i o n r u n s where t h e DSL h a s been l o w e r e d t o 70% w h i l e t h e RSL r e m a i n s a t 98%. F o r p u r p o s e s o f c o m p a r i s o n , S i m u l a t i o n s X and XI a r e r u n w i t h t h e s e v a l u e s o f DSL a n d RSL and n o r m a l d i s t r i b u t i o n s o f l e a d t i m e s a t a l l l o c a t i o n s . S i m u l a t i o n X a l s o h a s a n o r m a l d i s t r i b u t i o n o f demand a t a l l RDC's w h i l e S i m u l a t i o n X I u s e s a n o r m a l d i s t r i b u t i o n t r u n c a t e d a t z e r o . RDC's 1,4 and 7, ( T a b l e 5, S i m u l a t i o n X ) , h a v e c a l c u l a t e d v a l u e s o f CSL n o t i n c l u d e d i n t h e i r 9 5 % c o n f i d e n c e i n t e r v a l s . The h e u r i s t i c y i e l d s v a l u e s o f CSL w h i c h a r e l o w e r t h a n t h e s i m u l a t e d r e s u l t s . The p - v a l u e s a r e r e l a t i v e l y s m a l l and r a n g e f r o m l e s s t h a n .001 t o .021 l e a d i n g us t o i n f e r t h a t a d e c r e a s e i n DSL r e s u l t s i n a 44 p o o r e r p e r f o r m a n c e by t h e h e u r i s t i c . F i g u r e 9 i l l u s t r a t e s t h e number o f o r d e r s o u s t a n d i n g a t t h e RDC's a t any one t i m e i s somewhat h i g h e r when c o m p a r e d t o r e s u l t s f r o m S i m u l a t i o n I where t h e DSL i s s e t a t 8 0 % . T h i s i s p r o b a b l y a r e f l e c t i o n o f t h e l o n g e r l e a d t i m e s o f r e p l e n i s h m e n t f r o m t h e DC t o t h e RDC's c a u s e d by r e p e a t e d z e r o s t o c k o c c u r r e n c e s when t h e DSL i s 70% s i n c e o t h e r p a r a m e t e r v a l u e s a r e i d e n t i c a l . " When a n o r m a l d i s t r i b u t i o n o f demand t r u n c a t e d a t z e r o i s i n e f f e c t a t t h e r e g i o n a l c e n t r e s , RDC's 2, 6, 7 a n d 8 a r e f o u n d t o h a v e c a l c u l a t e d CSL v a l u e s o u t s i d e t h e 9 5 % c o n f i d e n c e i n t e r v a l o f t h e s i m u l a t e d r e s u l t s w i t h p - v a l u e s r a n g i n g f r o m .022 t o .046 ( T a b l e 5, S i m u l a t i o n X I ) . The v a l u e s o f CSL p r e d i c t e d by t h e h e u r i s t i c a r e a g a i n l o w e r t h a n t h e s i m u l a t e d r e s u l t s . F i g u r e 9 p o r t r a y s t h e i n c r e a s e d number o f o r d e r s o u t s t a n d i n g when DSL i s l o w e r e d f r o m 8 0 % t o 70 % . A g a i n , we c o n c l u d e t h a t a l o w e r e d DSL v a l u e r e s u l t s i n l o n g e r l e a d t i m e s o f r e p l e n i s h m e n t a t t h e RDC's a f f e c t i n g n e g a t i v e l y t h e p r e d i c t i v e v a l u e o f t h e h e u r i s t i c . 6.3 UNIFORM DISTRIBUTION OF LEAD TIME The u n i f o r m d i s t r i b u t i o n o f l e a d t i m e o f r e p l e n i s h m e n t i n u s e a t t h e DC i n S i m u l a t i o n X I I h a s an u n c h a n g e d mean o f 20 d a y s a n d a h a l f r a n g e o f 8.6 d a y s . RDC's 3 a n d 7, ( T a b l e 6, S i m u l a t i o n X I I ) , b o t h h a v e c a l c u l a t e d CSL v a l u e s o u t s i d e t h e i r 9 5 % c o n f i d e n c e i n t e r v a l w i t h p - v a l u e s o f .046 a n d .026 4 I n p u t v a l u e s t o S i m u l a t i o n s X - X I V a r e l i s t e d i n T a b l e A4. 45 r e s p e c t i v e l y . I n S i m u l a t i o n X I I I t h e l e a d t i m e o f r e p l e n i s h m e n t a t t h e DC i s r e s e t t o t h e o r i g i n a l n o r m a l d i s t r i b u t i o n u s e d i n S i m u l a t i o n X I a n d t h e l e a d t i m e s o f r e p l e n i s h m e n t a t a l l RDC's a r e r e p l a c e d by u n i f o r m d i s t r i b u t i o n s w i t h p a r a m e t e r v a l u e s i d e n t i c a l t o t h o s e o f S i m u l a t i o n X I . T a b l e 6 shows t h a t i n S i m u l a t i o n X I I I , RDC's 1, 3 a n d 5 h a v e c a l c u l a t e d v a l u e s o f CSL w h i c h a r e l o w e r t h a n t h e v a l u e s i n c l u d e d i n t h e 95% c o n f i d e n c e i n t e r v a l o f t h e s i m u l a t e d r e s u l t s w i t h p - v a l u e s r a n g i n g f r o m .049 t o .011. T h e s e r e s u l t s i n d i c a t e a d e t e r i o r a t i o n o f s e r v i c e a t t h e c u s t o m e r l e v e l when u n i f o r m l e a d t i m e s a r e i n e f f e c t a t t h e r e g i o n a l c e n t r e s . When a u n i f o r m d i s t r i b u t i o n r e p l a c e s a l l p r e v i o u s l y n o r m a l l y d i s t r i b u t e d l e a d t i m e s o f r e p l e n i s h m e n t , i . e . a t t h e DC and a l l e i g h t RDC's, t h e f i r s t s i x RDC's h a v e CSL v a l u e s c a l c u l a t e d by t h e h e u r i s t i c w h i c h a r e h i g h e r t h a n t h e s i m u l a t e d r e s u l t s a n d f a l l o u t s i d e t h e 95% c o n f i d e n c e i n t e r v a l o f t h e s i m u l a t e d v a l u e s ( T a b l e 6, S i m u l a t i o n X I V ) . P - v a l u e s now r a n g e f r o m .038 t o l e s s t h a n .001 i n d i c a t i n g t h e h e u r i s t i c r e s u l t s a r e b e c o m i n g l e s s r e p r e s e n t a t i v e o f t h e s i m u l a t e d v a l u e s . F i g u r e 10 i l l u s t r a t e s t h e number o f o u t s t a n d i n g o r d e r s a t t h e RDC's a s t h e u n i f o r m d i s t r i b u t i o n i s s u b s t i t u t e d i n t h e i n v e n t o r y s y s t e m i n S i m u l a t i o n s X I I t o X I V . As t h e h e u r i s t i c r e s u l t s become l e s s p r e d i c t i v e o f t h e s i m u l a t e d v a l u e s o f CSL, t h e number o f o u t s t a n d i n g o r d e r s a t e a c h 46 r e g i o n a l c e n t r e i s s e e n t o i n c r e a s e . T h e s e r e s u l t s seem t o i n d i c a t e t h a t t h e h e u r i s t i c i s h i g h l y d e p e n d e n t on t h e u s e o f n o r m a l l y d i s t r i b u t e d l e a d t i m e s o f r e p l e n i s h m e n t a t t h e DC a n d t h e RDC's, w i t h t h e w o r s t r e s u l t s o b t a i n e d when t h e a s s u m p t i o n o f n o r m a l i t y i s r e l a x e d a t b o t h l e v e l s o f t h e i n v e n t o r y s y s t e m . 6.4 TRUNCATING THE DISTRIBUTION OF DEMAND The f o l l o w i n g n i n e s i m u l a t i o n s i n v e s t i g a t e t h e r o b u s t n e s s o f t h e h e u r i s t i c when t h e n o r m a l l y d i s t r i b u t e d demand a t t h e RDC's i s t r u n c a t e d a t z e r o , M/2, a n d M w h i l e t h e c o e f f i c i e n t o f v a r i a t i o n , ffj>j)/MRD' i - n c r e a s e s i p v a l u e f r o m .21 t o 6.0. T r u n c a t i o n a t z e r o was c h o s e n t o i n v e s t i g a t e an i n v e n t o r y s y s t e m where no r e t u r n s o c c u r r e d . P r e v i o u s a n a l y s i s o f a r e a l l i f e i n v e n t o r y s y s t e m r e v e a l e d t h e d i s t r i b u t i o n o f demand a t t h e RDC's t o be a p p r o x i m a t e l y e x p o n e n t i a l . T r u n c a t i o n o f t h e n o r m a l d i s t r i b u t i o n a t M was c h o s e n b e c a u s e i t l e a v e s a d i s t r i b u t i o n c l o s e l y r e s e m b l i n g t h e e x p o n e n t i a l d i s t r i b u t i o n . The t h i r d c h o i c e f o r t r u n c a t i o n M/2, was c h o s e n a s a m i d - p o i n t b e t w e e n t h e f i r s t t w o. T r u n c a t i n g a n o r m a l d i s t r i b u t i o n f r o m b e l o w c a u s e s t h e mean t o i n c r e a s e a n d t h e s t a n d a r d d e v i a t i o n t o d e c r e a s e . T h e s e p a r a m e t e r s must t h e r e f o r e be r e d e f i n e d a s d e s c r i b e d i n J o h n s o n a nd K o t z . [ 6 ] . H o w e v e r , s i n c e we c o n c e r n o u r s e l v e s o n l y w i t h t r u n c a t i o n f r o m b e l o w , t h e e x p e c t e d v a l u e a n d 47 v a r i a n c e c a n be s i m p l i f i e d t o E [ X j = u + a n d A-M1 I a (15) V A R [ X ] = 1 + 1 - $ 1 - $ A - M (16) w h e r e A i s t h e t r u n c a t i o n p o i n t M, a a r e t h e mean a n d s t a n d a r d d e v i a t i o n 0 ( x ) i s t h e u n i t n o r m a l d e n s i t y f u n c t i o n , a n d r K • * (K) = J _ c c 0 ( x ) d x , F i g u r e 11 i l l u s t r a t e s t h e r e l a t i o n s h i p e x i s t i n g b e t w e e n t h e c o e f f i c i e n t o f v a r i a t i o n o f t h e n o r m a l d i s t r i b u t i o n t r u n c a t e d a t v a r i o u s p o i n t s a n d t h e c o e f f i c i e n t o f v a r i a t i o n o f t h e n o r m a l d i s t r i b u t i o n . The c u r v e r i s e s v e r y s h a r p l y when t r u n c a t i n g o c c u r s a t z e r o i n c o n t r a s t t o t h e c u r v e r e p r e s e n t i n g t r u n c a t i o n a t t h e m e a n , M. T a b l e 7 s u m m a r i z e s t h e o u t c o m e o f s i m u l a t i n g w i t h a d i s t r i b u t i o n of demand a t t h e R D C ' s t r u n c a t e d a t z e r o w h i l e t h e r a t i o o f ffRrj/MRD v a r ^ e s t r ° m «21 t o 6 . 0 . F o r e a s e o f c o m p a r i s o n , t h e r e s u l t s o b t a i n e d i n S i m u l a t i o n II a r e r e p r o d u c e d h e r e . R e c a l l t h a t t r u n c a t i o n a t z e r o o c c u r s i n t h e i n v e n t o r y s y s t e m m o d e l e d by S i m u l a t i o n II i n o r d e r t o a v o i d d e a l i n g w i t h n e g a t i v e d e m a n d . We n o t e t h a t a l l c a l c u l a t e d v a l u e s o f C S L f a l l w i t h i n t h e i r r e s p e c t i v e 95% c o n f i d e n c e i n t e r v a l o f t h e s i m u l a t e d r e s u l t s e x c e p t a t RDC2 48 i n S i m u l a t i o n XV. T h i s e x c e p t i o n c a n be e x p l a i n e d by t h e r a n d o m n e s s o f e v e n t s a n d s u g g e s t s t h a t t h e h e u r i s t i c i s q u i t e r o b u s t when t h e d i s t r i b u t i o n o f .demand a t t h e RDC's i s t r u n c a t e d a t z e r o a n d t h e r a t i o o f ^ R Q / M R Q i s v a r i e d f r o m .21 t o 6.0. 5 F i g u r e 12 p o r t r a y s t h e a v e r a g e number o f o r d e r s o u t s t a n d i n g a t any one t i m e a t t h e e i g h t RDC's a s t h e c o e f f i c i e n t o f v a r i a t i o n i n c r e a s e s . We n o t e t h a t t h e d i f f e r e n c e i s n o t s i g n i f i c a n t i n any one r u n . The n e x t t h r e e s i m u l a t i o n s m o d e l i n v e n t o r y s y s t e m s where t h e i n d i v i d u a l demand d i s t r i b u t i o n a t e a c h RDC i s n o r m a l l y d i s t r i b u t e d w i t h t r u n c a t i o n a t M/2. The r a n g e o f c o e f f i c i e n t o f v a r i a t i o n v a l u e s i s r e p e a t e d a n d t h e outcome o f t h e a n a l y s i s i s l i s t e d i n T a b l e 8. We n o t e t h a t i n e a c h s i m u l a t i o n o n l y one RDC h a s a c a l c u l a t e d v a l u e o f CSL o u t s i d e i t s 9 5 % c o n f i d e n c e i n t e r v a l . T h i s s u g g e s t s t h a t e v e n when t h e demand d i s t r i b u t i o n i s t r u n c a t e d a t M/2, t h e h e u r i s t i c i s a good p r e d i c t o r - o f s e r v i c e a t t h e c u s t o m e r l e v e l o v e r a f a i r l y w i d e r a n g e o f v a r i a b i l i t y . 6 F i g u r e 13 i l l u s t r a t e s t h e a v e r a g e number o f o r d e r s o u t s t a n d i n g a t any t i m e i n t h e s i m u l a t i o n s . We o b s e r v e t h a t an o r d e r f o r EOQ i s a l w a y s o u t s t a n d i n g w h i c h e n s u r e s t h a t t h e DC e x p e r i e n c e s a n o r m a l l y d i s t r i b u t e d demand o v e r i t s 5 I n p u t v a l u e s t o S i m u l a t i o n s XV a n d XVI a r e e n u m e r a t e d i n T a b l e s A5 a n d A6 o f A p p e n d i x A. 6 A 1 1 i n p u t s t o S i m u l a t i o n s X V I I - X I X a r e l i s t e d i n T a b l e s A7-A9. 