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The development of a manpower planning model McCrea, James Lewis 1968

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THE DEVELOPMENT OP A MANPOWER PLANNING MODEL by JAMES LEWIS McCREA BSc, Queen's University, 1962 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF BUSINESS ADMINISTRATION In the Department of Commerce and Business Administration We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June, 1968 In p r e sen t ing t h i s t h e s i s in p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the 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 for reference and Study. I fu r the r agree that permiss ion for ex t ens ive copying of t h i s t he s i s for s c h o l a r l y purposes may be granted by the Head of my Department or by h.iis r e p r e s e n t a t i v e s . It i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s for f i n a n c i a l gain s h a l l not be a l lowed wi thout my w r i t t e n p e r m i s s i o n . Department of Commerce and Business 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 of B r i t i s h Columbia Vancouver 8, Canada ° a t e J u l y , 11 , 1 969 i i ABSTRACT In r e c e n t years a number of personnel p l a n n i n g t e c h -niques and manpower models have-been developed to improve l o n g range p l a n n i n g i n the personnel f i e l d . A review of the l i t e r a t u r e on manpower p l a n n i n g r e v e a l e d that models had been developed to c o n s i d e r q u i t e s p e c i f i c problems and that the q u a n t i t a t i v e techniques had co n s i d e r e d only a very simple manpower s t r u c t u r e . The s i m p l i c i t y of the e x i s t i n g models, together w i t h the w i d e l y v a r y i n g assumptions upon which the models were based, i n d i c a t e d that the f a c t o r s to be i n c l u d e d i n a gen e r a l manpower p l a n n i n g model r e q u i r e d i n v e s t i g a t i o n . The i n v e s t i g a t i o n demonstrated t h a t one of the major weaknesses of the e x i s t i n g models was t h e i r f a i l u r e to i n c l u d e p r o v i s i o n f o r promoting employees through a h i e r a r c h i c a l s t r u c t u r e . The d e c i s i o n was made to c o n s t r u c t a f o r e c a s t i n g model which i n c l u d e d t h i s f e a t u r e together w i t h the other f a c t o r s r e q u i r e d to f o r e c a s t l a b o u r requirements f o r produc-t i o n workers and n o n r p r o f e s s i o n a l s t a f f p o s i t i o n s . A model was c o n s t r u c t e d to r e f l e c t these f a c t o r s and a computer programme w r i t t e n f o r the model. I n i t i a l i n v e s t -i g a t i o n s with the model i n d i c a t e d t h a t promotions i n c r e a s e d e x p o n e n t i a l l y as turnover i n c r e a s e d , and t h a t the t i m i n g of h i r i n g d e c i s i o n s depended upon the t r a i n i n g times i n the o r g a n i z a t i o n a l s t r u c t u r e . The c o n c l u s i o n of t h i s i n v e s t i g a t i o n was that the h i e r a r c h i c a l s t r u c t u r e would be r e q u i r e d i n a g e n e r a l model. The e x i s t i n g models may be u n d e r e s t i m a t i n g the time l a g s and t r a i n i n g c o s t s by f a l l i n g to c o n s i d e r promotions. The study concluded w i t h an a n a l y s i s of the problems that would be encountered i n c o n s t r u c t i n g a more complex model and i n adding c o s t - o p t i m i z i n g f e a t u r e s to i t . TABLE OF CONTENTS CHAPTER PAGE I. INTRODUCTION 1 The Problem 1 Statement of the problem 1 Importance of the study 1 L i m i t a t i o n s of the study 2 Chapter O u t l i n e and D e f i n i t i o n of Terms 3 Chapter o u t l i n e 3 D e f i n i t i o n s of terms 3 A Review of E x i s t i n g Models 4 G o t t e r e r ' s model 5 F o r r e s t e r ' s model 8 Nemhauser's model 8 Aggregate p r o d u c t i o n models 9 T h e o r e t i c a l models 10 I I . CONSIDERATIONS IN A GENERAL MANPOWER MODEL 12 Determination of Work Force L e v e l s 12 Labour f o r c e r e q u i r e d 12 S i z e of labour f o r c e 13 Job c a t e g o r i e s 14 Absenteeism 14 Regular labour f o r c e 15 V CHAPTER PAGE Entering the Work Force 15 Labour pool 15 Hiring 18 Training 20 Types of training 20 Determination of training time 23 Measuring training time 27 Promotions 29 Leaving the Work Force 31 Effects of terminations 31 Determinants of turnover 33 Theoretical Indicators 33 Turnover as a function of employment stability 35 Turnover as a function of length of service 36 Discharges 39 Lay-offs . 40 Conclusions 42 Basic requirements of a general model 42 Specific models 42 III. DEVELOPMENT OF THE MODEL 46 Assumptions 46 General assumptions 46 Simplifying assumptions 47 v i CHAPTER PAGE S p e c i f i c assumptions 48 B a s i s f o r promotion 48 Promotion c o n s t r a i n t 49 Quit r a t e f o r t r a i n e e s 50 H i r i n g 50 T r a i n i n g time 51 Demotions and l a y - o f f s 52 T r a i n i n g time l i m i t a t i o n 53 C a l c u l a t i o n procedure 53 H i r i n g c o n s t r a i n t 53 Nomenclature 54 B u i l d i n g the Model 55 General p e r s p e c t i v e 55 B a s i c equations 57 Sample c a l c u l a t i o n 58 The g e n e r a l model 62 Summary 70 IV. OPERATION OF THE MODEL 71 Sample C a l c u l a t i o n s 71 E f f e c t o f Parameters on the Model 76 E f f e c t of q u i t r a t e 76 Input data 76 Output data and a n a l y s i s 77 E f f e c t o f t r a i n i n g time 82 Input data 82 v i i CHAPTER PAGE Output data and a n a l y s i s 82 Conc l u s i o n s 87 V. AREAS FOR FUTURE DEVELOPMENT 88 Development of the E x i s t i n g Model 88 Quit r a t e 89 H i r i n g 89 Promotions 90 T r a i n i n g delay 90 Labour requirement 90 Demotions and l a y - o f f s 91 P r o d u c t i v i t y and la b o u r requirements 93 A C o s t - o r i e n t e d Model 94 Cost o p t i m i z a t i o n 95 Cost equations 96 Aggregate P r o d u c t i o n P l a n n i n g 99 S i m u l a t i o n 99 A n a l y t i c a l techniques 100 L i m i t a t i o n s 100 A l g