49 s c h e d u l i n g i n t e r v a l o f 40 d a y s . When t r u n c a t i o n o c c u r s a t t h e mean, n, o f e a c h n o r m a l l y d i s t r i b u t e d demand a t t h e RDC's, we n o t e t h a t i n S i m u l a t i o n XX, ( T a b l e 9 ) , when v a r i a b i l i t y i s s m a l l , o n l y RDC7 h a s a c a l c u l a t e d v a l u e o f CSL n o t w i t h i n t h e 95% c o n f i d e n c e i n t e r v a l . We o b s e r v e i n S i m u l a t i o n X X I I t h a t RDC's 2 and 3 a l s o h a v e c a l c u l a t e d CSL v a l u e s o u t s i d e t h e i r c o n f i d e n c e i n t e r v a l w i t h p - v a l u e s o f .024 a n d .026 r e s p e c t i v e l y . We c o n c l u d e f r o m t h e s e r e s u l t s t h a t t h e h e u r i s t i c i s f a i r l y r o b u s t i n i t s p r e d i c t i o n o f s e r v i c e l e v e l e v e n when t r u n c a t i o n o f t h e n o r m a l l y d i s t r i b u t e d demand a t t h e RDC's o c c u r s a t t h e mean and when v a r i a b i l i t y o f t h e o r i g i n a l d i s t r i b u t i o n e q u a l s 6.0. 7 F i g u r e 14 shows t h e a v e r a g e number o f o r d e r s o u t s t a n d i n g t o be g r e a t e r t h a n one a t a l l RDC's e n s u r i n g t h a t t h e demand on t h e DC i s s t i l l n o r m a l l y d i s t r i b u t e d o v e r i t s s c h e d u l i n g i n t e r v a l . ' I n p u t v a l u e s t o S i m u l a t i o n s X X - X X I I a r e t o be f o u n d i n T a b l e s A10-A12. 50 TABLE 5 : R e s u l t s f r o m S i m u l a t i o n X a n d XI - D i s t r i b u t i o n  o f Demand i s N o r m a l a n d N o r m a l T r u n c a t e d a t Z e r o DSL=70% E [ I ] = 4 0 d a y s RSL=98% a t e a c h RDC S . D . [ l ] = 5 d a y s H S 95% C . I . P - V A L U E (1 (3 's) f o r S S i m u l a t i o n X RDC 1 8 8 . . 2 6 9 0 . . 1 4 [ 8 8 . . 5 9 , 9 1 . , 7 0 ] * . 0 2 1 RDC 2 8 9 , . 4 3 9 0 . .81 [ 8 8 . . 2 9 , 9 3 . ,32 ] . 2 6 4 RDC 3 8 5 , . 8 6 8 5 . .88 [ 8 3 , . 8 7 , 8 7 . , 8 8 ] . 9 8 4 RDC 4 9 0 , .31 9 3 . .28 [ 9 1 , . 8 7 , 9 4 . , 6 8 ] * <. 00 1 RDC 5 8 7 , . 7 3 8 6 . .93 [ 8 4 . . 6 3 , 8 9 . , 2 2 ] . 4 7 4 RDC 6 91 , . 2 0 9 2 . .43 [ 9 0 , . 7 0 , 9 4 . . 1 5 ] . 1 53 RDC 7 91 , .91 9 4 . . 1 9 [ 9 2 , . 9 4 , 9 5 . . 4 3 ] * . 0 0 1 RDC 8 91 , . 1 0 9 2 . . 8 9 [ 9 0 , . 8 5 , 9 4 . , 9 3 ] . 0 7 7 S i m u l a t i o n XI RDC 1 8 9 . . 7 5 [ 8 7 , . 6 7 , 9 1 . , 8 3 ] . 150 RDC 2 91 , . 2 9 [ 8 9 , . 7 1 , 9 2 . , 8 7 ] * . 0 3 8 RDC 3 8 6 , .21 [ 8 3 , . 9 1 , 8 8 . .51 ] . 7 5 2 RDC 4 91 , . 6 0 [ 8 9 , . 3 3 , 9 3 . . 8 7 ] . 2 4 9 RDC 5 8 7 , .32 [ 8 4 , . 4 5 , 9 0 . . 1 9 ] . 7 6 7 RDC 6 92 , . 9 3 [91 , . 2 4 , 9 4 . . 6 2 ] * . 0 4 6 RDC 7 9 3 , . 7 9 [ 9 2 , . 2 2 , 9 5 , . 3 6 ] * . 0 2 2 RDC 8 92 , . 8 0 [ 9 1 , . 2 3 , 9 4 . . 3 7 ] * . 0 3 6 H = c a l c u l a t e d CSL S = a v e r a g e s i m u l a t e d CSL * i n d i c a t e s t h e c a l c u l a t e d C S L , H , i s o u t s i d e t h e C o n f i d e n c e I n t e r v a l 51 FIGURE 9: 1.40-1 1.35-O Q < 1.30 CO 1.25-O S5 1 - 2 0 Q Q z : LxJ 1.15 1.10-1.05 The A v e r a g e Number o f O r d e r s O u t s t a n d i n g a t any one T ime a t t h e R D C ' s when t h e Demand D i s t r i b u t i o n i s N o r m a l T r u n c a t e d a t Z e r o w i t h RSL=98% a n d DSL=70% a n d 8 0 % . Legend ^ DSL IS SET AT 80% • DSL IS SET AT 70% A 1. 1 w I v. V A P la 7 A A $0 |4 ft I ill 1 i $P ^ ^ ^ ^ ^ t f ^ c * i i I WA $A 52 T A B L E 6 : R e s u l t s f r o m S i m u l a t i o n s X I I - X I V - U n i f o r m L e a d  T i m e D i s t r i b u t i o n The U n i f o r m d i s t r i b u t i o n i s u s e d a t t h e D C , t h e R D C ' s , a n d b o t h t h e DC a n d t h e R D C ' s r e s p e c t i v e l y DSL=70% E [ I ] = 4 0 d a y s RSL=98% a t e a c h RDC S . D . [ I ] = 5 d a y s H S 95% C . I . P - V A L U E (%) (%) f o r S S i m u l a t i o n XI I RDC 1 8 8 . 2 6 8 7 . 9 5 [ 8 5 . 9 3 , 8 9 . 9 6 ] . 7 5 3 RDC 2 8 9 . 4 3 8 9 . 6 8 [ 8 7 . 4 0 , 9 1 . 9 5 ] .821 RDC 3 8 5 . 8 6 8 3 . 2 6 [ 8 0 . 7 2 , 8 5 . 8 0 ] * . 0 4 6 RDC 4 9 0 . 3 1 91 . 3 4 [ 8 9 . 0 5 , 9 3 . 6 2 ] . 3 5 9 RDC 5 8 7 . 7 3 8 5 . 8 3 [ 8 2 . 5 6 , 8 9 . 0 9 ] . 2 3 7 RDC 6 91 . 2 0 9 1 . 1 7 [ 8 9 . 3 2 , 9 3 . 0 2 ] . 9 7 6 RDC 7 91 .91 9 3 . 7 3 [ 9 2 . 1 5 , 9 5 . 3 1 ] * . 0 2 6 RDC 8 9 1 . 1 0 91 . 2 8 [ 8 8 . 7 9 , 9 3 . 7 6 ] . 8 8 2 S i m u l a t i o n X I I I RDC 1 8 8 . 2 6 8 5 . 7 4 [ 8 3 . 7 4 , 8 7 . 7 5 ] * . 0 1 7 RDC 2 8 9 . 4 3 8 8 . 4 8 [ 8 6 . 6 9 , 9 0 . 2 6 ] . 2 7 7 RDC 3 8 5 . 8 6 8 3 . 4 0 [ 8 1 . 5 8 , 8 5 . 2 3 ] * .011 RDC 4 9 0 . 3 1 8 8 . 9 8 [ 8 6 . 6 9 , 9 1 . 2 8 ] .241 RDC 5 8 7 . 7 3 8 5 . 0 4 [ 8 2 . 3 6 , 8 7 . 7 2 ] * . 0 4 9 RDC 6 91 . 2 0 8 9 . 7 0 [ 8 7 . 8 6 , 9 1 . 5 3 ] . 1 05 RDC 7 91 .91 91 . 5 5 [ 8 9 . 9 1 , 9 3 . 1 9 ] .651 RDC 8 9 1 . 1 0 8 9 . 7 6 [ 8 8 . 1 7 , 9 1 . 3 5 ] . 0 9 4 S i m u l a t i o n X I V RDC 1 8 8 . 2 6 8 4 . 7 5 [ 8 2 . 3 1 , 8 7 . 1 9 ] * . 0 0 7 RDC 2 8 9 . 4 3 . 8 5 . 2 3 [ 8 3 . 5 7 , 8 6 . 9 0 ] * <.0001 RDC 3 8 5 . 8 6 8 0 . 0 1 [ 7 7 . 6 7 , 8 2 . 3 6 ] * <.0001 RDC 4 9 0 . 3 1 8 7 . 7 1 [ 8 5 . 2 7 , 9 0 . 1 4 ] * . 0 3 8 RDC 5 8 7 . 7 3 8 4 . 0 4 [ 8 1 . 7 1 , 8 6 . 3 8 ] * . 0 0 4 RDC 6 91 . 2 0 8 7 . 2 4 [ 8 4 . 9 8 , 8 9 . 5 0 ] * . 0 0 2 RDC 7 91 .91 9 0 . 2 4 [ 8 8 . 5 5 , 9 1 . 9 3 ] . 0 5 2 RDC 8 9 1 . 1 0 8 9 . 5 1 [ 8 7 . 5 7 , 9 1 . 4 4 ] . 1 0 2 H = c a l c u l a t e d CSL S = a v e r a g e s i m u l a t e d C S L * i n d i c a t e s t h e c a l c u l a t e d C S L , H , i s o u t s i d e t h e C o n f i d e n c e I n t e r v a l 53 FIGURE 10 1.45 The A v e r a g e Number o f O r d e r s O u t s t a n d i n g a t any one Time a t t h e RDC's when t h e Demand D i s t r i b u t i o n i s N o r m a l T r u n c a t e d a t Z e r o , t h e L e a d Time D i s t r i b u t i o n i s U n i f o r m a t t h e DC, t h e RDC's and B o t h t h e DC and t h e RDC'S w i t h DSL=70% a n d RSL=98%. Legend ^ NORMAL TRUNCATED AT ZERO d UNIFORM AT THE DC EES! UNIFORM AT THE RDC'S EZ3 UNIFORM AT BOTH LEVELS tf>tf $fi> $ff> ^ 0 ^fP 54 FIGURE 11 : The C o e f f i c i e n t s o f V a r i a t i o n o f t h e N o r m a l D i s t r i b u t i o n T r u n c a t e d a t Z e r o , Mean/2, and t h e Mean P l o t t e d a s F u n c t i o n s o f t h e C o e f f i c i e n t o f V a r i a t i o n o f t h e S t a n d a r d N o r m a l D i s t r i b u t i o n . COEFFICIENT OF VARIATION OF NORMAL 55 T A B L E 7 : R e s u l t s f r o m S i m u l a t i o n I I , X V - X V I - N o r m a l D i s t r i b u t i o n o f Demand T r u n c a t e d a t Z e r o DSL=80% E [ I ] = 40 d a y s RSL=98% a t e a c h RDC S . D . [ I ] = 5 d a y s a R D H S 95% C . I . P-VALU1 M R D (%) (% ) f o r S S i m u l a t i o n II RDC 1 0 . 2 1 9 3 . 15 9 2 . 73 [ 9 1 . 0 9 , 9 4 . 3 8 ] . 6 0 2 RDC 2 0 . 2 4 9 3 . 8 1 9 4 . 40 [ 9 3 . 2 3 , 9 5 . 5 7 ] . 3 0 6 RDC 3 0 . 2 2 91 . 6 8 91 . 26 [ 8 9 . 7 6 , 9 2 . 7 6 ] . 5 6 9 RDC 4 0 . 2 7 9 4 . 2 9 9 4 . 69 [ 9 3 . 3 0 , 9 6 . 0 8 ] . 5 5 5 RDC 5 0 . 3 0 9 2 . 8 1 91 . 23 [ 8 9 . 3 2 , 9 3 . 1 5 ] . 1 0 0 RDC 6 0 . 3 2 9 4 . 7 7 9 5 . 39 [ 9 4 . 3 3 , 9 6 . 4 6 ] . 2 3 7 RDC 7 0 . 2 2 9 5 . 1 5 9 4 . 57 [ 9 2 . 8 3 , 9 6 . 3 0 ] . . 4 9 2 RDC 8 0 . 2 6 9 4 . 7 3 9 5 . 30 [ 9 4 . 1 6 , 9 6 . 4 4 ] .311 S i m u l a t i o n XV RDC 1 1 . 5 0 9 4 . 1 9 9 2 . 27 [ 9 0 . 0 6 , 9 4 . 4 7 ] . 0 8 5 RDC 2 1 . 5 0 9 4 . 6 6 9 2 . 00 [ 8 9 . 7 2 , 9 4 . 2 8 ] * . 0 2 5 RDC3 1 . 5 0 9 2 . 9 8 91 . 90 [ 8 9 . 1 2 , 9 4 . 6 8 ] . 4 2 8 RDC 4 1 . 5 0 9 5 . 0 9 9 5 . 39 [ 9 4 . 2 8 , 9 6 . 5 0 ] . 9 5 3 RDC 5 1 . 5 0 9 3 . 8 2 9 3 . 00 [91 . 2 6 , 9 4 . 7 4 ] . 3 3 5 RDC 6 1 . 5 0 9 5 . 3 2 9 4 . 42 [ 9 2 . 5 3 , 9 6 . 3 1 ] . 3 3 0 RDC 7 1 . 5 0 9 5 . 7 1 9 4 . 23 [ 9 2 . 4 0 , 9 6 . 0 6 ] . 1 07 RDC 8 1 . 5 0 9 5 . 4 0 9 4 . 95 [ 9 3 . 4 6 , 9 6 . 4 3 ] . 5 3 6 S i m u l a t i o n XVI RDC 1 6 . 0 0 9 4 . 3 7 9 3 . 1 2 [91 . 0 5 , 9 5 . 1 8 ] . 2 1 9 RDC 2 6 . 0 0 9 4 . 8 0 9 4 . 40 [ 9 2 . 9 5 , 9 5 . 8 4 ] . 5 6 9 RDC 3 6 . 0 0 9 3 . 2 5 91 . 23 [ 8 9 . 0 3 , 9 3 . 4 2 ] . 0 6 9 RDC 4 6 . 0 0 9 5 . 2 3 9 5 . 51 [ 9 4 . 1 8 , 9 6 . 8 7 ] . 6 6 5 RDC 5 6 . 0 0 9 4 . 0 1 9 2 . 89 [ 9 0 . 8 8 , 9 4 . 9 0 ] . 2 5 6 RDC 6 6 . 0 0 9 5 . 3 8 9 4 . 62 [ 9 3 . 3 9 , 9 5 . 8 4 ] . 2 0 9 RDC 7 6 . 0 0 9 5 . 8 1 9 4 . 81 [ 9 3 . 6 6 , 9 5 . 9 6 ] . 0 8 5 RDC 8 6 . 0 0 9 5 . 5 3 9 6 . 01 [ 9 4 . 5 7 , 9 7 . 4 5 ] . 4 9 2 H = c a l c u l a t e d CSL S = a v e r a g e s i m u l a t e d CSL * i n d i c a t e s t h e c a l c u l a t e d C S L , H , i s o u t s i d e t h e C o n f i d e n c e I n t e r v a l FIGURE 12; o 2: Q z : CO r— Z) o CO or LJ Q or O u_ O or LJ CO < or Ld 1.35 n The A v e r a g e Number o f O r d e r s O u t s t a n d i n g a t a one Time a t t h e RDC's when t h e Demand N o r m a l T r u n c a t e d a t Z e r o , t h e V a r i a t i o n r a n g e f r o m .21 t o 6 RSL=98%. D i s t r i b u t i o n i s C o e f f i c i e n t s o f and DSL=80% a nd 1.30-1.25 1.20 1.15 1.10-1.05 Legend S.D./MEAN FROM .21 TO .32 S.D./MEAN = 1.5 S.D./MEAN = 6.0 ^ $f> V P 0 " tf>°* tf£ 0* 57 T A B L E 8 : R e s u l t s f r o m S i m u l a t i o n s X V I I - X I X - N o r m a l D i s t r i b u t i o n o f Demand T r u n c a t e d a t M/2 DSL= 80% E [ I ] = 4 0 d a y s RSL= 98% a t e a c h RDC S . D . [ I ] = 5 d a y s a R D H S 95% C . I . P--VALUI M R D (%) (%) f o r S S i m u l a t i o n XVI I RDC1 0 . 2 1 9 2 . 9 7 9 2 . 7 8 [ 9 1 . 1 7 , 9 4 . 3 9 ] . 8 0 5 RDC 2 0 . 2 4 9 3 . 6 2 9 3 . 0 5 [ 9 1 . 5 2 , 9 4 . 5 7 ] . 4 4 5 RDC 3 0 . 2 2 9 1 . 4 5 8 9 . 0 7 [ 8 6 . 8 8 , 9 1 . 2 6 ] * . 0 3 5 RDC 4 0 . 2 7 9 4 . 0 7 9 3 . 5 0 [ 9 1 . 9 4 , 9 5 . 0 7 ] . 4 5 7 RDC 5 0 . 3 0 9 2 . 4 3 91 . 2 2 [ 8 9 . 4 5 , 9 2 . 9 9 ] . 1 69 RDC 6 0 . 3 2 9 4 . 4 8 9 4 . 1 3 [ 9 3 . 4 0 , 9 4 . 8 5 ] . 3 2 5 RDC 7 0 . 2 2 9 5 . 0 2 9 5 . 2 1 [ 9 3 . 7 7 , 9 6 . 6 5 ] . 7 8 3 RDC 8 0 . 2 6 9 4 . 6 1 9 3 . 6 7 [ 9 2 . 0 8 , 9 5 . 2 5 ] . 2 3 1 S i m u l a t i o n X V I I I RDC 1 1 . 5 0 9 2 . 7 9 9 0 . 2 3 [ 8 8 . 1 2 , 9 2 . 3 4 ] * . 0 2 0 RDC 2 1 . 5 0 9 4 . 3 0 9 3 . 7 9 [ 9 2 . 1 9 , 9 5 . 3 9 ] . 5 1 1 RDC 3 1 . 5 0 9 2 . 4 6 91 . 3 7 [ 8 9 . 7 3 , 9 3 . 0 1 ] . 1 8 1 RDC 4 1 . 5 0 9 4 . 7 5 9 4 . 3 6 [ 9 3 . 3 4 , 9 5 . 3 7 ] . 4 3 4 RDC 5 1 . 5 0 9 3 . 3 5 9 3 . 0 0 [ 9 1 . 3 4 , 9 4 . 6 5 ] . 6 5 8 RDC 6 1 . 5 0 9 5 . 0 3 9 4 . 6 9 [ 9 3 . 4 2 , 9 5 . 9 6 ] . 5 8 2 RDC 7 1 . 5 0 9 5 . 4 8 9 5 . 2 8 [ 9 4 . 0 8 , 9 6 . 4 9 ] . 7 3 0 RDC 8 1 . 5 0 9 5 . 1 0 9 5 . 6 5 [ 9 4 . 5 2 , 9 6 . 7 7 ] . 3 2 1 S i m u l a t i o n X IX RDC 1 6 . 0 0 9 4 . 2 0 91 . 7 2 [ 8 9 . 7 7 , 9 3 . 6 8 ] * . 0 1 6 RDC 2 6 . 0 0 9 4 . 6 6 9 3 . 0 0 [ 9 0 . 7 0 , 9 5 . 3 0 ] . 1 47 RDC 3 6 . 0 0 9 3 . 0 3 9 2 . 18 [ 9 0 . 3 0 , 9 4 . 0 5 ] . 3 5 4 RDC 4 6 . 0 0 9 5 . 0 8 9 5 . 1 4 [ 9 3 . 4 4 , 9 6 . 8 4 ] . 9 4 5 RDC 5 6 . 0 0 9 3 . 8 6 9 4 . 0 8 [ 9 2 . 8 8 , 9 5 . 2 8 ] . 3 5 4 RDC 6 6 . 0 0 9 5 . 3 2 9 4 . 4 9 [ 9 3 . 3 2 , 9 5 . 6 7 ] . 1 55 RDC 7 6 . 0 0 9 5 . 7 0 9 5 . 0 9 [ 9 3 . 4 5 , 9 6 . 7 4 ] . 2 2 3 RDC 8 6 . 0 0 9 5 . 4 0 9 5 . 2 3 [ 9 3 . 9 1 , 9 6 . 5 5 ] . 7 9 0 H = c a l c u l a t e d CSL S = a v e r a g e s i m u l a t e d CSL * i n d i c a t e s t h e c a l c u l a t e d C S L , H , i s o u t s i d e t h e C o n f i d e n c e I n t e r v a l 58 F IGURE 13 o or: L J CD < or: The Average Number of Orders O u t s t a n d i n g at any one Time a t the RDC's when the Demand D i s t r i b u t i o n i s Normal T r u n c a t e d at Mean/2 w i t h the C o e f f i c i e n t s of V a r i a t i o n r a n g i n g from . 2 1 t o 6.0, and DSL=80% and RSL=98%. 1.40-1 1.35 J 1.30 J O -z. Q fS if) ZD O 1.25 (/) or LU Q or O 1.20-1.15 UJ 1.10-1.05-Legend ^ S.0./MEAN FROM .21 TO .32 2D S.D./MEAN = 1.5 ^ S.D./MEAN = 6.0 $P ^ ^ tf><* tf><* tf><*> .0* 5 9 T A B L E 9 : R e s u l t s f r o m S i m u l a t i o n s X X - X X I I - N o r m a l  D i s t r i b u t i o n o f Demand T r u n c a t e d a t y DSL=80% E [ I ] = 4 0 d a y s RSL=98% a t e a c h RDC S . D . [ I ] = 5 d a y s a R D H S 95% C . I . P-VALUI M R D (%) (%) f o r S S i m u l a t i o n XX RDC 1 0 . 2 1 9 2 . 4 7 9 2 . 0 3 [ 9 0 . 3 1 , 9 3 . 7 9 ] . 5 9 5 RDC 2 0 . 2 4 9 3 . 1 3 9 2 . 5 4 [ 9 1 . 3 2 , 9 3 . 7 6 ] . 3 2 5 RDC 3 0 . 2 2 9 1 . 4 1 8 9 . 8 3 [ 8 7 . 9 5 , 9 1 . 6 9 ] . 0 9 4 RDC 4 0 . 2 7 9 3 . 5 5 9 5 . 0 1 [ 9 3 . 5 3 , 9 6 . 4 9 ] . 0 5 2 RDC 5 0 . 3 0 9 1 . 7 1 91 . 2 0 [ 8 9 . 6 4 , 9 2 . 7 7 ] . 5 1 1 RDC 6 0 . 3 2 9 4 . 0 1 9 5 . 0 5 [ 9 3 . 9 2 , 9 6 . 1 8 ] . 0 7 0 RDC 7 0 . 2 2 9 4 . 7 3 9 6 . 0 7 [ 9 5 . 0 4 , 9 7 . 1 0 ] * . 0 1 4 RDC 8 0 . 2 1 9 4 . 1 4 9 4 . 8 9 [ 9 3 . 5 1 , 9 6 . 2 8 ] . 2 7 3 S i m u l a t i o n XXI RDC 1 1 . 5 0 9 3 . 6 0 9 2 . 8 5 [ 9 1 . 2 9 , 9 4 . 4 1 ] . 3 2 5 RDC 2 1 . 5 0 9 4 . 1 5 9 3 . 9 4 [ 9 2 . 3 2 , 9 5 . 5 5 ] .821 RDC 3 1 . 5 0 9 2 . 2 3 91 . 2 5 [ 8 9 . 7 2 , 9 2 . 7 8 ] . 1 9 6 RDC 4 1 . 5 0 9 4 . 5 7 9 3 . 7 8 [ 9 2 . 4 3 , 9 5 . 1 3 ] . 2 3 4 RDC 5 1 . 5 0 9 3 . 12 9 2 . 7 1 [ 9 1 . 1 7 , 9 4 . 2 4 ] . 5 8 2 RDC 6 1 . 5 0 9 4 . 9 1 9 4 . 7 3 [ 9 3 . 4 4 , 9 6 . 0 1 ] . 7 7 5 RDC 7 1 . 5 0 9 5 . 3 8 9 4 . 8 4 [ 9 3 . 0 7 , 9 6 . 6 1 ] . 5 3 0 RDC 8 1 . 5 0 9 5 . 0 0 9 5 . 12 [ 9 3 . 9 0 , 9 6 . 3 3 ] . 8 3 6 S i m u l a t i o n XXI I RDC 1 6 . 0 0 9 4 . 1 3 9 2 . 8 7 [ 9 0 . 7 6 , 9 4 . 9 7 ] . 2 2 6 RDC 2 6 . 0 0 9 4 . 5 8 9 2 . 7 0 [ 9 1 . 1 0 , 9 4 . 3 0 ] * . 0 2 4 RDC 3 6 . 0 0 9 2 . 9 0 9 0 . 8 8 [ 8 9 . 0 5 , 9 2 . 7 1 ] * . 0 2 6 RDC 4 6 . 0 0 9 5 . 0 0 9 4 . 9 8 [ 9 3 . 1 4 , 9 6 . 8 1 ] . 9 8 4 RDC 5 6 . 0 0 9 3 . 7 5 9 2 . 2 1 [ 8 9 . 7 1 , 9 4 . 7 0 ] . 2 1 3 RDC 6 6 . 0 0 9 5 . 2 5 9 4 . 18 [ 9 2 . 3 5 , 9 6 . 0 1 ] . 2 3 3 RDC 7 6 . 0 0 9 5 . 6 7 9 5 . 2 8 [ 9 3 . 9 8 , 9 6 . 5 8 ] . 5 3 6 RDC 8 6 . 0 0 9 5 . 3 6 9 5 . 2 9 [ 9 3 . 7 1 , 9 6 . 8 6 ] . 9 2 9 H = c a l c u l a t e d C S L S = a v e r a g e s i m u l a t e d CSL * i n d i c a t e s t h e c a l c u l a t e d C S L , H , i s o u t s i d e t h e C o n f i d e n c e I n t e r v a l 60 FIGURE 14: o z Q f< CO I— ZD o CO o: LxJ Q cc o o L J CQ < Cxi L J 1.7 i 1.6 -I The A v e r a g e Number o f O r d e r s O u t s t a n d i n g a t any one Time a t t h e RDC's when t h e Demand D i s t r i b u t i o n i s N o r m a l T r u n c a t e d a t t h e Mean w i t h C o e f f i c i e n t s o f V a r i a t i o n R a n g i n g f r o m .21 t o 6.0, and DSL=80% a nd RSL=98%. Legend ^ S.D./MEAN FROM .21 TO .32 ZD S.D./MEAN = 1.5 m S.D./MEAN = 6.0 $f> ^f> .0* C h a p t e r 7 CONCLUSIONS The h e u r i s t i c a p p e a r s t o be a g o o d p r e d i c t o r o f c u s t o m e r s e r v i c e l e v e l i n a t w o - e c h e l o n i n v e n t o r y s y s t e m w i t h n o r m a l l y d i s t r i b u t e d demand a t t h e R D C ' s a n d n o r m a l l y d i s t r i b u t e d l e a d t i m e s o f r e p l e n i s h m e n t . I t r e m a i n s a u s e f u l t o o l f o r e s t i m a t i n g t h e c u s t o m e r s e r v i c e l e v e l e v e n when demand a t t h e R D C ' s i s t r u n c a t e d a n d t h e c o e f f i c i e n t s o f v a r i a b i l i t y a r e i n c r e a s e d . The a s s u m p t i o n t h a t demand a t t h e DC f o l l o w s a n o r m a l d i s t r i b u t i o n c a n be m a i n t a i n e d e v e n when EOQ s i z e i s i n c r e a s e d o r t h e number o f R D C ' s i s d e c r e a s e d . T h i s a s s u m p t i o n c a n be s e e n t o b r e a k down i f EOQ s i z e i s v e r y l a r g e o r t h e number o f R D C ' s i n t h e s y s t e m i s r e d u c e d t o t h r e e . The h e u r i s t i c b e c o m e s l e s s p r e d i c t a b l e when t h e n o r m a l l y d i s t r i b u t e d l e a d t i m e s of r e p l e n i s h m e n t a r e r e p l a c e d by u n i f o r m l y d i s t r i b u t e d l e a d t i m e s . T h i s i s an a s s u m p t i o n o f t h e i n v e n t o r y s y s t e m a n d i s n o t s t r e s s e d i n R o s e n b a u m ' s p a p e r a s b e i n g o f p a r t i c u l a r i m p o r t a n c e . I t a p p e a r s h o w e v e r , t o be a d i s t i n c l y s e n s i t i v e p a r a m e t e r o f t h e h e u r i s t i c . K e e p i n g t h e s e c o m m e n t s i n m i n d , i t c a n be s t a t e d t h a t t h e h e u r i s t i c i s a f a i r l y r o b u s t one a n d c a n be u s e d i n a v a r i e t y o f i n v e n t o r y s i t u a t i o n s . F u r t h e r a n a l y s i s c o u l d be done t o i n v e s t i g a t e t h e s u b s t i t u t i o n o f an e x p o n e n t i a l l e a d t i m e o f r e p l e n i s h m e n t . E x p o n e n t i a l l y d i s t r i b u t e d l e a d t i m e s a r e more r e a l i s t i c t h a n 61 62 t h e n o r m a l l e a d t i m e s assumed i n d e v e l o p i n g t h e h e u r i s t i c . I f t h e h e u r i s t i c r e m a i n s r o b u s t i n t h i s c o n t e x t , i t w o u l d e x p a n d i t s d o m a i n o f a p p l i c a t i o n s . However, i t was s e e n t h a t t h i s p a r t i c u l a r p a r a m e t e r i s v e r y s e n s i t i v e t o c h a n g e a n d t h e h e u r i s t i c may h a v e t o be m o d i f i e d b e f o r e i t c a n be o f u s e i n t h i s e n v i r o n m e n t . The d i s t r i b u t i o n o f demand i s a f a i r l y r o b u s t p a r a m e t e r a n d v a r i o u s d i s t r i b u t i o n s c o u l d be s u b s t i t u t e d a n d i n v e s t i g a t e d . A s y s t e m where t h e r e p l e n i s h m e n t p o l i c y i s c y c l i c r a t h e r t h a n p e r i o d i c a n d d a i l y r e v i e w c o u l d be a n o t h e r a r e a w o r t h l o o k i n g a t . REFERENCES [ I ] B o w e r s o x , D o n a l d J . , e t a l , "Dynamic S i m u l a t i o n o f P h y s i c a l D i s t r i b u t i o n S y s t e m s , " MSU B u s i n e s s S t u d i e s ( 1 9 7 2) [ 2 ] C l a r k , Andrew J . , "An I n f o r m a l S u r v e y o f M u l t i - E c h e l o n I n v e n t o r y T h e o r y , " N a v a l R e s e a r c h L o g i s t i c s  Q u a r t e r l y 19, No. 4 ( 1 9 7 4 ) , 6 2 1 - 6 5 2 . [ 3 ] C r o w s t o n , W.B., Wagner, M.H., a n d Henshaw, A., "A C o m p a r i s o n o f E x a c t a n d H e u r i s t i c R o u t i n e s f o r L o t - S i z e D e t e r m i n a t i o n i n M u l t i - S t a g e A s s e m b l y System,"' A l I E T r a n s a c t i o n s (December 1 9 7 2 ) , 3 1 3 -317. [ 4 ] E p p e n , G a r y , a nd S c h r a g e , L i n u s , " C e n t r a l i z e d O r d e r i n g P o l i c i e s i n a M u l t i - W a r e h o u s e S y s t e m w i t h L e a d t i m e s and Random Demand," TIMS S t u d i e s i n t h e  Management S c i e n c e s , No. 16^ ( 1 9 8 1 ) , 51-67. [ 5 ] G r a v e s , S t e p h e n C.,and S c h w a r z , L e r o y B., " S i n g l e C y c l e C o n t i n u o u s R e v i e w P o l i c i e s f o r A r b o r e s c e n t P r o d u c t i o n / I n v e n t o r y S y s t e m s , " Management  S c i e n c e , V o l . 23, No. 5, J a n u a r y 1977, 529-540. [ 6 ] J o h n s o n , Norman L., K o t z , S a m u e l , " D i s t r i b u t i o n s i n S t a t i s t i c s r C o n t i n u o u s U n i v a r i a t e D i s t r i b u t i o n s - I , " J o h n W i l e y a n d S o n s , New Y o r k ( 1 9 7 0 ) , 8 1 - 8 2 . [ 7 ] P a g e , E., " A p p r o x i m a t i o n s t o t h e C u m u l a t i v e N o r m a l F u n c t i o n a n d i t s I n v e r s e f o r Use on a P o c k e t C a l c u l a t o r , " A p p l i e d S t a t i s t i c s V o l . 26, ( 1 9 7 7 ) , 7 5 -76. [ 8 ] Rosenbaum, B a r b a r a A., " S e r v i c e L e v e l R e l a t i o n s h i p s i n a M u l t i - E c h e l o n I n v e n t o r y S y s t e m , " Management  S c i e n c e , V o l . 27, No. 8, A u g u s t 1981, 926-945. [ 9 ] Rosenbaum, B a r b a r a A., " I n v e n t o r y P l a c e m e n t i n a T w o - E c h e l o n I n v e n t o r y S ystem:An A p p l i c a t i o n , " TIMS S t u d i e s i n t h e Management S c i e n c e s , 16, ( 1 9 8 1 ) , 195-207. [ 1 0 ] S a n d , Gene, " P r e d i c t i n g Demand on t h e S e c o n d a r y E c h e l o n : A C a s e S t u d y , " TIMS S t u d i e s i n t h e  Management S c i e n c e s , 16~ ( 1 9 8 1 ) , 2 0 9 - 2 2 3 . [ I I ] S c h r i b e r , Thomas J . , " S i m u l a t i o n u s i n g GPSS," J o h n W i l e y a n d S o n s , New Y o r k ( 1 9 7 4 ) . 63 64 [ 1 2 ] T o c h e r , K.D., "The A r t o f S i m u l a t i o n , " Van N o s t r a n d , P r i n c e t o n N . J . ( 1 9 6 3 ) . APPENDIX A TABLE A1 : I n p u t s t o S i m u l a t i o n s I a n d I I DSL=80% S= 206,884 n A=225,000 oh= 28,307 RSL=98% a t e a c h RDC E [ I ] = 4 0 d a y s S . D . [ I ] = 5 d a y s a i ? n E f T B ] E [ L T ] S.D.[LT] R EOQ K J J K J J ( d a y s ) ( d a y s ) ( d a y s ) RDC 1 168 800 6.5 7.5 1 .8 7,663 5,200 RDC 2 1 50 625 7.4 8.0 1 .9 6,349 4,625 RDC 3 165 750 5.2 6.0 1 .5 5,850 3,900 RDC 4 243 900 8.0 10.0 2.0 11,094 7,200 RDC 5 1 50 500 6.6 7.0 1 .5 4,383 3,300 RDC 6 208 650 8.5 9.5 2.2 7,883 5,525 RDC 7 187 850 9.0 11.0 2.5 11 ,785 7,650 RDC 8 143 550 8.2 10.5 2.3 7,270 4,510 The f o l l o w i n g p a r a m e t e r s w i l l be f o u n d i n a l l t h e t a b l e s o f t h e A p p e n d i x : S = o r d e r up t o q u a n t i t y a t t h e DC M A , o A = t h e mean and s t a n d a r d d e v i a t i o n o f demand o v e r I E [ l ] = m e a n o f t h e s c h e d u l i n g i n t e r v a l a t t h e DC S . D . [ I ] = s t a n d a r d d e v i a t i o n o f s c h e d u l i n g i n t e r v a l M R r j, o R D=mean and s t a n d a r d d e v i a t i o n o f demand a t t h e RDC's E [ T B ] = e x p e c t e d number o f d a y s t o d e p l e t e an EOQ a t e a c h RDC E [ L T ] = e x p e c t e d l e a d t i m e ( p r o c e s s i n g + t r a n s i t t i m e ) a t e a c h RDC S . D . [ L T ] = s t a n d a r d d e v i a t i o n o f l e a d t i m e a t e a c h RDC R = r e o r d e r p o i n t a t e a c h RDC EOQ=order q u a n t i t y a t e a c h RDC 65 66 T A B L E A 2 : I n p u t s t o S i m u l a t i o n s I I I - V I - V a r y i n g Number o f R D C ' s DSL=75% RSL=98% a t e a c h RDC E [ l ] = 4 0 d a y s S . D . [ l ] = 5 d a y s °RD M R D E [ T B ] E [ L T ] S . D . [ L T ] R EOQ ( d a y s ) ( d a y s ) ( d a y s ) S i m u l a t i o n s I I I a n d IV S = 1 9 9 , 8 0 7 M A = 2 2 5 , 0 0 0 a A = 2 8 , 3 0 7 RDC 1 168 800 6 . 5 7 . 5 1 . 8 7 , 6 6 3 5 , 2 0 0 RDC 2 150 625 7 . 4 8 . 0 1 . 9 6 , 3 4 9 4 , 6 2 5 RDC 3 165 750 5 . 2 6 . 0 1 . 5 5 , 8 5 0 3 , 9 0 0 RDC 4 243 900 8 . 0 10 . 0 2 . 0 1 1 , 0 9 4 7 , 2 0 0 RDC 5 1 50 500 6 . 6 7 . 0 1 . 5 4 , 3 8 3 3 , 3 0 0 RDC 6 208 650 8 . 5 9 . 5 2 . 2 7 , 8 8 3 5 , 5 2 5 RDC 7 187 850 9 . 0 1 1 . 0 2 . 5 1 1 , 7 8 5 7 , 6 5 0 RDC 8 143 550 8 . 2 10 . 5 2 . 