o r i t h m i c techniques 101 H e u r i s t i c techniques 103 Comparison of techniques 105 VI. CONCLUSIONS 107 BIBLIOGRAPHY 111 APPENDIX 114 LIST OP TABLES TABLE PAGE I . Sample C a l c u l a t i o n Output Data 73 LIST OF FIGURES FIGURE PAGE 1-1 P r o d u c t i o n - D i s t r i b u t i o n System 6 1 - 2 P e r s o n n e l System 7 1 1 - 1 , 1 1 - 2 T y p i c a l L e a r n i n g Curves 2 5 I I - 3 A l t e r n a t i v e Types o f Models 44 I I I - l T i m i n g of D e c i s i o n s 5& I I I - 2 T y p i c a l D e c i s i o n Node 57 I I I - 3 Sample C a l c u l a t i o n 6l I I I - 4 Sample C a l c u l a t i o n f o r Two Time P e r i o d s 6 3 I I I - 5 M o d i f i e d Flow C h a r t i n g Technique 64 IV-1 Q u i t Rate F u n c t i o n s 7 8 I V - 2 E f f e c t o f Q u i t Rate on P romotions 79 IV-3 E f f e c t o f Q u i t Rate on Number H i r e d 80 IV-4 E f f e c t o f Q u i t Rate on Q u i t s 81 IV-5 E f f e c t o f Q u i t Rate 83 IV-6 E f f e c t o f T r a i n i n g D e l a y s on Number H i r e d 84 IV-7 E f f e c t o f T r a i n i n g D elay on Q u i t s 85 IV-8 E f f e c t o f T r a i n i n g D elay on P romotions 86 V - l E f f e c t o f A l t e r n a t i v e P r o m o t i o n P a t t e r n s on the R e g u l a r Work F o r c e 9 2 i x ACKNOWLEDGMENT The w r i t e r wishes to acknowledge the a s s i s t a n c e of Dr. J . S w i r l e s and Dr. J . Montague and p a r t i c u l a r l y Dr. L. P. Moore without whose guidance and a s s i s t a n c e t h i s t h e s i s would not have been p o s s i b l e . S p e c i a l thanks are a l s o due to Dr. B. Schwab f o r h i s guidance i n de v e l o p i n g the model. CHAPTER I INTRODUCTION The increasing organizational complexity of society has l e d to the development of decision-making procedures and techniques i n a number of areas. For many years, while progress was being made i n other f i e l d s , manpower u t i l i z a t i o n decisions were based on bar charts and other simple graphical techniques. Recently, a number of investigators have r e a l -ized the poten t i a l for new developments i n this f i e l d . This has led to the development of methods for making manpower planning decisions under ce r t a i n , well s p e c i f i e d , conditions. I. THE PROBLEM Statement of the Problem. The purpose of t h i s study was to (1) Investigate the factors to be considered i n a general manpower planning model, (2) construct a general model which could be used for manpower planning by a number of organizations, (3) investigate the effects of c e r t a i n parameters on the manpower system. Importance of the Study. As corporations grow In size and d i v e r s i t y of operations and try to cope with new markets and rapid technological change, sophisticated long range plans become increasingly important. Governments must plan, b u i l d and maintain complex administrative services i n a large 2 number of fi e l d s . Because of the overriding importance of personnel, manpower planning is an important component of any aggregate planning system. Manpower planning is also becoming important as a f i e l d by i t s e l f . The increasing complexity of many Industrial operations has led to the need for a fu l l y trained work force at a l l times. The increasing rate of technological change and the specialization required for many jobs has made i t d i f f i c u l t to hire personnel with the requisite s k i l l s and has placed greater demands on industrial training. The undesirable location of some operations has led to a continuing shortage of skilled personnel in certain industries. Thus, whether manpower planning is to be considered as part of an aggregate plan or as a separate entity, i t is extremely important to both corporate and governmental organizations. Limitations of the Study. Manpower planning has been defined to include a specification of the kinds and numbers of men required to accomplish the organization's objectives; a forecast, from current personnel inventories, of how well the future needs can be met; and, by comparing needs to supply, the formulation of plans for recruiting, assigning and developing personnel.-'- This study was limited to the forecasting aspects of manpower planning. The specification lw.R. D i l l , D.P. Gaver and W.L. Weber, "Models and Modelling for Manpower Planning," Management Science. XIII, No. 4, (December, 1966), pp. 142. 3 of h i r i n g requirements, the h i r i n g process and t r a i n i n g were not i n v e s t i g a t e d except as they r e l a t e to the f o r e -c a s t i n g procedure. Because the study was l i m i t e d to the f o r e c a s t i n g aspects of p l a n n i n g , i n d i v i d u a l c h a r a c t e r i s t i c s of the workers were n e g l e c t e d . The worker was c o n s i d e r e d s t r i c t l y as a member of a group e x h i b i t i n g c e r t a i n c h a r a c t e r i s t i c s r e l a t e d to t h e i r employment. I I . CHAPTER OUTLINE AND DEFINITION OF TERMS Chapter O u t l i n e The remainder of t h i s chapter i s devoted to the d e f i n i t i o n of s p e c i a l terms used In the study and to a review of e x i s t i n g manpower models. Chapter I I c o n t a i n s a d e t a i l e d d i s c u s s i o n of the f a c t o r s to be c o n s i d e r e d i n b u i l d i n g a g e n e r a l manpower p l a n n i n g model. A s i m u l a t i o n model, which would be a p p l i c a b l e to c e r t a i n non-managerial employees, i s developed i n Chapter I I I . Chapter IV c o n t a i n s a few b r i e f examples of the model's d e c i s i o n s together with a d i s c u s s i o n of the e f f e c t s of s e v e r a l major parameters. The study concludes w i t h a comparison of the g e n e r a l model to other types and a d i s c u s s i o n of the f u t u r e developments i n the use of manpower p l a n n i n g models. D e f i n i t i o n s of Terms Job Category. A group of tasks f o r which t r a i n i n g i s r e q u i r e d . The job i n the o r g a n i z a t i o n must be grouped 4 a c c o r d i n g to the t r a i n i n g r e q u i r e d and the p o s i t i