3 7 , 2 7 0 4 , 5 1 0 S i m u l a t i o n V S = 1 2 6 , 9 3 4 M A = 1 4 3 , 0 0 0 a A = 1 8 , 0 5 2 RDC 1 1 68 800 6 . 5 7 . 5 1 . 8 7 , 6 6 3 5 , 2 0 0 RDC 2 1 50 625 7 . 4 8 . 0 1 . 9 6 , 3 4 9 4 , 6 2 5 RDC 3 165 750 5 . 2 6 . 0 1 . 5 5 , 8 5 0 3 , 9 0 0 RDC 4 243 900 8 . 0 10 . 0 2 . 0 1 1 , 0 9 4 7 , 2 0 0 RDC 5 1 50 500 6 . 6 7 . 0 1 . 5 4 , 3 8 3 3 , 3 0 0 S i m u l a t i o n VI S= 7 7 , 3 0 5 M A = 8 7 , 0 0 0 a A = 1 1 , 0 1 7 RDC 1 168 800 6 . 5 7 . 5 1 . 8 7 , 6 6 3 5 , 2 0 0 RDC 2 150 625 7 . 4 8 . 0 1 . 9 6 , 3 4 9 4 , 6 2 5 RDC 3 1 65 750 5 . 2 6 . 0 1 . 5 5 , 8 5 0 3 , 9 0 0 67 T A B L E A 3 : I n p u t s t o S i m u l a t i o n s V I I - I X - I n c r e a s i n g EOQ  S i z e s DSL=75% S = 1 9 9 , 8 0 7 M a = 2 2 5 , 0 0 0 a A = 2 8 , 3 0 7 RSL=98% a t e a c h RDC E [ l ] = 4 0 d a y s S . D . [ l ] = 5 d a y s a R D "RD E [ T B ] ( d a y s ) E [ L T ] ( d a y s ) S . D . [ L T ] ( d a y s ) R EOQ S i m u l a t i o n V I I : 2 EOQ RDC 1 1 68 800 1 3 . 0 7 . 5 1 . 8 7 , 0 8 9 1 0 , 4 0 0 RDC 2 1 50 625 1 4 . 8 8 . 0 1 . 9 5 , 7 6 9 9 , 2 5 0 RDC 3 165 750 1 0 . 4 6 . 0 1 . 5 5 , 3 9 6 7 , 8 0 0 RDC 4 243 900 1 6 . 0 1 0 . 0 2 . 0 1 0 , 3 3 1 1 4 , 4 0 0 RDC 5 150 500 1 3 . 2 7 . 0 1 . 5 4 , 0 5 2 6 , 6 0 0 RDC 6 208 650 1 7 . 0 9 . 5 2 . 2 7 , 2 8 8 1 1 , 0 5 0 RDC 7 187 850 1 8 . 0 1 1 . 0 2 . 5 1 0 , 9 4 4 1 5 , 3 0 0 RDC 8 1 43 550 1 6 . 4 1 0 . 5 2 . 3 6 , 7 7 2 9 , 0 2 0 S i m u l a t i o n V I I : 3 EOQ RDC 1 1 68 800 1 9 . 5 7 . 5 1 . 8 6 , 7 1 1 1 5 , 6 0 0 RDC 2 1 50 625 2 2 . 2 8 . 0 1 .9 5 , 5 4 2 1 3 , 8 7 5 RDC 3 165 750 1 5 . 6 6 . 0 1 . 5 5 , 1 1 0 1 1 , 7 0 0 RDC 4 243 900 2 4 . 0 1 0 . 0 2 . 0 9 , 8 4 2 2 1 , 6 0 0 RDC 5 1 50 500 1 9 . 8 7 . 0 1 . 5 3 , 8 3 1 9 , 9 0 0 RDC 6 208 650 2 5 . 5 9 . 5 2 . 2 6 , 8 9 6 1 6 , 5 7 5 RDC 7 187 850 2 7 . 0 1 1 . 0 2 . 5 1 0 , 3 9 1 2 2 , 9 5 0 RDC 8 1 43 550 2 4 . 6 1 0 . 5 2 . 3 6 , 4 3 5 1 3 , 5 3 0 S i m u l a t i o n V I I I : 8 EOQ RDC 1 1 68 800 5 2 . 0 7 . 5 1 .8 5 , 5 9 2 4 1 , 6 0 0 RDC 2 1 50 625 5 9 . 2 8 . 0 1 . 9 4 , 5 8 4 3 7 , 0 0 0 RDC 3 1 65 750 4 1 . 6 6 . 0 1 . 5 4 , 2 2 5 3 1 , 2 0 0 RDC 4 243 900 6 4 . 0 1 0 . 0 2 . 0 8 , 3 5 4 5 7 , 6 0 0 RDC 5 1 50 500 5 2 . 8 7 . 0 1 . 5 3 , 1 69 2 6 , 4 0 0 RDC 6 208 650 6 8 . 0 9 . 5 2 . 2 5 , 7 0 5 4 4 , 2 0 0 RDC 7 1 87 850 7 2 . 0 1 1 . 0 2 . 5 8 , 7 3 0 6 1 , 2 0 0 RDC 8 143 550 6 5 . 6 1 0 . 5 2 . 3 5 , 4 3 8 3 6 , 0 8 0 68 T A B L E A 4 : I n p u t s t o S i m u l a t i o n s X - X I V - B a s e Run a n d  U n i f o r m L e a d T i m e DSL=70% S = 1 9 3 , 0 1 3 M a = 2 2 5 , 0 0 0 o A = 2 8 , 3 0 7 RSL=98% a t e a c h RDC E [ l ] = 4 0 d a y s S . D . [ I ] = 5 d a y s 0 R D M r d E [ T B ] E [ L T ] S . D . [ L T ] R EOQ ( d a y s ) ( d a y s ) ( d a y s ) S i m u l a t i o n s X - XI I RDC 1 168 800 6 . 5 7 . 5 1 . 8 7 , 6 6 3 5 , 2 0 0 RDC 2 150 625 7 . 4 8 . 0 1 . 9 6 , 3 4 9 4 , 6 2 5 RDC 3 165 750 5 . 2 6 . 0 1 . 5 5 , 8 5 0 3 , 9 0 0 RDC 4 . 243 900 8 . 0 1 0 . 0 2 . 0 1 1 , 0 9 4 7 , 2 0 0 RDC 5 150 500 6 . 6 7 . 0 1 . 5 4 , 3 8 3 3 , 3 0 0 RDC 6 208 650 8 . 5 9 . 5 2 . 2 7 , 8 8 3 5 , 5 2 5 RDC 7 187 850 9 . 0 1 1 . 0 2 . 5 1 1 , 7 8 5 7 , 6 5 0 RDC 8 •143 550 8 . 2 1 0 . 5 2 . 3 7 , 2 7 0 4 , 5 1 0 °T3T) E [ T B ] E [ L T ] HALF -WIDTH R EOQ KD KiJ ( d a y s ) ( d a y s ) ( d a y s ) S i m u l a t i o n s X I I I and X IV RDC 1 168 800 6 . 5 7 . 5 3 . 1 7 , 6 6 3 5 , 2 0 0 RDC 2 1 50 625 7 . 4 8 . 0 3 . 3 6 , 3 4 9 4 , 6 2 5 RDC 3 165 750 5 . 2 6 . 0 2 . 6 5 , 8 5 0 3 , 9 0 0 RDC 4 243 900 8 . 0 1 0 . 0 3 . 5 1 1 , 0 9 4 7 , 2 0 0 RDC 5 150 500 6 . 6 7 . 0 2 . 6 4 , 3 8 3 3 , 3 0 0 RDC 6 208 650 8 . 5 9 . 5 3 . 8 7 , 8 8 3 5 , 5 2 5 RDC 7 187 850 9 . 0 1 1 . 0 4 . 3 1 1 , 7 8 5 7 , 6 5 0 RDC 8 1 43 550 8 . 2 1 0 . 5 4 . 0 7 , 2 7 0 4 , 5 1 0 N o t e : S i m u l a t i o n s XI I a n d X IV u s e a U n i f o r m d i s t r i b u t i o n o f l e a d t i m e a t t h e DC w i t h a mean o f 20 d a y s a n d a h a l f r a n g e of 8 . 6 d a y s . 69 T A B L E A 5 : I n p u t s t o S i m u l a t i o n s XV a n d H e u r i s t i c  N o r m a l D i s t r i b u t i o n T r u n c a t e d a t Z e r o DSL=80% S = 1 5 3 , 2 0 6 M a = 1 6 6 , 0 0 0 a A = 2 1 , 6 8 5 RSL=98% a t e a c h RDC E [ l ] = 4 0 d a y s S . D . [ I ] = 5 d a y s ARD M R D E [ T B ] E [ L T ] S . D . [ L T ] R EOQ ( d a y s ) ( d a y s ) ( d a y s ) S i m u l a t i o n s X V : a D r . / / i D n = 1 . 5 RDC 1 365 243 1 0 . 7 0 7 . 5 1 . 8 4 , 2 7 5 2 , 6 0 0 RDC 2 456 304 1 2 . 1 7 8 . 0 1 . 9 5 , 6 1 2 3 , 7 0 0 RDC 3 547 365 8 . 5 5 6 . 0 1 . 5 5 , 2 9 3 3 , 1 20 RDC 4 501 334 1 3 . 1 7 1 0 . 0 2 . 0 7 , 4 2 4 4 , 4 0 0 RDC 5 592 395 1 0 . 8 6 7 . 0 1 . 5 6 , 3 3 0 4 , 2 9 0 RDC 6 410 273 1 4 . 0 1 9 . 5 2 . 2 5 , 8 9 3 3 , 8 2 5 RDC 7 273 182 1 4 . 8 4 1 1 . 0 2 . 5 4,5-16 2 , 7 0 0 RDC 8 638 425 1 3 . 5 1 1 0 . 5 2 . 3 1 0 , 0 7 6 5 , 7 4 0 H e u r i s t i c RDC 1 264 400 6 . 5 7 . 5 1 .8 4 , 2 7 5 2 , 6 0 0 RDC 2 330 500 7 . 4 8 . 0 1 . 9 5 , 6 1 2 3 , 7 0 0 RDC 3 396 600 5 . 2 6 . 0 1 . 5 5 , 2 9 3 3 , 120 RDC 4 363 550 8 . 0 1 0 . 0 2 . 0 7 , 4 2 4 4 , 4 0 0 RDC 5 429 650 6 . 6 7 . 0 1 . 5 6 , 3 3 0 4 , 2 9 0 RDC 6 297 450 8 . 5 9 . 5 2 . 2 5 , 8 9 3 3 , 8 2 5 RDC 7 1 98 300 9 . 0 1 1 . 0 2 . 5 4 , 5 1 6 2 , 7 0 0 RDC 8 462 700 8 . 2 1 0 . 5 2 . 3 1 0 , 0 7 6 5 , 7 4 0 70 T A B L E A 6 : I n p u t s t o S i m u l a t i o n s XVI a n d H e u r i s t i c N o r m a l D i s t r i b u t i o n T r u n c a t e d a t Z e r o DSL=80% S = 1 5 3 , 2 8 7 M A = 1 6 6 , 0 0 0 c A = 2 1 , 9 1 9 RSL=98% a t e a c h RDC E [ I ] =40 d a y s S . D . [ I ] = 5 d a y s " o n M R D E [ T B ] E [ L T ] S . D . [ L T ] R EOQ ( d a y s ) ( d a y s ) ( d a y s ) S i m u l a t i o n X V I : a R D / / M R D = 6 . 0 RDC 1 465 7 7 . 5 3 3 . 5 5 7 . 5 1 . 8 4 , 3 8 8 2 , 6 0 0 RDC 2 582 97 3 8 . 1 4 8 . 0 1 . 9 5 , 7 5 2 3 , 7 0 0 RDC 3 698 1 16 2 6 . 9 0 6 . 0 1 . 5 5 , 4 6 4 3 , 1 20 RDC 4 640 1 07 4 1 . 1 2 1 0 . 0 2 . 0 7 , 5 9 9 4 , 4 0 0 RDC 5 756 126 3 4 . 0 5 7 . 0 1 . 5 6 , 5 0 6 4 , 2 9 0 RDC 6 524 87 4 3 . 9 7 9 . 5 2 . 2 . 6 , 0 0 0 3 , 8 2 5 RDC 7 349 58 4 6 . 5 5 1 1 . 0 2 . 5 4 , 6 1 4 2 , 7 0 0 RDC 8 814 1 36 4 2 . 2 1 1 0 . 5 2 . 3 1 0 , 3 0 4 5 , 7 4 0 H e u r i s t i c RDC 1 296 400 6 . 5 7 . 5 1 . 8 4 , 3 8 8 2 , 6 0 0 RDC 2 370 500 7 . 4 8 . 0 1 . 9 5 , 7 5 2 3 , 7 0 0 RDC 3 444 600 5 . 2 6 . 0 1 . 5 5 , 4 6 4 3 , 120 RDC 4 407 550 8 . 0 1 0 . 0 2 . 0 7 , 5 9 9 4 , 4 0 0 RDC 5 481 650 6 . 6 7 . 0 1 . 5 6 , 5 0 6 4 , 2 9 0 RDC 6 333 450 8 . 5 9 . 5 2 . 2 6 , 0 0 0 3 , 8 2 5 RDC 7 222 300 9 . 0 1 1 . 0 2 . 5 4 , 6 1 4 2 , 7 0 0 RDC 8 518 700 8 . 2 1 0 . 5 2 . 3 1 0 , 3 0 4 5 , 7 4 0 71 TABLE A 7 : I n p u t s t o S i m u l a t i o n XV I I a n d H e u r i s t i c  N o r m a l D i s t r i b u t i o n T r u n c a t e d a t y/2 DSL=80% S = 2 0 9 , 5 2 7 M a = 2 2 8 , 4 8 0 a A = 2 8 , 7 l 6 RSL=98% a t e a c h RDC E [ l ] = 4 0 d a y s S . D . [ l ] = 5 d a y s °RD M R D E f T B ] E [ L T ] S . D . [ L T ] R EOQ ( d a y s ) ( d a y s ) ( d a y s ) S i m u l a t i o n s XVI I : ffRD/MRD= .21 RDC 1 168 800 6 . 5 7 . 5 RDC 2 1 50 625 7 . 4 8 . 0 RDC 3 165 750 5 . 2 6 . 0 RDC 4 243 900 8 . 0 1 0 . 0 RDC 5 150 500 6 . 6 7 . 0 RDC 6 208 650 8 . 5 9 . 5 RDC 7 187 850 9 . 0 1 1 . 0 RDC 8 143 550 8 . 2 1 0 . 5 H e u r i s t i c RDC 1 163 804 6 . 4 7 7 . 5 RDC 2 142 632 7 . 3 2 8 . 0 RDC 3 159 755 5 . 1 7 6 . 0 RDC 4 225 918 7 . 8 4 1 0 . 0 RDC 5 135 516 6 . 4 7 . 0 RDC 6 185 676 8 . 1 7 9 . 5 RDC 7 173 856 8 . 9 4 1 1 . 0 RDC 8 1 38 555 8 . 1 3 1 0 . 5 . 3 2 1 . 8 7 , 6 9 5 5 , 2 0 0 1 . 9 6 , 4 1 1 4 , 6 2 5 1 . 5 5 , 8 8 4 3 , 9 0 0 2 . 0 1 1 , 2 8 7 7 , 2 0 0 1 . 5 4 , 4 9 8 3 , 3 0 0 2 . 2 8 , 1 58 5 , 5 2 5 2 . 5 1 1 , 8 5 4 7 , 6 5 0 2 . 3 7 , 3 4 3 4 , 5 1 0 1 . 8 7 , 6 9 5 ' 5 , 2 0 0 1 . 9 6 , 4 1 1 4 , 6 2 5 1 . 5 5 , 8 8 4 3 , 9 0 0 2 . 0 1 1 , 2 8 7 7 , 2 0 0 1 . 5 4 , 4 9 8 3 , 3 0 0 2 . 2 8 , 1 58 5 , 5 2 5 2 . 5 1 1 , 8 5 4 7 , 6 5 0 2 . 3 7 , 3 4 3 4 , 5 1 0 72 T A B L E A 8 : I n p u t s t o S i m u l a t i o n X V I I I a n d H e u r i s t i c N o r m a l D i s t r i b u t i o n T r u n c a t e d a t M/2 DSL=80% S = 1 5 2 , 7 6 7 M A = 1 6 6 , 0 0 0 a A = 2 1 , 3 4 3 RSL=98% a t e a c h RDC E [ I ] =40 d a y s S . D . [ I ] = 5 d a y s a R D M R n E [ T B ] E [ L T ] S . D . [ L T ] R EOQ f\JJ ( d a y s ) ( d a y s ) ( d a y s ) S i m u l a t i o n X V I 1 1 : a R D / M R D = 1 . 5 RDC 1 316 21 1 1 2 . 3 2 7 . 5 1 .8 3 , 8 2 9 2 , 6 0 0 RDC 2 395 263 1 4 . 0 7 8 . 0 1 . 9 5 , 3 9 7 3 , 7 0 0 RDC 3 474 316 9 . 8 7 6 . 0 1 . 5 5 , 0 5 6 3 , 1 20 RDC 4 434 289 1 5 . 2 2 1 0 . 0 2 . 0 7 , 1 56 4 , 4 0 0 RDC 5 513 342 1 2 . 5 4 7 . 0 1 . 5 6 , 0 5 0 4 , 2 9 0 RDC 6 355 237 1 6 . 1 4 9 . 5 2 . 2 5 , 6 8 7 3 , 8 2 5 RDC 7 237 1 58 1 7 . 0 9 1 1 . 0 2 . 5 4 , 3 7 7 2 , 7 0 0 RDC 8 552 368 1 5 . 6 0 1 0 . 5 2 . 3 9 , 7 3 1 5 , 7 4 0 H e u r i s t i c RDC 1 209 400 6 . 5 7 . 5 1 . 8 3 , 8 2 9 2 , 6 0 0 RDC 2 262 500 7 . 4 8 . 0 1 . 9 5 , 3 9 7 3 , 7 0 0 RDC 3 314 600 5 . 2 6 . 0 1 . 5 5 , 0 5 6 3 , 1 20 RDC 4 288 550 8 . 0 1 0 . 0 2 . 0 7 , 156 4 , 4 0 0 RDC 5 340 650 6 . 6 7 . 0 1 . 5 6 , 0 5 0 4 , 2 9 0 RDC 6 236 450 8 . 5 9 . 5 2 . 2 5 , 6 8 7 3 , 8 2 5 RDC 7 1 57 300 9 . 0 1 1 . 0 2 . 5 4 , 3 7 7 2 , 7 0 0 RDC 8 367 700 8 . 2 1 0 . 5 2 . 3 9 , 7 3 1 5 , 7 4 0 73 T A B L E A 9 : I n p u t s t o S i m u l a t i o n X I X a n d H e u r i s t i c N o r m a l D i s t r i b u t i o n T r u n c a t e d a t u/2 DSL=80% S= 1 5 3 , 1 8 4 M A = 1 6 6 , 0 0 0 a A = 21 , 7 2 2 RSL=98% a t e a c h RDC E [ I ] =40 d a y s S . D . [ I ] = 5 d a y s E [ TB ] E [ L T ] S . D . [ L T ] R EOQ ( d a y s ) ( d a y s ) ( d a y s ) S i m u l a t i o n X I X : a RD / / * X RD = 6 . 0 RDC 1 438 73 3 5 . 6 2 7 . 5 1 . 8 4 , 2 8 8 2 , 6 0 0 RDC 2 548 91 4 0 . 6 6 8 . 0 1 . 9 5 , 6 2 7 3 , 7 0 0 RDC 3 657 1 1 0 2 8 . 3 6 6 . 0 1 . 5 5 , 3 2 5 3 , 1 2 0 RDC 4 602 100 4 4 . 0 0 1 0 . 0 2 . 0 7 , 4 4 3 4 , 4 0 0 RDC 5 712 119 3 6 . 0 5 7 . 0 1 . 5 6 , 3 6 6 4 , 2 9 0 RDC 6 493 82 4 6 . 6 5 9 . 5 2 . 2 5 , 9 0 8 3 , 8 2 5 RDC 7 329 55 4 9 . 0 9 1 1 . 0 2 . 5 4 , 5 2 6 2 , 7 0 0 RDC 8 767 128 4 4 . 8 4 1 0 . 5 2 . 3 1 0 , 102 5 , 7 4 0 H e u r i s t i c RDC 1 269 400 6 . 5 7 . 5 1 . 8 4 , 2 8 8 2 , 6 0 0 RDC 2 336 500 7 . 4 8 . 0 1 . 9 5 , 6 2 7 3 , 7 0 0 RDC 3 404 600 5 . 2 6 . 0 1 . 5 5 , 3 2 5 3 , 120 RDC 4 370 550 8 . 0 1 0 . 0 2 . 0 7 , 4 4 3 4 , 4 0 0 RDC 5 437 650 6 . 6 7 . 0 1 . 5 6 , 3 6 6 4 , 2 9 0 RDC 6 303 450 8 . 5 9 . 5 2 . 2 5 , 9 0 8 3 , 8 2 5 RDC 7 202 300 9 . 0 1 1 . 0 2 . 5 4 , 5 2 6 2 , 7 0 0 RDC 8 471 700 8 . 2 1 0 . 5 2 . 3 1 0 , 102 5 , 7 4 0 74 T A B L E A 1 0 : I n p u t s t o S i m u l a t i o n s XX a n d H e u r i s t i c N o r m a l D i s t r i b u t i o n T r u n c a t e d a t JU DSL=80% S= 2 4 8 , 5 1 2 M A = 2 7 0 , 1 6 0 a A = 3 3 , 8 2 5 RSL=98% a t e a c h RDC E [ I ] = 40 d a y s S . D . [ I ] =5 d a y s E [ TB ] E [ L T ] S . D . [ L T ] R EOQ ( d a y s ) ( d a y s ) ( d a y s ) S i m u l a t i o n s ; X X : a R D / M R D = ' 21 t o . 32 RDC 1 168 800 6 . 5 7 . 5 1 . 8 8 , 9 3 8 5 , 2 0 0 RDC 2 1 50 625 7 . 4 8 . 0 1 . 9 7 , 5 8 5 4 , 6 2 5 RDC 3 165 750 5 . 2 6 . 0 1 . 5 6 , 8 9 3 3 , 9 0 0 RDC 4 243 900 8 . 0 1 0 . 0 2 . 0 1 3 , 4 6 8 7 , 2 0 0 RDC 5 1 50 500 6 . 6 7 . 0 1 . 5 5 , 3 9 6 3 , 3 0 0 RDC 6 208 650 8 . 5 9 . 5 2 . 2 9 , 9 0 0 5 , 5 2 5 RDC 7 187 850 9 . 0 1 1 . 0 2 . 5 1 3 , 9 1 8 7 , 6 5 0 RDC 8 1 43 550 8 . 2 1 0 . 5 2 . 3 8 , 8 0 3 4 , 5 1 0 H e u r i s t i c RDC 1 101 934 5 . 5 7 7 . 5 1 . 8 8 , 9 3 8 5 , 2 0 0 RDC 2 90 745 6 . 2 1 8 . 0 1 . 9 7 , 5 8 5 4 , 6 2 5 RDC 3 99 882 5 . 2 4 6 . 0 1 . 5 6 , 8 9 3 3 , 9 0 0 RDC 4 1 47 1 094 6 . 5 8 1 0 . 0 2 . 0 1 3 , 4 6 8 7 , 2 0 0 RDC 5 90 620 5 . 3 2 7 . 0 1 . 5 5 , 3 9 6 3 , 3 0 0 RDC 6 1 25 816 6 . 7 7 9 . 5 2 . 2 9 , 9 0 0 5 , 5 2 5 RDC 7 1 1 3 999 7 . 6 6 1 1 . 0 2 . 5 1 3 , 9 1 8 7 , 6 5 0 RDC 8 86 664 6 . 7 9 1 0 . 5 2 . 3 8 , 8 0 3 4 , 5 1 0 75 T A B L E A 1 1 : I n p u t s t o S i m u l a t i o n s XXI a n d H e u r i s t i c N o r m a l D i s t r i b u t i o n T r u n c a t e d a t M DSL=! 80% S= 1 5 2 , 9 0 6 M A = 1 6 6 , 0 0 0 o =21 A , 1 1 9 RSL=' 98% a t e a c h RDC E [ I ] = 40 d a y s S . D . [ I ] = 5 d a y s MT?n E [ T B ] E [ L T ] S . D . [ L T ] R EOQ t\L> K J J ( d a y s ) ( d a y s ) ( d a y s ) S i m u l a t i o n X X I : a R D / M R D = 1 . 5 RDC 1 273 182 1 4 . 2 9 7 . 5 1 . 8 3 , 9 8 6 2 , 6 0 0 RDC 2 341 227 1 6 . 3 0 8 . 0 1 . 9 5 , 2 4 8 3 , 7 0 0 RDC 3 410 273 1 1 . 4 3 6 . 0 1 . 5 4 , 8 9 1 3 , 120 RDC 4 376 251 1 7 . 5 3 1 0 . 0 2 . 0 6 , 9 5 7 4 , 4 0 0 RDC 5 444 296 1 4 . 8 3 7 . 0 1 . 5 5 , 8 5 1 4 , 2 9 0 RDC 6 307 205 1 8 . 6 6 9 . 5 2 . 2 5 , 5 4 4 3 , 8 2 5 RDC 7 205 1 37 1 9 . 7 1 1 1 . 0 2 . 5 4 , 2 7 5 2 , 7 0 0 RDC 8 478 319 1 7 . 9 9 1 0 . 5 2 . 3 9 , 5 1 0 5 , 7 4 0 H e u r i s t i c RDC 1 165 400 6 . 5 7 . 5 1 . 8 3 , 9 8 6 2 , 6 0 0 RDC 2 206 500 7 . 4 8 . 0 1 . 9 5 , 2 4 8 3 , 7 0 0 RDC 3 247 600 5 . 2 6 . 0 1 . 5 4 , 8 9 1 3 , 1 20 RDC 4 227 550 8 . 0 1 0 . 0 2 . 0 6 , 9 5 7 4 , 4 0 0 RDC 5 268 650 6 . 6 7 . 0 1 . 5 5 , 8 5 1 4 , 2 9 0 RDC 6 185 450 8 . 5 9 . 5 2 . 2 5 , 5 4 4 3 , 8 2 5 RDC 7 124 300 9 . 0 1 1 . 0 2 . 5 4 , 2 7 5 2 , 7 0 0 RDC 8 288 700 8 . 2 1 0 . 5 2 . 3 9 , 5 1 0 5 , 7 4 0 76 T A B L E A 1 2 : I n p u t s t o S i m u l a t i o n s XX I I a n d H e u r i s t i c N o r m a l D i s t r i b u t i o n T r u n c a t e d a t u DSL=I 30% S = 1 5 3 , 0 9 9 M A = 1 6 6 , 0 0 0 a A = 2 1 , 5 0 1 RSL=! 98% a t e a c h RDC E [ I ] = 40 d a y s S . D . [ I ] =5 d a y s aT?n M R n E [ TB ] E [ L T ] S . D . [ L T ] R EOQ KlJ ( d a y s ) ( d a y s ) ( d a y s ) S i m u l a t i o n XX I I : a R D / ' M R D = 6 . 0 RDC1 415 69 3 7 . 6 8 7 . 5 1 . 8 4 , 2 3 3 2 , 6 0 0 RDC2 518 86 4 3 . 0 2 8 . 0 1 . 9 5 , 5 4 5 3 , 7 0 0 RDC3 622 1 04 3 0 . 0 0 6 . 0 1 . 5 5 , 2 3 3 3 , 1 20 RDC4 570 95 4 6 . 3 2 1 0 . 0 2 . 0 7 , 3 4 0 4 , 4 0 0 RDC5 674 1 1 2 3 8 . 3 0 7 . 0 1 . 5 6 , 2 6 2 4 , 2 9 0 RDC6 467 78 4 9 . 0 4 9 . 5 2 . 2 5 , 8 2 8 3 , 8 2 5 RDC7 311 52 51 . 9 2 1 1 . 0 2 . 5 4 , 4 7 9 2 , 7 0 0 RDC8 726 121 4 7 . 4 4 1 0 . 5 2 . 3 9 , 9 8 8 5 , 7 4 0 H e u r i s t i c RDC1 2 50 400 6 . 5 7 . 5 1 . 8 4 , 2 3 3 2 , 6 0 0 RDC2 313 500 7 . 4 8 . 0 1 . 9 5 , 5 4 5 3 , 7 0 0 RDC3 375 600 5 . 2 6 . 0 1 . 5 5 , 2 3 3 3 , 120 RDC4 344 550 8 . 0 0 1 0 . 0 2 . 0 7 , 3 4 0 4 , 4 0 0 RDC5 406 650 6 . 6 7 . 0 1 . 5 6 , 2 6 2 4 , 2 9 0 RDC6 281 450 4 . 5 9 . 5 2 . 2 5 , 8 2 8 3 , 8 2 5 RDC7 188 300 9 . 0 1 1 . 0 2 . 5 4 , 479 2 , 7 0 0 RDC8 4 38 700 8 . 2 1 0 . 5 2 . 3 9 , 9 8 8 5 , 7 4 0 APPENDIX B The B a s i c p r o g r a m w r i t t e n t o c a l c u l a t e t h e CSL u s i n g Rosenbaum's h e u r i s t i c i s d e v e l o p e d i n t h e f o l l o w i n g manner: The u n i t n o r m a l d e n s i t y f u n c t i o n i s d e f i n e d t o be 72? where n i s e s t i m a t e d t o be 3.1416. The c u m u l a t i v e n o r m a l i s a p p r o x i m a t e d t o t h e g e n e r a l f o r m d e s c r i b e d by P a g e [ 7 ] : e z y / ( 1 + e 2 y ) where y = a , x ( 1 + a 2 x 2 ) . The v a l u e s o f t h e c o e f f i c i e n t s a r e a 1=i/(2/7r) and a 2 = 0.044715. The f o l l o w i n g p r e v i o u s l y c a l c u l a t e d v a l u e s a r e i n p u t t o t h e p r o g r a m : S, t h e o r d e r up t o q u a n t i t y a t t h e DC R, t h e r e o r d e r p o i n t a t t h e RDC M a a n d o A , t h e mean a n d s t a n d a r d d e v i a t i o n o f demand on t h e DC o v e r t h e s c h e d u l i n g i n t e r v a l M d d and o D D , t h e mean a n d s t a n d a r d d e v i a t i o n o f d a i l y demand on t h e DC EOQ, t h e o r d e r q u a n t i t y a t t h e RDC M r d a n d o R D , t h e mean a n d s t a n d a r d d e v i a t i o n o f d a i l y demand a t t h e RDC E [ T B ] , t h e number of d a y s t o d e p l e t e an EOQ o f s t o c k The l o w e r a n d u p p e r l i m i t s a r e c a l c u l a t e d (TH and B E ) . T h e s e l i m i t s a n d t h e a b o v e a p p r o x i m a t i o n s p e r m i t t h e e s t i m a t i o n o f t h e t h r e e t e r m s r e q u i r e d t o a r r i v e a t 77 78 E [ T - Y | Y < T ] a n d t h e f i v e t e r m s w h i c h c o m p o s e V a r [ T - Y | Y < T ] . The v a l u e s o f t h e mean a n d s t a n d a r d d e v i a t i o n o f l e a d t i m e , E [ L T ] a n d S . D . [ L T ] a r e e n t e r e d a n d t h e p r o g r a m c o m p u t e s a n d r e t u r n s t h e v a l u e s o f E [ L T ' ] a n d S . D . [ L T ' ] . The v a l u e s f o r M b . a n d a f i , a r e e v a l u a t e d n e x t a n d u s e d t o c a l c u l a t e E [ C | N = 0 ] , t h e number o f u n i t s b a c k o r d e r e d a t t h e RDC when t h e DC h a s no s t o c k . The l e n g t h of t h e r e v i e w p e r i o d a t t h e D C , L , i s t h e n e n t e r e d a n d t h e p r o g r a m e v a l u a t e s t h e number o f u n i t s b a c k o r d e r e d p e r y e a r a t t h e RDC. The s e r v i c e l e v e l s , RSL a n d D S L , a r e i n p u t t e d a n d t h e c u s t o m e r s e r v i c e l e v e l C S L , i s c o m p u t e d a n d p r i n t e d . 7 9 $ L o g O u t p u t : F I N X , 1 0 : 3 0 : 1 4 F r i Aug 0 9 / 8 5 10 DEF F N P ( X ) = E X P ( - X * X / 2 ) / S Q R ( 2 * 3 . 1 4 1 6 ) 20 DEF F N T ( X ) = 1 - E X P ( 2 * F N Y ( X ) ) / ( 1 + E X P ( 2 * F N Y ( X ) ) ) 30 DEF F N Y ( X ) = . 7 9 7 8 8 4 5 * X * ( 1 + . 0 4 4 7 1 5 * X * X ) 40 INPUT " o r d e r up t o S = " ; S 50 INPUT " r e o r d e r l e v e l R = " ; R 60 INPUT "mean a t dc MA=";MA 70 INPUT " s i g m a a t dc S A = " ; S A 80 INPUT " d a i l y demand a t dc MDD=";MDD 90 INPUT " E ( T B ) = " ; E T B 100 INPUT " b a t c h s i z e Q = " ; Q 110 INPUT "mean a t r d c MRD=";MRD 120 INPUT " s i g m a a t r d c SRD=" ;SRD 130 T H = ( S - M A ) / S A 140 BE=TH+MDD*ETB/SA 150 A = ( F N P ( T H ) - F N P ( B E ) - T H * ( F N T ( T H ) - F N T ( B E ) ) ) / ( 2 * M D D * F N T ( T H ) / S A ) 160 B = ( F N P ( B E ) - T H * F N T ( B E ) ) * S A / ( M D D * F N T ( T H ) ) 165 EY=Q*.5/MRD+SRDa2*.5/MRDa2 170 C = E Y * F N T ( B E ) / F N T ( T H ) 175 PRINT A , B , C 180 ETY=A+B-C 190 PRINT " E ( T - Y , Y < T ) = " E T Y 200 D = ( 2 * T H * F N P ( B E ) - T H * F N P ( T H ) - B E * F N P ( B E ) + ( 1 + T H * T H ) * ( F N T ( T H ) - F N T ( B E ) ) )*SA*SA/(3*MDD*MDD*FNT(TH) ) 210 E= ( (1+TH*TH)*FNT (BE )+ (BE~2*TH)*FNP(BE ) )*SA*SA/ (MDD*MDD*FNT(TH) ) 220 F=2*EY*B 230 G=Q*SRDa2*.5/MRDa3+Qa2/MRDa2/ l2+1.25*SRDa4/MRDa4 240 H = ( G + E Y a 2 ) * F N T ( B E ) / F N T ( T H ) 250 VTY=D+E -F+H -ETYa2 251 PRINT D , E , F , G , H 260 PRINT " V ( T - Y , Y < T ) = " VTY 270 INPUT " l e a d t i m e a t r d c E L T = " ; E L T 280 INPUT " v a r o f LT a t r d c V L T = " ; V L T 290 NELT=ELT+ETY 300 NVLT=VLT+VTY 305 PRINT " a d j u s t e d e x p L T a t r d c = " NELT 310 PRINT " a d j u s t e d v a r o f L T a t RDC=" NVLT 320 MBDASH=MRD*NELT 330 SBDASH=SQR(NELT*SRDa2+NVLT*MRDa2) 340 ADJR=(R -MBDASH)/SBDASH 3 50 ECN=SBDASH*(FNP(ADJR)~ADJR*FNT (ADJR) ) 360 PRINT " E ( C , N = 0 ) = " ECN 370 INPUT " f i x e d dc r e v i e w t i m e L = " ; L 375 K=2*A/ETB+FNT(BE )/FNT (TH) 376 PRINT " P ( Y < T ) = " K 380 EGN=ECN*FNT(TH)*K/L/MRD 390 PRINT " e q u a t i o n 5=" EGN 395 INPUT " n o m i n a l s e r v i v e a t RDC R S L = " ; R S L 396 INPUT " s e r v i c e l e v e l a t dc D S L = " ; D S L 400 C S L = 1 - ( 1 - R S L ) * D S L - E G N 410 PRINT " a c t u a l s e r v i v e a t RDC C S L = " C S L GLOSSARY The v a r i a b l e s u s e d i n t h e B a s i c p r o g r a m a r e d e f i n e d h e r e i n a l p h a b e t i c a l o r d e r . a = r a i s e t o t h e power o f A,B,C = t h e t h r e e t e r m s o f E[T-Y|Y<T] ADJR = R - M B , / O B , BE = t h e u p p e r l i m i t CSL - c u s t o m e r s e r v i c e l e v e l D,E,F,G,H = t h e f i v e t e r m s m a k i n g up t h e v a r i a n c e o f Y DSL = s e r v i c e l e v e l a t t h e DC ECN = E[C|N=0] t h e b a c k o r d e r e d u n i t s a t t h e RDC when DC h a s no s t o c k EGN = E[G|N=0]-Pr(N=0) ELT = e x p e c t e d l e a d t i m e E [ L T ] E ( T B ) = t h e number o f d a y s t o d e p l e t e an EOQ ETY = E[T-Y|Y<T] EXP = e EY = E [ Y ] F N P ( X ) = t h e u n i t n o r m a l d e n s i t y f u n c t i o n F N T (X) = 1 - t h e c u m u l a t i v e n o r m a l a p p r o x i m a t e d a s d e s c r i b e d by Page a n d d e f i n e d e a r l i e r F N Y ( X ) = e v a l u a t e s y, t h e e x p o n e n t o f e i n t h e a p p r o x i m a t i o n K = P(Y<T) L = t h e DC r e v i e w p e r i o d MA = t h e mean o f t h e d i s t r i b u t i o n o f demand a t t h e DC 80 MBDASH = Mo.mean of the demand d i s t r i b u t i o n over LT S3 MDD = the mean of the d a i l y demand a t the DC MRD = the mean of the demand d i s t r i b u t i o n a t the RDC NELT = E[LT'] NVLT = V a r [ L T ' ] Q = the r e o r d e r q u a n t i t y a t the RDC R = the r e o r d e r p o i n t a t the RDC RSL = s e r v i c e l e v e l a t the RDC S = the o r d e r up t o q u a n t i t y a t the DC SA = the s t a n d a r d d e v i a t i o n of the demand a t the DC SBDASH = a B , s t a n d a r d d e v i a t i o n of demand over LT SQR = square r o o t SRD = the s t a n d a r d d e v i a t i o n of demand a t the RDC TH = the lower l i m i t VLT = v a r i a n c e of the l e a d time V a r [ L T ] VTY = V a r [ Y ] * = m u l t i p l i c a t i o n APPENDIX C I n t h e GPSS p r o g r a m t h e d i s t r i b u t i o n c e n t r e i s l a b e l e d a s A. I t s s t o c k p o s i t i o n i s STOCA a n d i t s i n v e n t o r y p o s i t i o n INVA. The o r d e r q u a n t i t y i s c a l c u l a t e d by t h e v a r i a b l e ROQA and i s e q u a l t o S m i n u s I P t h e i n v e n t o r y p o s i t i o n a t t h e t i m e t h e o r d e r i s p l a c e d . I P i s c a l c u l a t e d a s t h e s t o c k + o r d e r s - b a c k o r d e r s . The o r d e r q u a n t i t y i s s t o r e d i n NEXTA, a n d i f a s e c o n d o r d e r i s o u t s t a n d i n g i t s q u a n t i t y i s s t o r e d i n HOLDA. The r e g i o n a l c e n t r e s a r e l a b e l e d f r o m B t o I . The s t o c k s a r e STOCB t o STOCI and t h e i n v e n t o r y p o s i t i o n s a r e INVB t o I N V I . B a c k o r d e r s a r e a c c u m u l a t e d i n BORDB t o BORDI. B a c k o r d e r s a r e c a l c u l a t e d by t h e v a r i a b l e s BACKB t o BACKI -as t h e demand m i n u s t h e on-hand u n i t s a t e a c h l o c a t i o n . NEXTB t o NEXTI d e f i n e t h e q u a n t i t y t o be o r d e r e d by a l o c a t i o n when t h e l a s t o r d e r was EOQ m i n u s OH a t t h e DC. I f a s e c o n d p a r t o r d e r i s s e n t o u t , i t s q u a n t i t y i s s t o r e d i n HOLDB t o HOLDI. OHAB t o OHAI s t o r e t h e q u a n t i t y t h a t was on hand a t t h e DC when t h e RDC p u t i n an o r d e r f o r EOQ a n d t h e DC d i d n o t have enough u n i t s i n s t o c k t o s a t i s f y t h e demand. D a i l y demand a t t h e RDC's i s t a b l e d i n D2 t o D9. The demand v a r i a b l e s a r e l a b e l e d DMND2 t o DMND9 f o r t h e r e g i o n a l c e n t r e s . LTIME i s t h e v a r i a b l e w h i c h d e f i n e s t h e d i s t r i b u t i o n o f demand f o r t h e DC a n d t h e RDC's. I t d r a w s a s t a n d a r d d e v i a t i o n a n d a. mean f r o m p r e d e f i n e d d i s t r i b u t i o n s . The d i s t r i b u t i o n s a r e d e f i n e d s o t h a t e a c h l o c a t i o n i s a s s i g n e d a number f r o m 1 t o 9. The DC i s 1 a n d t h e RDC's a r e 82 83 2 t o 9. E a c h number i s a s s o c i a t e d w i t h t h e c o r r e c t mean a n d s t a n d a r d d e v i a t i o n f o r t h e l o c a t i o n i t r e p r e s e n t s . F u r t h e r comments r e g a r d i n g t h e GPSS p r o g r a m a r e w r i t t e n i n t h e p r o g r a m i t s e l f . 