o n of the job i n the o r g a n i z a t i o n ' s h i e r a r c h i c a l s t r u c t u r e . Labour Force Required. The "labour f o r c e r e q u i r e d " i s the number of personnel d e s i r e d f o r each job category i n each f u t u r e d e c i s i o n p e r i o d . Regular Labour Force. The " r e g u l a r l a b o u r f o r c e " i s the number of f u l l y t r a i n e d employees a v a i l a b l e f o r work at the present time. T r a i n i n g Delay. The " t r a i n i n g d e l a y " i s d e f i n e d as the time l a p s e between when the d e c i s i o n i s made to h i r e o r promote a worker and when the worker j o i n s the r e g u l a r work f o r c e . I t i n c l u d e s both the time l a g i n h i r i n g and the t r a i n i n g time. Labour P o o l . The "labour p o o l " i s the maximum number of employees t h a t may be h i r e d i n a d e c i s i o n p e r i o d . Labour Turnover. For the purposes of t h i s study "labour turnover" c o n s i d e r s o n l y the employees who ' v o l u n t a r i l y terminate t h e i r employment. The "turnover r a t e " i s a c t u a l l y the q u i t r a t e and does not i n c l u d e personnel who are d i s c h a r g e d or l a i d o f f . I I I . A REVIEW OF EXISTING MODELS A number of manpower p l a n n i n g models have been c o n s t r u c t e d and r e p o r t e d i n the l i t e r a t u r e . In most i n s t a n c e s these models have been developed to d e a l w i t h s p e c i f i c and r a t h e r l i m i t e d s i t u a t i o n s . S e v e r a l of the more d e t a i l e d 5 models are discussed below, together with a brief outline of other models which have considered the manpower function. Gotterer's Model One of the more general models was built by Gotterer to consider the effects of delays in labour force changes. The model was a computer simulation of a company producing a standardized product and consisted of a simple production-distribution system (Figure I - l ) together with a personnel 2 system (Figure 1-2). Although a detailed description of the model was not available i t was apparent that the following assumptions were made: 1. The quit rate was a function of the lay-off rate. 2. A l l employees were engaged in the same type of work, i.e., there was no hierarchical structure for production workers. 3. Delays occurred in recruiting, hiring and laying-off of personnel. 4. A number of assumptions were made regarding the productivity of employees during the training and termination periods. Malcolm H. Gotterer, A Study of the Effects of Delays  in Changes in a Work Force, in Symposium on Simulation  Models: Methodology and Applications to the Behavioral  Sciences. Austin C. Hoggatt and Frederick E. BalderSton, editors, (Cincinnati, Ohio: South-Western Publishing Co., 19^3), pp. 192 - 202. Merchandise Retail Merchandise Orders Wholesale Factory Orders Figure I - l Production-Distribution System ON Voluntary Turnover Labor Pool I Terminated Employees Employees in Training Hiring Decision Firing Decision Labor Change Required Production Schedule Labor Force Required Regular Work Force V V Actual Labor Force Figure 1-2 Personnel System -o 8 Forrester's Model Forrester has developed a manpower planning model as a component of an aggregate planning system.-^ The model was strongly oriented towards the problem of adjusting the work force to meet production and inventory requirements. Forrester assumed that the work force was employed on one type of work and included provision for hiring, training and laying-off personnel. Because the model was to represent a one job category situation there was no provision for promot-ing the worker or for providing the worker with additional training.after he entered the work force. A major limitation of the model was that i t assumed that employees only l e f t the work force when they were la i d off. The possibility of a worker quitting was not considered. Nemhauser's Model The problem of hiring, training and scheduling telephone operators led to the development of a manpower model for this purpose.^ Although this was a rather specific case, the assumptions provided some guidelines towards developing a general model. The major assumptions were as follows: 1. A l l employees were engaged in the same type of work. 3 j a y W. Forrester, Industrial Dynamics. (Cambridge, Massachusetts: M.I.T. Press, 1 9 6 1 ) , pp. 208 - 2 5 1 . ^George L. Nemhauser and Henry L.W. Nuttie, "A Quantitative Approach to Employemtn Planning," Management Science, XI, No. 8 , (June, 1 9 6 5 ) , PP- 155 - 1 6 5 / 9 2. The r e s i g n a t i o n r a t e was a f u n c t i o n o f the l e n g t h o f s e r v i c e . 3. New employees were t r a i n e d by o t h e r employees who had t o be r e l i e v e d from t h e i r u s u a l d u t i e s . 4. H i r e s and l o s s e s d u r i n g the month o c c u r r e d a t a c o n s t a n t r a t e . 5 . The l e a g t h o f the t r a i n i n g p e r i o d and t h e number o f i n s t r u c t o r s p e r s t u d e n t was c o n s t a n t . A l t h o u g h n o t s p e c i f i c a l l y s t a t e d , Nemhauser seemed t o n e g l e c t the e f f e c t o f h i r i n g d e l a y s , the p o s s i b i l i t y o f the worker b e i n g l a i d o f f , and the p r o d u c t i v i t y o f the t r a i n e e s . D e s p i t e these l i m i t a t i o n s the s t u d y was g e n e r a l l y i n d i c a t i v e o f the problems and the f a c t o r s t h a t must be c o n s i d e r e d i n a g e n e r a l model. Aggregate P r o d u c t i o n Models A number of t e c h n i q u e s have been d e v e l o p e d i n r e c e n t y e a r s t o cope w i t h the problems o f aggregate p r o d u c t i o n p l a n n i n g ^ ( i . e . , p r o d u c t i o n - i n v e n t o r y - w o r k f o r c e s y s t e m s ) . Because the w r i t e r s were m a i n l y concerned w i t h t h e d e v e l o p -ment o f the t e c h n i q u e , r a t h e r t h a n i t s a p p l i c a t i o n , t h e i r t r e a t m e n t o f the manpower p l a n n i n g a s p e c t s has been r a t h e r cursory.. A l l the t e c h n i q u e s assumed a homogeneous work f o r c e , n e g l e c t e d the time l a g s i n the d e c i s i o n s and n e g l e c t e d -'For example, L i n e a r D e c i s i o n R u l e s , L i n e a r Programming and P a r a m e t r i c P r o d u c t i o n P l a n n i n g . The a p p l i c a t i o n o f the t e c h n i q u e s t o manpower p l a n n i n g a r e d i s c u s s e d i n Chapter V. the probability of a worker quitting. Consequently, they would be of l i t t l e use to manpower planning in their present form. Theoretical Models In addition to the empirical models mentioned above, considerable research has been done with mathematical models of the personnel function. D i l l reported that models based on Markov chains can be reasonably accurate. In the same report, D i l l and his co-workers developed a number of mathe-matical models to consider r i g i d and flexible hierarchical structures, promotion by seniority, promotion by a b i l i t y and so on. In a l l instances the probability of quitting was assumed to be an exponential function of the length of service in a particular position. Despite the conceptual validity of these models there would be a number of d i f f i c u l t i e s In applying them to practical situations. Time delays, the effect of trainees on productivity, and lay-offs are not considered. Until models are developed to treat a number of factors which are important in short-term planning their applicability is restricted to the investigation of theoretical' relationships and to long range studies of large groups such as military personnel. Conclusions. The empirical models developed to date were constructed D i l l , Gaver and Weber, op.cit.. pp. 144. 11 to consider specific problems. The overriding question was whether one or more of these models could be applied to general manpower planning situations. The main limitation of the existing models is that they consider the work force to be a homogenous group of workers employed in the same task. This is ih:marked contrast to the organizational structure of many organizations. In most cases workers are employed in a number of tasks which require different training and experience. It is also common practice for there to be opportunities for employees to advance to more senior positions in the organization. In order to r e a l i s t i c a l l y represent this in a model, provision must be made to promote and train employees as the more senior employees quit. The investigation of the existing models also demon-strated that widely varying assumptions have been made with regard to turnover and training. While these assumptions were presumably valid for the particular situation, they provide l i t t l e information on the cr i t e r i a and assumptions required in a general model. CHAPTER II CONSIDERATIONS IN A GENERAL MANPOWER MODEL The purpose of this chapter is to investigate the factors that should be considered in developing a manpower planning model. Throughout the discussion of these factors, the basic c r i t e r i a are that ( 1 ) the resulting model must be a r e a l i s t i c simulation of actual events and (2) the. infor-mation required must be readily obtainable by the organlization. Aspects of the model that are relatively straightforewar.d or dependent upon management policy are discussed brie f l y . The complex aspects of the model are discussed more thoroughly, particularly with regard to the measurement of these factors' by the organization. The remainder of the chapter has been sub-divided into three major sections. The f i r s t considers the factors i n -volved in determining work force levels. The second considers the aspects of bringing an employee into the work force and the third, the factors which cause him to leave i t . I. DETERMINATION OP WORK FORCE LEVELS Labour Force Required The f i r s t requirement for a manpower planning model is information regarding the labour force requirements for future time periods. This information is the only variable 13 which is entirely exogenous to the manpower system and can be thought of as the basic input to the system. If the man-power model is a sub-system within a larger system of the firm, the information is generated by the production-inventory sales sub-systems and fed into the manpower model. If, as in the present case, the manpower model is a separate entity unrelated to a larger system, the labour force requirement Is a true exogenous variable. It may be related to future production requirements i f the objective is to analyze the effect of the variable on production and costs under certain conditions. Alternatively, i f the objective is to study the effect of changes in the labour force under varying conditions or policies, specification of the pattern and size of the changes in the labour force would be sufficient. In either situation, the following information is required to satisfy the objectives of a r e a l i s t i c model based on obtainable data. Size of Labour Force.•' The number of workers required in each future time period must be specified. If the labour force is based upon future production requirements, worker productivity must be implicitly considered in determining the labour force required. . In instances where productivity can be measured, the labour force required can be readily calcu-lated once production requirements are known. In other cases productivity is Immeasurable and the decision-maker must rely on past experience in determining the labour force. 