84 L i s t i n g o f E 0 0 a t 1 2 : 4 9 : 2 1 o n SEP 1 7 . 1985 f o r C C i d = N A D H P a g e 1 R E A L L O C A T E FAC , 1 , C O M , 4 8 5 7 2 2 R E A L L O C A T E S T O , 1 . C O M , 6 0 5 3 2 3 R E A L L O C A T E F U N . 3 . C O M . 6 6 9 0 0 4 R E A L L O C A T E Q U E , 9 , C O M , 7 6 2 1 2 5 R E A L L O C A T E V A R , 3 0 , C O M , 8 4 3 7 2 6 R E A L L O C A T E L O G , 1 . C O M , 9 0 3 6 6 7 R E A L L O C A T E T A B . 2 0 , C O M . 9 4 206 8 * 9 S I M U L A T E 10 11 * N O N - S T A N O A R D RANDOM NUMBER GENERATOR 12 13 RMULT 1 14 15 * F U N C T I O N D E F I N I T I O N S 16 * 17 SNORM F U N C T I O N R N 1 . C 2 5 STANDARD 18 O, - 5 / . 0 0 0 0 3 . - 4 / . 0 0 1 3 5 . - 3 / . 0 0 6 2 1 . - 2 . 5 / . 0 2 2 7 5 , - 2 NORMAL 19 . 0 6 6 8 1 . - 1 . 5 / . 1 1 5 0 7 . - 1 . 2 / . 1 5 8 6 6 , - 1 / . 2 1 1 8 6 , - . 8 / . 2 7 4 2 5 . - . 6 D I S T R I B U T I O N 2 0 . 3 4 4 5 8 . - . 4 / . 4 2 0 7 4 . - . 2 / . 5 . 0 / . 5 7 9 2 6 , . 2 / . 6 5 5 4 2 . . 4 F U N C T I O N 21 . 7 2 5 7 5 . . 6 / . 7 8 8 1 4 . . 8 / . 8 4 1 3 4 , 1 / . 8 8 4 9 3 . 1 . 2 / . 9 3 3 1 9 . 1 .5 2 2 . 9 7 7 2 5 . 2 / . 9 9 3 7 9 , 2 . 5 / . 9 9 8 6 5 . 3 / . 9 9 9 9 7 , 4 / 1 . 5 23 MEAN F U N C T I O N P 2 0 . D 9 MEANS AND 24 1 . 2 0 0 / 2 . 7 5 / 3 . 8 0 / 4 , 6 0 / 5 . 1 0 0 / 6 . 7 0 / 7 , 9 5 / 8 . 1 1 0 / 9 . 1 0 5 STANDARD 25 S T D E V F U N C T I O N P 2 0 . D 9 D E V I A T I O N S 26 1 , 5 0 / 2 , 1 8 / 3 , 1 9 / 4 . 1 5 / 5 . 2 0 / 6 . 1 5 / 7 , 2 2 / 8 . 2 5 / 9 . 2 3 OF LEAD T IMES 27 28 2 9 * S A V E V A L U E I N I T I A L I Z A T I O N S 3 0 31 I N I T I A L X S R O P B . 0 7 6 6 3 / X $ R 0 P C , 0 6 3 4 9 / X S R O P D . 0 5 8 5 0 REORDER 32 I N I T I A L X S R O P E , 1 1 O 9 4 / X $ R 0 P F . 0 4 3 8 3 / X S R O P G . 0 7 8 8 3 P O I N T S 33 I N I T I A L X S R O P H , 1 1 7 8 5 / X $ R 0 P I . 7 2 7 0 34 I N I T I A L X $ R O O B . O 5 2 O O / X $ R O 0 C , 4 6 2 5 / X $ R 0 0 D , 3 9 O O EOO 35 I N I T I A L X S R O O E , 0 7 2 0 0 / X $ R 0 0 F , O 3 3 O O / X $ R 0 0 G . 0 5 5 2 5 Q U A N T I T I E S 36 I N I T I A L X $ R 0 Q H , O 7 6 5 O / X $ R 0 Q I , 4 5 1 0 37 I N I T I A L X S S T O C A . 1 9 3 0 1 3 / X S S T O C B . 1 O 2 6 3 / X S S T 0 C C . 8 6 6 2 I N I T I A L 38 I N I T I A L X S S T O C D , 7 8 O O / X $ S T 0 C E . 1 4 6 9 4 / X $ S T O C F , 6 0 3 3 STOCKS 39 I N I T I A L X S S T O C G , 1 0 6 4 6 / X $ S T 0 C H . 1 5 6 1 O / X S S T 0 C I , 0 9 5 2 5 4 0 I N I T I A L X S I N V A . 1 9 3 0 1 3 / X $ I N V B . 1 0 2 6 3 / X $ I N V C . 0 8 6 6 2 I N I T I A L 41 I N I T I A L X $ I N V D , 0 7 8 0 0 / X $ I N V E . 1 4 6 9 4 / X $ I N V F . 0 6 0 3 3 INVENTORY 42 I N I T I A L X $ I N V G , 1 0 6 4 6 / X $ I N V H , 1 5 6 1 0 / X S I N V I . 0 9 5 2 5 P O S I T I O N S 43 I N I T I A L X $ D E M A . O 44 I N I T I A L X $ B 0 R D A , O / X $ B O R D B . O / X $ B 0 R D C , O / X $ B 0 R D D . O 4 5 I N I T I A L X $ B 0 R D E , O / X $ B 0 R D F , O / X $ B 0 R D G . O / X $ B 0 R D H . O 4 6 I N I T I A L X S B O R D I . O 4 7 I N I T I A L X S N E X T A . O 48 I N I T I A L X $ N E X T B , 0 / X $ N E X T C , 0 / X $ N E X T O . O / X $ N E X T E . O 4 9 I N I T I A L X $ N E X T F , 0 / X $ N E X T G , 0 / X $ N E X T H . O / X $ N E X T I . 0 5 0 I N I T I A L X $ O R D R B . O / X $ O R D R C , 0 / X $ O R D R D , 0 / X $ O R D R E . 0 51 I N I T I A L X S O R D R F , O / X S O R D R G , O / X S O R D R H , O / X S O R D R I . 0 52 I N I T I A L X $ 0 H A B , O / X $ 0 H A C , O / X $ 0 H A D . O / X $ 0 H A E . 0 53 I N I T I A L X S O H A F , O / X S O H A G , 0 / X $ O H A H . O / X S O H A I . 0 54 I N I T I A L X S B A C K A . O 55 I N I T I A L X $ N O B , 0 / X $ N O C . O / X $ N O D . O / X $ N O E . O 56 I N I T I A L X $ N O F . O / X S N O G , O / X S N O H , O / X S N O I , 0 57 I N I T I A L X S H O L D A . O 58 I N I T I A L X $ H O L D B , 0 / X $ H O L D C , 0 / X $ H O L D D . O / X $ H O L D E . O 85 i n g o f E 0 0 a t 12 : 4 9 21 o n SEP 1 7 , 1985 f o r C C i d = N A D H P a g e 5 9 I N I T I A L X $ H O L D F , 0 / X $ H O L D G , O / X S H O L D H . O / X S H O L D I . 0 6 0 61 T A B L E D E F I N I T I O N S 62 * 6 3 D2 T A B L E P 2 . 0 . 1 0 0 0 , 1 5 T A B U L A T E D A I L Y DEMAND AT B 64 D3 T A B L E P 3 . 0 . 1 0 0 0 . 1 5 " " C 65 D4 T A B L E P 4 . 0 , 1 0 0 0 , 1 5 T A B U L A T E D A I L Y DEMAND AT D 6 6 D5 T A B L E P 5 . 0 . 1 0 0 0 . 1 5 " " E 6 7 D6 T A B L E P 6 . 0 . 1 0 0 0 . 1 5 it F 68 D7 T A B L E P7 . 0 . 1 0 0 0 . 1 5 T A B U L A T E D A I L Y DEMAND AT G 6 9 D8 T A B L E P 8 . 0 , 1 0 0 0 . 1 5 " " " " H 7 0 D9 T A B L E P 9 . 0 . 1 0 0 0 , 1 5 " " I 7 1 BCKB T A B L E P 1 2 . 0 . 1 0 0 0 . 3 0 T A B U L A T E BACK ORDERS AT B 72 BCKC T A B L E P 1 3 . 0 . 1 0 0 0 , 3 0 " " " " C 73 BCKD T A B L E P 1 4 . 0 . 1 0 0 0 . 3 0 " " " D 74 B C K E T A B L E P 1 5 . 0 . 1 0 0 0 , 3 0 " " " " E 75 BCKF T A B L E P 1 6 . 0 . 1 0 0 0 . 3 0 " i, „ " F 76 BCKG T A B L E P 1 7 . 0 . 1 0 0 0 . 3 0 " II .. G 77 B C K H T A B L E P 1 8 . 0 . 1 0 0 0 . 3 0 " ,i „ " H 78 BCK I T A B L E P 1 9 . 0 . 1 O O O . 3 0 " 1 8 0 * 8 1 * V A R I A B L E D E F I N I T I O N S 82 83 84 85 86 8 7 88 8 9 9 0 91 92 93 94 95 96 97 9 8 9 9 100 101 102 103 104 105 106 107 108 109 1 10 1 1 1 1 12 1 13 1 14 115 1 16 1 17 DMND2 F V A R I A B L E 1 6 8 * FN$SNORM+800 D A I I L Y DEMAND D I S T R I B U T I O N AT B DMND3 F V A R I A B L E 1 5 O * F N $ S N 0 R M + 6 2 5 " " II i, C DMND4 F V A R I A B L E 1 6 5 * F N $ S N 0 R M + 7 5 0 " " D DMND5 F V A R I A B L E 2 4 3 * F N $ S N 0 R M + 9 O O i. n E DMND6 F V A R I A B L E 15O*FN$SN0RM+5OO II ti F DMND7 F V A R I A B L E 2 O 8 * F N $ S N 0 R M + 6 5 O " G DMND8 F V A R I A B L E 1 8 7 * F N $ S N 0 R M + 8 5 0 " " H DMND9 F V A R I A B L E 1 4 3 * F N $ S N 0 R M + 5 5 0 II i, " I L T I M E F V A R I A B L E ( F N $ S T D E V * F N $ S N O R M * F N $ M E A N ) / 1 0 LEAD T IME D I S T ' N BCKB V A R I A B L E P 2 - X S S T 0 C B DA ILY BACKORDERS AT B BCKC V A R I A B L E P 3 - X J S T 0 C C " C BCKD V A R I A B L E P 4 - X $ S T 0 C D II " D B C K E V A R I A B L E P 5 - X $ S T 0 C E E B C K F V A R I A B L E P 6 - X $ S T 0 C F .1 ., F B C K G V A R I A B L E P 7 - X S S T 0 C G " G B C K H V A R I A B L E P 8 - X S S T 0 C H " H BCK I V A R I A B L E P 9 - X S S T 0 C I " " I B A C K B V A R I A B L E X $ R 0 0 B - X $ S T 0 C A BACKORDERS FROM A TO B B A C K C V A R I A B L E X $ R O O C - X $ S T 0 C A FROM A TO C BACKD V A R I A B L E X $ R 0 0 D - X $ S T 0 C A FROM A TO D B A C K E V A R I A B L E X $ R 0 0 E - X $ S T 0 C A FROM A TO E B A C K F V A R I A B L E X $ R 0 0 F - X $ S T 0 C A FROM A TO F B A C K G V A R I A B L E X $ R 0 0 G - X $ S T 0 C A FROM A TO G B A C K H V A R I A B L E X $ R O Q H - X $ S T O C A FROM A TO H B A C K I V A R I A B L E X S R O O I - X $ S T O C A FROM A TO I ROOA V A R I A B L E 1 9 3 0 1 3 - X S I N V A ORDER UP TO Q U A N T I T Y AT DC MODEL SEGMENT 1 A2 G E N E R A T E S A V E V A L U E ADVANCE A S S I G N T E S T GE . 2 3 1 1 . , 1+ , 0 2 ,VSDMND2 P 2 . 0 . A 2 DEMAND SEGMENT SET COUNTER FOR REV IEW PER IOD AT DC S E T P 2 = D A I L Y DEMAND AT B CHECK THAT DEMAND IS P O S I T I V E 86 L i s t i n g o f EDO a t 1 2 : 4 9 : 2 1 o n SEP 17 . 1985 f o r CC i d=NADH P a g e 1 18 T A B U L A T E D2 P L A C E D A I L Y DEMAND IN T A B L E 1 19 A3 ADVANCE 0 120 A S S I G N 3 .V$DMND3 SET P3 =DAILY DEMAND AT C 12 1 T E S T GE P 3 . 0 . A 3 122 T A B U L A T E 03 123 A4 ADVANCE 0 124 A S S I G N 4 ,VSDMND4 SET P4 = D A I L Y DEMAND AT D 125 T E S T GE P 4 , 0 , A 4 126 T A B U L A T E D4 127 A5 ADVANCE 0 128 A S S I G N 5 .VSDMND5 SET P5 = DA I LY DEMAND AT E 129 T E S T GE P 5 . 0 . A 5 130 T A B U L A T E D5 13 1 A6 ADVANCE 0 132 A S S I G N 6 .VSDMND6 SET P6 = D A I L Y DEMAND AT F 133 T E S T GE P 6 . 0 . A 6 134 T A B U L A T E D6 135 A7 ADVANCE 0 13G A S S I G N 7 .V$DMND7 SET P7 = DA IL Y DEMAND AT G 137 T E S T GE P 7 . 0 . A 7 138 T A B U L A T E D7 139 A8 ADVANCE 0 140 A S S I G N 8 .VSDMND8 SET P8 = DA IL Y DEMAND AT H 14 1 T E S T GE P 8 . 0 . A 8 142 T A B U L A T E D8 143 A9 ADVANCE 0 144 A S S I G N 9 ,VSDMND9 SET P9 = D A I L Y DEMAND AT I 145 T E S T GE P 9 . 0 . A 9 146 T A B U L A T E D9 147 T E S T GE X S S T 0 C B . P 2 , ,TRUB2 CAN DEMAND AT B BE MET? 148 SAV2 S A V E V A L U E S T O C B - . P 2 YES . D E P L E T E STOCK AT B 149 S A V E V A L U E I N V B - , P 2 D E P L E T E INVENTORY AT B 150 T E S T GE X $ S T 0 C C . P 3 , , TRUB3 CAN DEMAND AT C BE MET? 151 SAV3 S A V E V A L U E S T O C C - , P 3 152 S A V E V A L U E I N V C - , P 3 153 T E S T GE X $ S T 0 C D , P 4 , ,TRUB4 CAN DEMAND AT D BE MET? 154 SAV4 S A V E V A L U E S T O C D - , P 4 155 S A V E V A L U E I N V D - , P 4 156 T E S T GE X $ S T O C E . P 5 .TRUB5 CAN DEMAND AT E BE MET? 157 S A V 5 S A V E V A L U E S T O C E - . P 5 158 S A V E V A L U E I N V E - , P 5 159 T E S T GE X $ S T 0 C F , P 6 . ,TRUB6 CAN DEMAND AT F BE MET? 160 S A V 6 S A V E V A L U E S T O C F - , P 6 161 S A V E V A L U E I N V F - , P 6 162 T E S T GE X S S T O C G , P 7 , ,TRUB7 CAN DEMAND AT G BE MET? 163 S A V 7 S A V E V A L U E S T O C G - . P 7 164 S A V E V A L U E I N V G - . P 7 165 T E S T GE X $ S T 0 C H , P 8 . . TRUB8 CAN DEMAND AT H BE MET? 166 SAV8 S A V E V A L U E S T O C H - , P 8 167 S A V E V A L U E I N V H - , P 8 168 T E S T GE- X S S T O C I . P 9 ,TRUB9 CAN DEMAND AT I BE MET? 169 S A V 9 S A V E V A L U E S T 0 C I - . P 9 170 S A V E V A L U E I N V I - , P 9 171 T A B U L A T E BCKB RECORD BACK ORDERS AT B 172 T A B U L A T E BCKC " C 173 T A B U L A T E BCKD " it n " D 174 T A B U L A T E BCKE " " " " E 175 T A B U L A T E BCKF n " " ". F 87 L i s t i n g o f EOQ a t 1 2 : 4 9 : 2 1 o n SEP 1 7 . 1985 f o r C C i d = N A D H P a g e 176 177 178 180 18 1 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 2 0 0 201 2 0 2 2 0 3 2 0 4 2 0 5 2 0 6 2 0 7 2 0 8 2 0 9 2 10 21 1 2 12 2 13 2 14 2 1 5 2 1 6 2 1 7 2 1 8 2 19 2 2 0 22 1 2 2 2 2 2 3 2 2 4 2 2 5 2 2 6 2 2 7 2 2 8 2 2 9 2 3 0 231 2 3 2 2 3 3 2 3 4 TRUB2 TRU2 T R U B 3 TRU3 TRUB4 TRU4 T R U B 5 TRU5 TRUB6 TRU6 T R U B 7 TRU7 TRUB8 TRU8 T R U B 9 T R U 9 T A B U L A T E T A B U L A T E T A B U L A T E T E R M I N A T E T E S T G A S S I G N S A V E V A L U E T R A N S F E R A S S I G N S A V E V A L U E T R A N S F E R T E S T G A S S I G N S A V E V A L U E T R A N S F E R A S S I G N S A V E V A L U E T R A N S F E R T E S T G A S S I G N S A V E V A L U E T R A N S F E R A S S I G N S A V E V A L U E T R A N S F E R T E S T G A S S I G N S A V E V A L U E T R A N S F E R A S S I G N S A V E V A L U E T R A N S F E R T E S T G A S S I G N S A V E V A L U E T R A N S F E R A S S I G N S A V E V A L U E T R A N S F E R T E S T G A S S I G N S A V E V A L U E T R A N S F E R A S S I G N S A V E V A L U E T R A N S F E R T E S T G A S S I G N S A V E V A L U E T R A N S F E R A S S I G N S A V E V A L U E T R A N S F E R T E S T G A S S I G N S A V E V A L U E T R A N S F E R A S S I G N BCKG BCKH BCK I X S S T O C B , 0 . T R U 2 12 . VSBCKB N O B + . V S B C K B , S A V 2 12 . P2 N 0 B + . P 2 . SAV2 X S S T 0 C C . 