14 Depending upon the purpose of the model and the degree of sophistication desired, the labour force could be specified as a deterministic or probabilistic figure. Job Categories. The manpower models reported to date have a l l considered the workers to be employed in the same type of work. In some cases the employees actually were i n one job category 1 but in most instances the investigators were dealing with a multi-Job plant and neglected this aspect entirely. While this omission simplified the models i t also produced an undesirable effect. By neglecting the Job hierarchy, the training delays and costs associated with promotions were overlooked. If the firm was subject to a large change in labour requirements or high turnover rates, the effect could be considerable. A detailed manpower model should consider the hierarchical nature of the organization by containing provision for a number of job categories. Absenteeism. Another factor which must be considered in estimating future manpower requirements is absenteeism and illne s s . The fraction of the labour force that is unavailable for work due to illness can be estimated on the basis of past experience. Expected absenteeism is more complex since the rate depends on worker morale, job satisfaction?and George L. Nemhauser and Henry L. W. Nuttie, "A Quantitative Approach to Employment PlanningT"'Management  Science. XI, No. 8, (1965), pp. 155 - 165. 2Victor H. Vroom, Work and Motivation. (New York, John Wiley & Sons, Inc., 1964), pp. 178 - 180. work group s t a b i l i t y . Major changes in any of these factors affect the absence rate and make historical data of limited usefulness in determining future rates. Since the decision-maker is constrained by the subjectivity of these factors i t is suggested that historical data be used in the i n i t i a l runs of the model. If the model predicts a period of high turnover, the expected absence rate should be adjusted. Regular Labour Force The regular labour force is defined as the group of f u l l y trained employees available for work during the planning period. The basic information required from the firm is the number of workers in each job category at the present time. Since the operation of the model consists of comparing this "Regular Labour Force" group to the labour requirements in future periods, other information i s also required. Depending upon the type of model being constructed, the workers' seniority, training, productivity or other factors may have to be specified. These information requirements are discussed in relation to the other aspects of the manpower model. II. ENTERING THE WORK FORCE Labour Pool The labour pool i s defined as the number of workers that are available for employment at "entrance" positions in the hierarchical structure during a certain period of time. 16 The term "entrance positions" is used to indicate a Job category for which workers can be hired. In many industrial organizations, seniority constraints limit the entrance positions to the lowest job category in the hierarchy and to positions, such as journeyman tradesman, which require formal training. Despite the lack of consideration given by other investigators to the question of labour supply in manpower planning, the supply problem is second only to the problem of forecasting labour demand in the firm. If the manpower model is to be used to analyze the effects of a large increase in the work force or the effects of high turnover rates i t is necessary to have some limitation on the maximum number of workers which can be hired in a certain time period. In studies such as Gotterer's-^ and Nemhauser • s** there was l i t t l e need for a supply constraint In analyzing their immediate problems. The f i r s t study was concerned with the effects of hiring under varying circumstances rather than being a practical model of real situations. The latter study dealt with a one category situation with relatively short training periods and unskilled workers. In such cases It Malcolm H. Gotterer, A Study of the Effects of Delays  i n Changes In a Work Force. In Symposium on Simulation Models:  Methodology and Applications to the Behavioral Sciences. Austin C. Hoggatt and Frederick E. Balderston, editors, (Cincinnati, Ohio: South-Western Publishing Co., 19^3), pp. 192 - 202. (Hereafter referred to as Effects of Delays). Nemhauser and Nuttle, op. c l t _ 17 was reasonable to assume that the labour supply would be so great relative to demand that a constraint was unnecessary. On the other hand, Forrester's study of an electronics firm was an instance where a supply constraint would appear to be desirable.5 Although i t was a one category study the workers were semi-skilled and required a moderately long training period.^ Despite the failure of these investigators to mention the problem of a restricted labour supply in their publi-cations, i t is improbable that they failed to consider i t in building their models. In a l l likelihood, they realized the d i f f i c u l t y in obtaining objective data on the supply and preferred to risk unrealistic hiring rates under certain conditions rather than introduce subjective data into their model. In a general model, however, i t would be desirable to include a labour supply constraint in order to Investigate the effect of different labour pool sizes on the work force and on total costs. The constraint also helps to emphasize the fact that there is a limit to the supply of labour and to encourage future Investigators to research this side of the problem. A number of factors must be considered in estimating 3Jay w. Forrester, Industrial Dynamics, (Cambridge, Massechusetts: M.I.T. Press, 1961), pp. 208 - 251. 6 I b i d . . pp. 231. 1 8 the size and the changes In the firm's labour pool. In a long-term study, demographic changes in the labour market and changing participation rates for the labour force must be considered. Government policies on minimum wages, labour laws, social security, immigration and employment influence the long-term labour supply. The policies of the organization and other labour users with respect to wages, fringe benefits and training, also affect the labour supply. Unfortunately the effect of policy changes and economic conditions on the firm's labour supply are d i f f i c u l t to determine. For the purposes of manpower planning, a subjective estimate of the labour supply can be made based on past hiring experience and forecasts of possible changes in the near future. The supply can then be varied and the sensitivity of manpower levels and costs relative to these changes can be determined. Hiring The hiring function plays a twofold role in manpower planning. The hiring decision is triggered by the information that future manpower requirements are greater than the manpower available at that time. Personnel must be recruited and selected for the openings and receive the required training at some time prior to when they are required for production work. One of the prime effects of hiring on the model is to introduce the time delay required for recruitment and selection. The other e f f e c t of the h i r i n g process i s to determine the number and qual i t y of the future employees i n the organ-i z a t i o n . The labour pool from which the firm hires i s not a s p e c i f i c number of people but a spectrum with the size of the pool increasing as qual i t y requirements decrease. I f an organization i s h i r i n g few men, r e l a t i v e to the size of the labour pool, i t w i l l be able to hire high c a l i b r e men within a short time. As the number of desired hires i n -creases, the firm w i l l find that i t must either accept lower c a l i b r e employees or expand i t s labour pool by increasing i t s r e c r u i t i n g e f f o r t s and thereby increasing the time delay. Thus the h i r i n g process appeared to be a complex function of the labour supply, the number to be hired, the job requirements, the c h a r a c t e r i s t i c s of the applicants and the h i r i n g time. A review of the l i t e r a t u r e revealed that the e f f o r t s to date have concentrated on matching the a p p l i -cants to the Jobs available but have not included the other fa c t o r s . Gotterer's study considered the e f f e c t of h i r i n g delays on t o t a l costs but did not attempt to include the other aspects of the h i r i n g process. In view of the present state of knowledge on the h i r i n g process, a manpower model would have to r e l y on the organization's personnel records. The h i r i n g time could be determined from these records together with an estimate of the future e f f e c t of the preceedlng factors. The quantity-q u a l i t y r e l a t i o n s h i p could be subjectively estimated i f there 20 i s strong evidence to suggest that i t w i l l change. Otherwise i t should be assumed to be constant. Training Training, within the organizational setting, has been defined as: That process which, under company auspices, seeks in a planned, coordinated, and continuous manner to develop In a l l employees those understandings, s k i l l s , and attitudes, which w i l l maximize individual present and future efficiency and the effectiveness of the overall company organization.? By this definition, the scope of training is as broad as the needs and philosophy of the organization. It Includes orientation training of new employees, retraining of older employees caused by changes in production patterns or tech-nology, brush-up courses to increase the efficiency of existing personnel and job s k i l l s training at any level in the organization. While i t is beyond the scope of this presentation to delve into the intricacies of developing and instituting effective training programmes, the areas where the training function impinges upon manpower planning must be investigated. Types of Training. Although there are many different types of training programmes, they may be divided into two basic types for the purpose of the manpower planning model. ?Frank A. DePhilips, William A. M. Berliner and James J. Crlbbin, Management of Training Programs. (Homewood, I l l i n o i s , Richard D. Irwin, Inc., i960), pp. 6. 21 The f i r s t group Includes programmes In which the trainee does not affect production while being trained. Off-the-job programmes such as lectures, plant tours, discussion groups, correspondence courses and so on, together with programmes where the trainee is on the job with an experienced worker but where there Is no Increase in production due to the trainee, are the most common cases in this group. A good example of the latter type of programme is found in proc-essing plants where a trainee i s placed with another operator and learns the job by observing and assisting the operator. When he is sufficiently trained he assumes the operator's job and the operator is transferred to another section of the plant. The other basic group of training programmes are the type where the trainee affects production while being trained. Apprenticeship training and most shop training programmes Q are examples of this group. Another example is Nemhauser's study of telephone operators. In this study, production workers were taken off their jobs to operate a formal training programme. Thus there was a negative relationship between the number of trainees and the number available for production jobs. 9 °Dale Yoder, Personnel Management and Industrial  Relations. (3rd. ed., New York, Prentice-Hall, Inc., 19^8), pp. 260 - 262. ^Nemhauser and Nuttle, op.cit.. pp. 158. 22 The reasons behind the division of training programmes into two groups, depending upon the contribution of the trainee to production,lies in the nature of the problems which these types of training resolve. The general aim of training is to provide a skilled, efficient work force of a certain size at some future point in time. This objective can be accomplished by the "zero contribution" types of training. The decision regarding the number of workers to be hired and trained is directly related to the number of trained workers that are expected to be available in the future. This number, in turn, depends on the number of experienced workers currently in the work force and the number that are currently being trained. A decision of this nature depends on historical data and Is independent of future decisions. In contrast to the "zero contribution" types of training, the treatment of "contribution" types of training requires a special technique. Because the "contribution" type affects production levels during the training period, the number of production workers required in some future period depends on the number being trained during that period. This situation, where current and future promotion decisions are interrelated i s known as the "deterministic sequential decision problem". 