0 . T R U 3 13 , V S B C K C N 0 C + . V S B C K C , S A V 3 13 . P3 N 0 C + , P 3 , S A V 3 X S S T 0 C D . O . T R U 4 14 , V$BCKD NOD+ .V$BCKD , SAV4 14 , P4 NOD+.P4 . SAV4 X S S T O C E . 0 . T R U 5 1 5 , V S B C K E N O E + , V $ B C K E . S A V 5 15 . P5 N O E + , P 5 , S A V 5 X S S T O C F , 0 . T R U 6 1 6 , V S B C K F N0F + , V S B C K F , SAV6 1 6 . P6 N O F + , P 6 , S A V 6 X S S T 0 C G . 0 . T R U 7 17 . V S B C K G N O G + , V S B C K G , SAV7 17 , P 7 NOG+,P7 . SAV7 X S S T O C H . O , T R U 8 1 8 . V S B C K H N O H + . V S B C K H , 5AV8 18, P8 NOH+,P8 , SAV8 X S S T O C I . 0 . T R U 9 19 , V S B C K I N O I + , V S B C K I , S A V 9 1 9 . P 9 IS STOCK AT B P O S I T I V E ? Y E S . B A C K O R D E R S AT B IN P12 ADD BACKORDERS AT B GO TO D E P L E T E STOCK AT B NO,DEMAND AT B IN P12 ADD DEMAND TO BACKORDERS GO TO D E P L E T E STOCK AT B SET P 1 5 = B A C K 0 R D E R S AT C SET P 14=BACK0RDERS AT D SET P 1 5 = B A C K 0 R D E R S AT E SET P 16 = BACK0RDERS AT F SET P 17 = B A C K 0 R D E R S AT G SET P 18 = BACKDRDERS AT H SET P19=BACK ORDERS AT I 88 s t i n g o f E 0 0 a t 1 2 : 4 9 : 2 1 o n SEP 17 . 1985 f o r CC 1 d=NADH P a g e 2 3 5 S A V E V A L U E N O I + , P 9 2 3 6 T R A N S F E R , S A V 9 2 3 7 * 2 3 8 * MODEL SEGMENT 2 DC S E C T I O N 2 3 9 * 2 4 0 G E N E R A T E . , . 3 . 8 . 2 3 . F 241 L 1 T E S T E X1 . 2 0 REV IEW T I M E ? 2 4 2 S A V E V A L U E 1 . 0 Y E S . SET COUNTER TO ZERO 2 4 3 T E S T E . X $ N E X T A , O . L A IS AN ORDER O U T S T A N D I N G ? 2 4 4 S A V E V A L U E N E X T A . V $ R D O A NO. C A L C U L A T E ORDER QUANT ITY 2 4 5 S A V E V A L U E INVA + . X S N E X T A ADD ORDER Q U A N T I T Y TO INVENTORY 2 4 6 OUEUE L I N E 1 SEND OUT THE ORDER 2 4 7 DR 1 A S S I G N 2 0 . 1 2 4 8 A S S I G N 21 . V S L T I M E F E T C H A LEAD T IME FOR DC ORDER 2 4 9 T E S T G P 2 1 . 0 . D R 1 LEAD T IME P O S I T I V E ? 2 5 0 ADVANCE P21 Y E S , WAIT 251 D E P A R T L I N E 1 ORDER A R R I V E S 2 5 2 S A V E V A L U E S T O C A + , X S N E X T A ADD ORDER Q U A N T I T Y TO STOCK 2 5 3 S A V E V A L U E N E X T A . 0 SET ORDER Q U A N T I T Y TO ZERO 254 T R A N S F E R . L 1 GO SEE IF REV IEW T IME AGA IN 2 5 5 LA S A V E V A L U E H O L D A , V S R O Q A Y E S , P L A C E ORDER OUANT ITY IN 2 5 6 S A V E V A L U E I N V A + , X S H O L D A HOLD. ADD Q U A N T I T Y TO INVENTOR V 2 5 7 OUEUE L I N E 1 SEND OUT THE ORDER 2 5 8 DR 1 1 A S S I G N 2 0 . 1 2 5 9 A S S I G N 2 2 . V $ LT I ME F E T C H A LEAD T IME FOR DC ORDER 2 6 0 T E S T G P 2 2 . 0 . D R 1 1 LEAD T IME P O S I T I V E ? 261 ADVANCE P22 Y E S , WAIT 2 6 2 D E P A R T L I N E 1 ORDER A R R I V E S 2 6 3 S A V E V A L U E S T O C A + . X S H O L D A ADD ORDER QUNT ITY TO STOCK 2 6 4 T R A N S F E R . L 1 GO SEE IF REV IEW TIME AGA IN 2 6 5 * 2 6 6 * MODEL SEGMENT 3 F I R S T R E G I O N A L CENTRE 2 6 7 * 2 6 8 G E N E R A T E , , . . 2 , 2 3 2 6 9 L2 T E S T LE X S I N V B . X S R O P B HAS REORDER PO INT B E E N REACHED? 2 7 0 OUEUE L I N E 2 Y E S . S E N D OUT AN ORDER 27 1 T E S T E X S O R D R B , 0 . F I LB WAS PART ORDER R E C E I V E D L A S T ? 2 7 2 T E S T GE X S S T O C A . X S R O O B . P A R T B N O , C A N DC SEND ROO? 2 7 3 S A V E V A L U E I N V A - . X S R O O B Y E S . D E P L E T E DC INVENTORY 2 7 4 S A V E V A L U E S T D C A - . X S R O O B D E P L E T E DC STOCK 2 7 5 S A V E V A L U E DEMA+,XSROOB ADD ROQ TO DEMAND AT DC 2 7 6 S A V E V A L U E INVB+ ,XSROOB ADD ROQ TO INVENTORY AT B 2 7 7 DR2 A S S I G N 2 0 . 2 2 7 8 A S S I G N 21 , V S L T I M E F E T C H L E A D T IME . FOR B 2 7 9 T E S T G P2 1 , 0 . D R 2 LEAD T IME P O S I T I V E ? 2 8 0 ADV2 ADVANCE P21 Y E S , ORDER ON ITS WAY 281 D E P A R T L I N E 2 ORDER A R R I V E S 2 8 2 S A V E V A L U E S T O C B + . X S R O O B ADD ROO TO STOCK AT B 2 8 3 T R A N S F E R . L2 GO CHECK IF REORDER PO INT AGA IN 2 8 4 P A R T B T E S T G X $ S T 0 C A , 0 , W T 2 IS THERE ANY STOCK AT DC? 2 8 5 S A V E V A L U E B O R D B + . V S B A C K B Y E S , ADD E O O - O H TO BACKORDERS 2 8 6 S A V E V A L U E B A C K A + , V S B A C K B 2 8 7 T E S T E X S N E X T B . 0 , L B IS ANOTHER PART ORDER WA IT ING? 2 8 8 S A V E V A L U E N E X T B , V S B A C K B NO . 2 8 9 SAVB S A V E V A L U E O H A B , X S S T O C A ON HAND AT A 2 9 0 S A V E V A L U E I N V B + . X S O H A B ADD ON-HAND TO INVENTORY 291 S A V E V A L U E S T O C A - . X S O H A B D E P L E T E STOCK AT DC BY OH 2 9 2 S A V E V A L U E I N V A - , X S O H A B INVENTORY AT DC BY OH 89 L i s t i n g o f EOQ a t 12:49:21 o n SEP 17. 1985 f o r CCid=NADH P a g e 29 3 SAVEVALUE ORDRB. 1 FLAG PART ORDER RECEIVED AT B 294 DR2 1 A S S I G N 20. 2 295 A S S I G N 2 2 , V S L T I M E FETCH LEAD TIME FOR ORDER AT B 296 TEST G P22.0.DR2 1 LEAD TIME P O S I T I V E ? 297 ADVANCE P22 ORDER ON ITS WAY 298 DEPART L I N E 2 ORDER ARRIVES 299 SAVEVALUE STOCB+.XSOHAB ADD OH TO STOCK 3 0 0 TRANSFER , L2 GO CHECK IF REORDER POINT AGAIN 301 LB SAVEVALUE HOLDB,VSBACKB ORDER QUANTITY I N HOLD 302 TRANSFER . SAVB 303 F I LB SAVEVALUE ORDRB.0 SET FLAG TO ZERO 304 TEST GE X$ST0CA.X$NEXTB,WP2 ARE THERE EOQ-OH UNITS AT DC 3 0 5 SAVEVALUE INVB+,XSNEXTB YES.ADD EOQ-OH TO INVENTORY B 306 SAVEVALUE STOCA-.XSNEXTB DEPLETE STOCK AT DC BY EOQ-OH 307 SAVEVALUE INVA-,X$NEXTB INVENTORY AT DC " 308 DR22 A S S I G N 20, 2 309 A S S I G N 2 3 . V S L T I M E FETCH LEAD TIME FOR ORDER AT B 3 1 0 TEST G P23.0.DR22 LEAD TIME P O S I T I V E ? 3 1 1 A D 2 ADVANCE P 2 3 ORDER ON ITS WAY 312 DEPART L I N E 2 ORDER ARRIVES 3 1 3 SAVEVALUE STOCE+.XSNEXTB ADD EOQ-OH TO STOCK AT B 314 SAVEVALUE NEXTB.XSHOLDB PUT 2ND ORDER IN FIRST PLACE 315 SAVEVALUE HOLDB,0 SET HOLD TO ZERO 316 TRANSFER , L 2 GO CHECK I F REORDER POINT AGAIN 317 WP2 SAVEVALUE B0RDB+,XSNEXTB NO. ADD BACKORDERS 318 SAVEVALUE BACKA+.XSNEXTB 319 SAVEVALUE I N V B J - , XSNEXTB ADD EOQ-OH TO INVENTORY AT B 32 0 SAVEVALUE INVA-.XSNEXTB DEPLETE DC INVENTORY BY EOQ-OH 32 1 TEST GE XSSTOCA,XSNEXTB WAIT T I L L DC STOCK=EOQ-OH 322 SAVEVALUE STOCA-,XSNEXTB DEPLETE DC STOCK BY EOQ-OH 323 TRANSFER .DR22 GO FETCH A LEAD TIME FOR ORDER 324 WT2 SAVEVALUE INVB+,XSROQB NO, ADD EOQ TO INVENTORY AT B 325 SAVEVALUE INVA-,XSROQB DEPLETE DC INVENTORY BY EOQ 326 SAVEVALUE BORDB+.XSROQB ADD EOQ TO BACKORDERS AT E 327 SAVEVALUE BACKA+.XSROQB " " DC 328 TEST GE XSSTOCA,XSROQB WAIT T I L L DC STOCK=E0O 329 SAVEVALUE STOCA-,XSROQB DEPLETE DC STOCK B Y EOQ 3 3 0 •JO i TRANSFER , DR2 GO FETCH A LEAD TIME FOR ORDER J J I 332 MODEL SEGMENT 4 SECOND REGIONAL CENTRE 3 » 334 GENERATE .... 2.23 335 L3 TEST LE XSINVC,XSROPC 336 QUEUE L I N E 3 337 TEST E X S O R D R C . 0 , F I L C 338 TEST GE XSSTOCA.XSROQC.PARTC 339 SAVEVALUE INVA 7,XSROQC 3 4 0 SAVEVALUE DEMA+,XSROQC 341 SAVEVALUE STOCA-.XSROQC 342 5AVEVALUE INVC+,XSROQC 343 DR3 A S S I G N 2 0 , 3 344 A S S I G N 21 .VSLTIME 345 TEST G P2 1 ,0,DR3 346 ADV3 ADVANCE P2 1 347 DEPART L I N E 3 348 SAVEVALUE STOCC+,XSROQC 349 TRANSFER , L3 3 5 0 PARTC TEST G XSSTOCA,0.WT3 90 L i s t i n g o f EOQ a t 1 2 : 4 9 : 2 1 o n SEP 17 . 1985 f o r C C i d = N A D H P a g e 351 S A V E V A L U E B O R D C + , V $ B A C K C 3 5 2 S A V E V A L U E B A C K A + , V S B A C K C 3 5 3 T E S T E X S N E X T C . O . L C 3 5 4 S A V E V A L U E N E X T C , V S B A C K C 3 5 5 SAVC S A V E V A L U E O H A C . X S S T O C A 3 5 6 S A V E V A L U E I N V C + , X $ O H A C 3 5 7 S A V E V A L U E S T O C A - . X S O H A C 3 5 8 S A V E V A L U E I N V A - . X S O H A C 3 5 9 S A V E V A L U E ' O R D R C . 1 3 6 0 DR31 A S S I G N 2 0 . 3 361 A S S I G N 2 2 , V S L T I M E 362 T E S T G P 2 2 . 0 . D R 3 1 3 6 3 ADVANCE P22 364 DEPART L I N E S 3 6 5 S A V E V A L U E S T O C C + , X S O H A C 3 6 6 T R A N S F E R ,L3 3 6 7 LC S A V E V A L U E H O L D C . V S B A C K C 3 6 8 T R A N S F E R . S A V C 3 6 9 F I L C S A V E V A L U E ORDRC. 0 3 7 0 T E S T GE X S S T O C A . X S N E X T C . W P 3 371 S A V E V A L U E I N V C + . X S N E X T C 3 7 2 S A V E V A L U E S T O C A - . X S N E X T C 3 7 3 S A V E V A L U E I N V A - , X S N E X T C 374 DR32 A S S I G N 2 0 . 3 3 7 5 A S S I G N 2 3 . V S L T I M E 3 7 6 T E S T G P 2 3 . 0 . D R 3 2 3 7 7 AD3 ADVANCE P 2 3 3 7 8 D E P A R T L I N E 3 3 7 9 S A V E V A L U E S T O C C + . X S N E X T C 3 8 0 S A V E V A L U E N E X T C . X S H O L D C 381 S A V E V A L U E H O L D C . 0 382 T R A N S F E R . L 3 3 8 3 WP3 S A V E V A L U E B O R D C + , X S N E X T C 384 S A V E V A L U E B A C K A + . X S N E X T C 3 8 5 S A V E V A L U E I N V C + , X S N E X T C 3 8 6 S A V E V A L U E I N V A - . X S N E X T C 3 8 7 T E S T GE X S S T O C A , X S N E X T C 3 8 8 S A V E V A L U E S T O C A - . X S N E X T C 3 8 9 T R A N S F E R .DR32 3 9 0 WT3 S A V E V A L U E I N V C + . X S R O Q C 391 S A V E V A L U E BORDC+.XSROQC 3 9 2 S A V E V A L U E B A C K A + , X S R O Q C 3 9 3 S A V E V A L U E I N V A - , X S R O Q C 3 9 4 T E S T GE X S S T O C A , X S R O Q C 3 9 5 S A V E V A L U E S T O C A - , X S R O Q C 3 9 6 T R A N S F E R ,DR3 3 9 7 * 3 9 8 * MODEL SEGMENT 5 TH IRD R E G I O N A L C E N T R E 3 9 9 * 4 0 0 G E N E R A T E . . , , 2 . 2 3 401 L4 T E S T LE X $ I N V D . X S R O P D 4 0 2 QUEUE L I N E 4 4 0 3 T E S T E X S O R D R D , 0 . F I L D 4 0 4 T E S T GE X S S T O C A . X S R O Q D . P A R T D 4 0 5 S A V E V A L U E I N V A - . X S R O Q D 4 0 6 S A V E V A L U E DEMA+,XSROQD 4 0 7 S A V E V A L U E INVD+.XSROQD 4 0 8 S A V E V A L U E S T O C A - . X S R O Q D 91 L i s t i n g o f EOQ a t 12:49:21 o n SEP 17, 1985 f o r CC1d=NADH P a g e 4 0 9 DR4 A S S I G N 20.4 4 1 0 A S S I G N 2 1 , V S L T I M E 41 1 TEST G P21.0.DR4 412 ADV4 ADVANCE P21 4 1 3 DEPART L I N E 4 4 14 SAVEVALUE STOCD+,XSROOD 4 1 5 TRANSFER ,L4 41G PARTD TEST G XSSTOCA,0,WT4 417 SAVEVALUE BORDD+,VSBACKD 418 SAVEVALUE BACKA+,VSBACKD 4 1 9 TEST E XSNEXTD.O.LD 4 2 0 SAVEVALUE NEXTD.VSBACKD 421 SAVD SAVEVALUE OHAD.XSSTOCA 422 SAVEVALUE INVD+,XSOHAD 423 SAVEVALUE STOCA-,XSOHAD 424 SAVEVALUE INVA-.XSOHAD 425 SAVEVALUE ORDRD. 