1 0 Dynamic programming techniques are 1°G. Hadley, Nonlinear and Dynamic Programming. (Reading, Massachusetts, Addison-Wesley Publishing Company, Inc., 1964), PP. 375 - 379-2 3 required to solve this type of decision problem. Regardless of how the trainees are grouped}the follow-ing Information Is required for manpower planning: (1) the number being trained, (2) their job category, and (3) the training time. If a cost optimizing model is being constructed, information must be obtained regarding the training costs. In the case of "contribution" types of training, the benefits of increased production during the training period would also have to be considered. Determination of Training Time. Another major aspect of the training problem is the delaying effect due to train-ing or the training time. For the purposes of manpower planning the training time to be used in the model i s the standard training time for a particular Job within the organ-ization. Since this delaying effect is relatively important, the factors involved in determining i t should be analyzed. The following discussion investigates the factors which affect training times and the problem of measuring It In certain situations. Training, in i t s broadest sense, Is a learning process. Therefore i t may be thought of as an activity whereby the Individual not only acquires, but also retains and ut i l i z e s certain s k i l l s , habits and attitudes. DePhillps describes this learning process as proceeding through four stages.11 ^DePhillps, Berliner and Cribbin, op.cit.. pp. 6 9 . 24 The f i r s t stage is one of "unconscious incompetance" in which the trainee is unaware of his lack of knowledge. As training commences, the trainee enters the second stage where he becomes aware of his ignorance and of the need for train-ing. The i n i t i a l training period is characterized by an incomplete understanding of the job and an expenditure of energy that i s out of proportion to the d i f f i c u l t y of the task. With further training the trainee enters a third stage where he has a clearer understanding of the task, better coordination, and a reduction in t r i a l and error learning. After a period of time the trainee proceeds to a fourth and f i n a l stage where he not only has a complete understanding of relationships between a l l aspects of the task but also has a sense of accomplishment in a job well done. These four stages are illustrated in Figure I I - l . It must be noted that these training stages and the associated learning curve consider the total learning process. In a l l likelihood^ sensory-motor ( s k i l l ) learning proceeds more rapidly than either conceptual or associational learning. An example of the learning curves for the various learning processes is shown in Figure II - 2 . The hypothesis of different learning rates creates a number of d i f f i c u l t i e s in determining the training time for a particular job. The trainee tends to feel that he is sufficiently trained when he can "do the job." Usually this is when the sensory-motor aspects of the task have been 25 K-YIOVAJ I -e cj ^ I L A' Figure I I - l KT>O UU l-e do) € C u . r >j-e Figure I I - 2 Typical Learning Curves 26 l e a r n e d . Since the sensory-motor elements are e a s i l y recog-n i z e d and e a s i l y measured, management may a l s o be l e d to b e l i e v e that the worker i s t r a i n e d when he reaches t h i s stage. In the example shown i n F i g u r e I I - 2 , t h i s would be e a r l y i n stage I I I . In many i n d u s t r i a l jobs sensory-motor s k i l l s o v e r r i d e the o t h e r s k i l l s to such an extent t h a t the worker i s q u i t e w e l l t r a i n e d . In other areas, such as the p r o c e s s -i n g i n d u s t r i e s , the employee Is f a r from b e i n g an experienced worker a t t h i s time. Another major f a c t o r i n d e t e r m i n i n g t r a i n i n g time i s the method of l e a r n i n g . Knowledge a c q u i r e d i n a l o g i c a l manner i s r e t a i n e d l o n g e r than l e a r n i n g by r o t e . I t has a l s o been found that a task that Is l e a r n e d w e l l i s r e t a i n e d l o n g e r and b e t t e r than one that has b a r e l y been l e a r n e d d u r i n g t r a i n i n g . ^ On the b a s i s of the d i s c u s s i o n t h u s f a r , i t can be seen t h a t the f a c t o r s a f f e c t i n g t r a i n i n g time are many and complex. In g e n e r a l terms, however, i t can be s a i d that the t r a i n i n g time f o r a p a r t i c u l a r job i s a f u n c t i o n of (1) the types of l e a r n i n g processes and the r e l a t i v e importance of each to the job, (2) the method of l e a r n i n g , (3) the stage of l e a r n i n g which must be a t t a i n e d In order to perform the job, (4 ) the frequency with which knowledge i s used, and (5) the a b i l i t y of the person b e i n g t r a i n e d . l 2 D e P h i l i p s , B e r l i n e r and C r i b b i n , o p . c i t . . pp. 112-117. 2 ? Measuring Training Time. The standard criterion for judging i f a person has been adequately trained is whether or not he can do the Job. In many instances, especially where the learning i s associatlonal or conceptual in nature, individual productivity cannot be measured. Usually the training time is judged to be the time when the learning rate reaches an intermediate plateau, i.e., at a point where the trainee appears to have stopped learning. At this point i t appears to both the trainee and the supervisor that the trainee is capable of doing the job. This factor, combined with the lack of quantitative methods for measuring the trainee's knowledge, often leads to training being curtailed before the worker is fully trained. On the other hand, i f the job requires considerable s k i l l learning or individual production can be measured, the training time is usually considered to be the time taken for the Individual to attain the average output of