1 42G DR41 A S S I G N 20.4 427 A S S I G N 2 2 , V S L T I M E 428 TEST G P22.0.DR41 4 2 9 ADVANCE P22 4 3 0 DEPART L I N E d 431 SAVEVALUE STOCD+.XSOHAD 432 TRANSFER ,L4 4 3 3 LD SAVEVALUE HOLDD,VSBACKD 434 TRANSFER .SAVD 435 F I L D SAVEVALUE ORDRD,O 436 TEST GE XSSTOCA.XSNEXTD,WP4 437 SAVEVALUE INVD+.XSNEXTD 438 SAVEVALUE STOCA-,XSNEXTD 4 3 9 SAVEVALUE INVA-,XSNEXTD 4 4 0 DR42 A S S I G N 20.4 441 A S S I G N 2 3 , V S L T I M E 442 TEST G P23.0.DR42 443 AD4 ADVANCE P23 444 DEPART L I N E 4 445 SAVEVALUE ST0CD+.XSNEXTD 44 6 SAVEVALUE NEXTD.XSHOLDD 447 SAVEVALUE HOLDD.O 448 TRANSFER .L4 4 4 9 WP4 SAVEVALUE BORDD+,XSNEXTD 4 5 0 SAVEVALUE BACKA+;XSNEXTD 451 SAVEVALUE INVD+,XSNEXTD 452 SAVEVALUE INVA-,XSNEXTD 4 5 3 TEST GE XSSTOCA,XSNEXTD 454 SAVEVALUE STOCA-,XSNEXTD 4 5 5 TRANSFER ,DR42 45 6 WT4 SAVEVALUE INVD+,XSROOD 457 SAVEVALUE BORDD+,XSROOD 458 SAVEVALUE BACKA+,XSROOD 45 9 SAVEVALUE INVA-,XSROOD 4 6 0 TEST GE XSSTOCA.XSROOD 461 SAVEVALUE STOCA-.X$ROQD 462 TRANSFER ,DR4 463 464 * MODEL SEGMENT 6 FOURTH REGIONAL CENTRE 4 6 5 * 46 6 GENERATE ....2.23 92 \ L i s t i n g o f EOQ a t 12:49:21 o n SEP 17, 1985 f o r CCid=NADH P a g e 4 6 7 L5 TEST LE 4 6 8 QUEUE 4 6 9 TEST E 4 7 0 TEST GE 47 1 SAVEVALUE 472 SAVEVALUE 4 7 3 SAVEVALUE 474 SAVEVALUE 475 DR5 A S S I G N 476 A S S I G N 477 TEST G 478 ADV5 ADVANCE 479 DEPART 4 8 0 SAVEVALUE 481 TRANSFER 482 PARTE TEST G 4 8 3 SAVEVALUE 484 SAVEVALUE 485 TEST E 486 SAVEVALUE 487 SAVE SAVEVALUE 488 SAVEVALUE 489 SAVEVALUE 4 9 0 SAVEVALUE 491 SAVEVALUE 492 DR51 A S S I G N 4 9 3 A S S I G N 494 TEST G 495 ADVANCE 496 DEPART 497 SAVEVALUE 4 9 8 TRANSFER 499 LE SAVEVALUE 5 0 0 TRANSFER 501 F I L E SAVEVALUE 502 TEST GE 5 0 3 SAVEVALUE 504 SAVEVALUE 505 SAVEVALUE 506 DR52 A S S I G N 507 A S S I G N 5 0 8 TEST G 5 0 9 AD5 ADVANCE 5 1 0 DEPART 511 SAVEVALUE 512 SAVEVALUE 5 1 3 SAVEVALUE 514 TRANSFER 515 WP5 SAVEVALUE 516 SAVEVALUE 517 SAVEVALUE 5 1 8 SAVEVALUE 519 TEST GE 5 2 0 SAVEVALUE 52 1 TRANSFER 522 WT5 SAVEVALUE 5 2 3 SAVEVALUE 524 SAVEVALUE XSINVE,XSROPE L I N E 5 X $ O RDRE,0,FILE XSSTOCA,XSROQE.PARTE INVA-.XSROOE DEMA+.XSROOE INVE+,XSROOE STOCA-,XSROOE .20, 5 21 .VSLTIME P21 .0.DR5 P2 1 L I N E 5 STOCE+.XSROQE . L5 XSSTOCA,0.WT5 BORDE+,VSBACKE BACKA+,VSBACKE XSNEXTE.0.LE NEXTE,VSBACKE OHAE,XSSTOCA INVE+.XSOHAE STOCA-,XSOHAE INVA-,XSOHAE ORDRE . 1 20.5 22 . VSLTIME P22.0.DR51 P22 L I N E 5 STOCE+,XSOHAE , L5 HOLDE.VSBACKE . SAVE ORDRE.0 XSSTOCA,XSNEXTE,WP5 INVE+,XSNEXTE STOCA-,XSNEXTE INVA-,XSNEXTE 20. 5 2 3 , V S L T I M E P23.O.DR52 P23 L I N E 5 STOCE+,XSNEXTE NEXTE,XSHOLDE HOLDE,O . L5 BORDE+,XSNEXTE BACKA+,XSNEXTE INVE+,XSNEXTE INVA-,XSNEXTE XSSTOCA,XSNEXTE STOCA-,XSNEXTE , DR52 INVE+,XSROQE BORDE+,XSROQE BACKA+.XSROQE 93 L i s t i n g o f EOQ a t 12:49:21 o n SEP 17. 1985 f o r CCid=NADH P a g e 525 SAVEVALUE INVA-.XSROQE 5 2 6 TEST GE XSSTOCA,XSROQE 527 SAVEVALUE STOCA-,XSROQE 528 TRANSFER ,DR5 - 529 5 3 0 * MODEL SEGMENT 7 F I F T H REGIONAL CENTRE 531 532 GENERATE ,.,.2,23 5 3 3 L6 TEST LE . XSINVF.XSROPF 534 QUEUE L I N E 6 5 3 5 TEST E XSORDR F . 0 . F I L F 536 TEST GE XSSTOCA,XSROQF.PARTF 537 SAVEVALUE INVA-,XSROQF 538 SAVEVALUE DEMA+,XSROQF 539 SAVEVALUE INVF+,XSROQF 5 4 0 SAVEVALUE STOCA-,XSROQF 541 DR6 A S S I G N 20.6 542 A S S I G N 2 1 . V S L T I M E 5 4 3 TEST G P21.0.DR6 544 ADV6 ADVANCE P21 545 DEPART L I N E 6 546 SAVEVALUE STOCF+,XSROQF 547 TRANSFER ,L6 548 PARTF TEST G X$STOCA.0.WT6 549 SAVEVALUE BORDF+,VSBACKF 5 5 0 SAVEVALUE BACKA+.VSBACKF 551 TEST E XSNEXTF.O.LF 552 SAVEVALUE NEXTF,VSBACKF 5 5 3 SAVF SAVEVALUE OHAF.XSSTOCA 554 SAVEVALUE INVF+.XSOHAF 555 SAVEVALUE STOCA-,XSOHAF 556 SAVEVALUE INVA-,XSOHAF 557 SAVEVALUE 0RDRF.1 558 DR61 A S S I G N 20.S 559 A S S I G N 2 2 , V S L T I M E 5 6 0 TEST G P22.0.DR61 56 1 ADVANCE P22 562 DEPART L I N E 6 5 6 3 SAVEVALUE ST0CF+,XSOHAF 564 TRANSFER ,L6 565 LF SAVEVALUE HOLDF.VSBACKF 566 TRANSFER ,SAVF 567 F I L F SAVEVALUE ORDRF,0 568 TEST GE XSSTOCA,XSNEXTF,WP6 569 SAVEVALUE INVF+,XSNEXTF 5 7 0 SAVEVALUE STOCA-,XSNEXTF 571 SAVEVALUE INVA-,XSNEXTF 572 DR62 A S S I G N 20.6 5 7 3 A S S I G N 2 3 , V S L T I M E 574 TEST G P23.0.DR62 5 7 5 AD6 ADVANCE P23 576 DEPART L I N E 6 577 SAVEVALUE STOCF+,XSNEXTF 578 SAVEVALUE NEXTF.XSHOLDF 5 7 9 SAVEVALUE HOLDF.O 5 8 0 TRANSFER .L6 581 WP6 SAVEVALUE BORDF+,XSNEXTF 582 SAVEVALUE BACKA+,XSNEXTF 94 L i s t i n g o f E00 a t 12:49:21 o n SEP 17, 1985 f o r CCid=NADH P a g e 5 8 3 SAVEVALUE INVF+.XSNEXTF 584 SAVEVALUE INVA-,XSNEXTF 585 TEST GE X$STOCA.X$NEXTF 586 SAVEVALUE STOCA-,X$NEXTF 587 TRANSFER .DR62 588 WT6 SAVEVALUE INVF+,XSROQF 5 8 9 SAVEVALUE BORDF+,XSROQF 5 9 0 SAVEVALUE BACKA+.XSROQF 591 SAVEVALUE • INVA-,XSROQF 592 TEST GE XSSTOCA.XSROQF 5 9 3 SAVEVALUE STOCA-,XSROQF 594 TRANSFER . DR6 595 596 MODEL SEGMENT 8 597 * 598 GENERATE ,,..2.23 599 L7 TEST LE XSINVG.XSROPG 6 0 0 ' QUEUE L I N E 7 601 TEST E XSORDRG.O.FILG 6 0 2 TEST GE XSSTOCA,XSROQG.PARTG 6 0 3 SAVEVALUE INVA-.XSROQG 604 SAVEVALUE DEMA*,XSROQG 6 0 5 SAVEVALUE INVG+,XSROQG 606 SAVEVALUE STOCA-,XSROQG 607 DR7 A S S I G N 20, 7 608 A S S I G N 2 1 , V S L T I M E 6 0 9 TEST G P2 1.0.DR7 6 1 0 ADV7 ADVANCE P2 1 61 1 DEPART L I N E 7 612 SAVEVALUE STOCG*,XSROOG 613 TRANSFER . L7 6 14 PARTG TEST G XSSTOCA.0.WT7 6 1 5 SAVEVALUE BORDG+.VSBACKG 616 SAVEVALUE BACKA-t- , VSBACKG 617 TEST E XSNEXTG,0,LG 6 1 8 SAVEVALUE NEXTG,VSBACKG 6 1 9 SAVG SAVEVALUE OHAG.XSSTOCA 6 2 0 SAVEVALUE INVG+,XSOHAG 62 1 SAVEVALUE STOCA-.XSOHAG 6 2 2 SAVEVALUE INVA-,XSOHAG 6 2 3 SAVEVALUE ORDRG, 1 624 DR7 1 A S S I G N 20. 7 6 2 5 A S S I G N 2 2 , V S L T I M E 6 2 6 TEST G P22.0.DR71 6 2 7 ADVANCE P22 6 2 8 DEPART L I N E 7 6 2 9 SAVEVALUE STOCG+.XSOHAG 6 3 0 TRANSFER . L7 631 LG SAVEVALUE HOLDG.VSBACKG 6 3 2 TRANSFER . SAVG 6 3 3 F I L G SAVEVALUE ORDRG,0 634 TEST GE XSSTOCA.XSNEXTG,WP7 6 3 5 SAVEVALUE INVG+,XSNEXTG 6 3 6 SAVEVALUE STOCA-,XSNEXTG 637 SAVEVALUE INVA-.XSNEXTG 6 3 8 DR72 A S S I G N 20.7 6 3 9 A S S I G N 2 3 , V S L T I M E 6 4 0 TEST G P23.0.DR72 S I X T H REGIONAL CENTRE 95 L i s t i n g o f EOQ a t 12:49:21 o n SEP 17, 1985 f o r CCid=NADH P a g e 64 1 AD7 ADVANCE P23 6 4 2 DEPART L I N E 7 6 4 3 SAVEVALUE STOCG+.XSNEXTG 644 SAVEVALUE NEXTG,XSHOLDG 6 4 5 SAVEVALUE HOLDG,0 64 6 TRANSFER . L7 6 4 7 WP7 SAVEVALUE BORDG+,XSNEXTG 64 8 SAVEVALUE BACKA+,XSNEXTG 6 4 9 SAVEVALUE INVG+,XSNEXTG 6 5 0 SAVEVALUE INVA-,XSNEXTG 651 TEST GE XSSTOCA.XSNEXTG 6 5 2 SAVEVALUE STOCA-.XSNEXTG 6 5 3 TRANSFER .DR72 654 WT7 SAVEVALUE INVG+,XSROQG 6 5 5 SAVEVALUE BORDG+.XSROQG 6 5 6 SAVEVALUE BACKA+,XSROQG 657 SAVEVALUE INVA-,XSROQG 6 5 8 TEST GE XSSTOCA.XSROQG 6 5 9 SAVEVALUE STOCA-,XSROQG 6 6 0 TRANSFER ,DR7 66 1 * 662 * MODEL SEGMENT 9 : 6 6 3 * 664 GENERATE . , , , 2.23 6 6 5 L8 TEST LE XSINVH.XSROPH 6 6 6 QUEUE L I N E 8 667 TEST E XSORDRH.O,FILH 668 TEST GE XSSTOCA,XSROQH,PARTH 6 6 9 SAVEVALUE INVA-.XSROQH 6 7 0 SAVEVALUE DEMA+.XSROQH 671 SAVEVALUE INVH+.XSROQH 672 SAVEVALUE STOCA-.XSROQH 6 7 3 DR8 A S S I G N 20. 8 674 A S S I G N 21 .VSLTIME 6 7 5 TEST G P21.0.DR8 6 7 6 ADV8 ADVANCE P2 1 677 DEPART L I N E 8 6 7 8 SAVEVALUE STOCH+.XSROQH 6 7 9 TRANSFER . L8 6 8 0 PARTH TEST G XSSTOCA,0.WT8 681 SAVEVALUE BORDH+,VSBACKH 6 8 2 SAVEVALUE BACKA+,VSBACKH 6 8 3 TEST E XSNEXTH,0,LH 684 SAVEVALUE NEXTH.VSBACKH 6 8 5 SAVH SAVEVALUE OHAH,XSSTOCA 6 8 6 SAVEVALUE INVH+,X$OHAH 68 7 SAVEVALUE STOCA-,XSOHAH 68 8 SAVEVALUE INVA-.XSOHAH 6 8 9 SAVEVALUE 0RDRH.1 6 9 0 DR81 A S S I G N 2 0 , 8 691 A S S I G N 2 2 . V S L T I M E 6 9 2 TEST G P22.0.DR81 6 9 3 ADVANCE P22 694 DEPART L I N E 8 6 9 5 SAVEVALUE STOCH+,XSOHAH 6 9 6 TRANSFER , L8 697 LH SAVEVALUE HOLDH,VSBACKH 69 8 TRANSFER , SAVH SEVENTH REGIONAL CENTRE 96 L i s t i n g o f EOQ a t 1 2 : 4 9 : 2 1 o n SEP 17 . 1985 f o r C C i d = N A D H P a g e 6 9 9 7 0 0 701 7 0 2 7 0 3 7 0 4 7 0 5 7 0 6 7 0 7 7 0 8 7 0 9 7 10 7 1 1 7 12 7 1 3 7 14 7 15 7 1 6 7 17 7 1 8 7 19 7 2 0 72 1 7 2 2 7 2 3 7 2 4 7 2 5 7 2 6 7 2 7 7 2 8 7 2 9 7 3 0 731 7 3 2 7 3 3 7 3 4 7 3 5 7 3 6 7 3 7 7 3 8 7 3 9 7 4 0 74 1 7 4 2 7 4 3 7 4 4 7 4 5 7 4 6 7 4 7 7 4 8 7 4 9 7 5 0 751 7 5 2 7 5 3 7 5 4 7 5 5 7 5 6 F I L H DR82 AD8 WP8 WT8 S A V E V A L U E T E S T GE S A V E V A L U E S A V E V A L U E S A V E V A L U E A S S I G N A S S I G N T E S T G ADVANCE D E P A R T S A V E V A L U E S A V E V A L U E S A V E V A L U E T R A N S F E R S A V E V A L U E S A V E V A L U E S A V E V A L U E S A V E V A L U E T E S T GE S A V E V A L U E T R A N S F E R S A V E V A L U E S A V E V A L U E S A V E V A L U E S A V E V A L U E T E S T GE S A V E V A L U E T R A N S F E R ORDRH.O X S S T O C A , X S N E X T H , W P 8 I N V H + . X S N E X T H S T O C A - . X S N E X T H I N V A - , X S N E X T H 2 0 , 8 2 3 , V S L T I M E P 2 3 . 0 . D R 8 2 P 2 3 L I N E 8 S T O C H + . X S N E X T H N E X T H . X S H O L D H H O L D H . O . L8 ESORDH+ . X S N E X T H B A C K A + , X S N E X T H I N V H + . X S N E X T H I N V A - , X S N E X T H X S S T O C A . X S N E X T H S T O C A - , X S N E X T H ,DR82 INVH+.XSROQH B O R D H * . X S R O Q H B A C K A + , X S R O Q H I N V A - . X S R O Q H X S S T O C A . X S R O Q H S T O C A - . X S R O Q H . DR8 MODEL SEGMENT 10 E I G H T H REG IONAL CENTRE G E N E R A T E L9 T E S T LE QUEUE T E S T E T E S T GE S A V E V A L U E S A V E V A L U E S A V E V A L U E S A V E V A L U E DR9 A S S I G N A S S I G N T E S T G ADV9 ADVANCE D E P A R T S A V E V A L U E T R A N S F E R PART I T E S T G S A V E V A L U E S A V E V A L U E T E S T E S A V E V A L U E SAV I S A V E V A L U E S A V E V A L U E S A V E V A L U E S A V E V A L U E S A V E V A L U E DR91 A S S I G N , . . . 2 , 2 3 X S I N V I . X S R O P I L I N E 9 X S O R D R I , 0 , F I L I X S S T O C A , X S R O Q I . P A R T I I N V A - , X S R O Q I DEMA+.XSROQ I I N V I + , X S R O Q I S T O C A - , X S R O Q I 2 0 , 9 21 . V S L T I M E P 2 1 . 0 . D R 9 P2 1 L I N E 9 S T O C I + . X S R O Q I . L 9 X S S T O C A , 0 . W T 9 B O R D I + , V S B A C K I B A C K A + . V S B A C K I X S N E X T I , 0 , L I N E X T I , V S B A C K I O H A I , X S S T O C A I N V I + . X S O H A I S T O C A - . X S O H A I I N V A - . X S O H A I ORDRI . 1 2 0 . 9 97 L i s t i n g o f E 0 0 a t 1 2 : 4 9 : 2 1 o n SEP 1 7 , 1985 f o r C C i d = N A D H P a g e 7 5 7 A S S I G N 2 2 , V S L T I M E 7 5 8 T E S T G P 2 2 . 0 . D R 9 1 7 5 9 ADVANCE P22 7 6 0 D E P A R T L I N E 9 761 S A V E V A L U E S T O C I + , X S O H A I 7 6 2 T R A N S F E R , L 9 7 6 3 L I S A V E V A L U E H O L D I , V S B A C K I 7 6 4 T R A N S F E R . SAV I 7 6 5 F I L I S A V E V A L U E O R D R I . O 7 6 6 T E S T GE X S S T O C A , X S N E X T I . W P 9 7 6 7 S A V E V A L U E I N V I + , X S N E X T I 7 6 8 S A V E V A L U E S T O C A - , X S N E X T I 7 6 9 S A V E V A L U E I N V A - , X S N E X T I 7 7 0 DR92 A S S I G N 2 0 , 9 771 A S S I G N 2 3 , V S L T I M E 7 7 2 T E S T G P 2 3 . 0 . D R 9 2 7 7 3 AD9 ADVANCE P 2 3 7 7 4 D E P A R T L I N E 9 7 7 5 S A V E V A L U E S T O C I + , X S N E X T I 7 7 6 S A V E V A L U E NEXT I . X S H O L D I 7 7 7 S A V E V A L U E H O L D I . O 7 7 8 T R A N S F E R . L 9 7 7 9 WP9 S A V E V A L U E B O R D I + , X S N E X T I 7 8 0 S A V E V A L U E B A C K A + , X S N E X T I 781 S A V E V A L U E I N V I + . X S N E X T I 7 8 2 S A V E V A L U E I N V A - , X S N E X T I 7 8 3 T E S T GE X $ S T O C A . X S N E X T I 7 8 4 S A V E V A L U E S T O C A - , X S N E X T I 7 8 5 T R A N S F E R ,DR92 7 8 6 WT9 S A V E V A L U E I N V I + . X S R O O I 7 8 7 S A V E V A L U E BORDI * . X S R O O I 7 8 8 S A V E V A L U E B A C K A + , X S R O Q I 7 8 9 S A V E V A L U E I N V A - , X $ R O O I 7 9 0 T E S T GE X S S T O C A , X S R O Q I 791 S A V E V A L U E S T O C A - , X S R O Q I 7 9 2 T R A N S F E R .DR9 7 9 3 7 9 4 * MODEL SEGMENT 11 7 9 5 7 9 6 G E N E R A T E 1 RUN FOR 1 DAY 7 9 7 T E R M I N A T E 1 C O L L E C T DATA E A C H DAY 7 9 8 * CONTROL CARDS 7 9 9 S T A R T 160 I N I T I A L I Z A T I O N PER IOD 8 0 0 R E S E T 801 S T A R T 2 6 0 RUN FOR ONE YEAR 8 0 2 END 

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