experienced operators. Neither of these c r i t e r i a should be accepted for general use i f they can be avoided. In instances where individual productivity cannot be measured, a subjective criterion must be used. If the subjective judgement is made considering the above-mentioned factors rather than simply when the trainee appears to know the sensory-motor aspects, the judgement may be quite accurate. In cases where individual productivity i s measurable, the costs and benefits of training may be considered. The 28 concept that training time is the length of time required to attain the average output of experienced workers has been justified on the basis that any output below this level is unporfltable. Clearly this Is not the case. Whether or not a worker is profitable depends on his contribution to production and i s independent of the average production of his co-workers. The "average production" criterion must be rejected for three reasons: (1) i t is unrelated to profit, (2) i t neglects to consider that the trainees are s t i l l learning when they complete their training programme, (to train workers until they reach this level may result in abnormally long training times and place the slower learners under unnecessary pressure), and (3) unless the trainee's prod-uctivity f a l l s off after the training programme, a l l trainees w i l l become "above average" workers. This w i l l raise the average productivity and may cause the firm to be unduly selective in recruiting and promoting employees. Having resolved that average productivity i s an unsatisfactory measurement of training time, a new criterion must be developed. Winthrop has led the way In this respect by developing a learning curve procedure for the acceptance and paying of apprentices.13 He develops a curve of unit 13Henry Winthrop, "Management Decision Technique in the Classification of Employee S k i l l s " , Management Technology. II, (December, 1962), pp. 101 - 107. — 29 cost versus output and determines the break-even point for various market prices of the product. It is then possible to determine which apprentices to reject and how profitable they are at each level of output. The same technique could also be applied to determining the length of training required before the trainee becomes profitable to the firm. Although neither Winthrop's art i c l e nor a similar study by Taylor 1^ deal specifically with marginal analysis, i t is obtainable from the unit cost versus hourly output and hourly output versus training time curves. If the changes in unit cost and training time for a certain change in the output rate can be measured, the benefit of additional training time at this particular output can be determined. The benefit can be compared to the cost and training terminated when the marginal cost exceeds the marginal benefit. Thus the learning curve procedure meets the requirements of marginal analysis and is a relatively easy and practical procedure for deter-mining the optimal training time when productivity can be measured. Promotions One of the major differences between a general model and the models reported in previous studies is that a general •^Marvin L. Taylor, "The Learning Curve - A Basic Cost Projection Tool", Management Informatlon-A Quantitative Accent. Thomas H. Williams and Charles H. Gr i f f i n , editors, (Homewood, I l l i n o i s : (Richard D. Irwin, Inc., 1967), pp. ^97 - 501. 30 model must Include provision for a hierarchical organization structure. A job hierarchy, by i t s very nature, implies that there are opportunities for employees to advance from one job to another. Thus the model must make provision for promoting the employee and training him as he progresses from one job category to another. The promotion decision is essentially the same as the hiring decision. The difference is that, where the hiring decision indicated the need to bring workers In from the labour pool, the promotion decision indicates the need to bring workers up from a lower job category. Thus the promotion decision Is entirely internal and dependent soley upon the organization's requirements and their promotion policies. The policy of the organization regarding promotions depends on the type of work which the labour force performs. Many industrial organizations have a policy of promoting their present employees and only hiring for the lowest job category. Others, because of the nature of the work or the costs of training, prefer to hire experienced workers when they can, and only promote employees when absolutely necessary. Between these two extremes there could be a number of c r i t e r i a for the fraction of the labour requirement that is to be hired and the fraction that is to be promoted. The decision to promote an individual worker may also be based on a number of factors. In many unionized plants, total seniority or a combination of total seniority and 31 plant seniority may be the only acceptable criterion for promotion. In other organizations promotions may be based on seniority in a particular job or on the worker's a b i l i t y . From the view-point of a general discussion, provision for promotions to occur must be Included in the model to-gether with the policies and c r i t e r i a that are used to determine how the worker is to be promoted. III.. LEAVING THE WORK FORCE The third major group of aspects to be considered in a manpower model are the factors and forces which cause an employee to leave the work force. The ensueing discussion is sub-divided into the three major causes of an employee leaving the work force. The employee may leave voluntarily (quit), he may leave at the request of the employer due to some fault of the employee (be discharged), or he may leave at the request of the employer but through no fault of his own (be lai d o f f ) . Since voluntary termination is the most common cause of termination, as well as the most complex, i t is discussed in considerable detail. Discharges and lay-offs are relatively straightforward decisions. The former is independent of the model while the latter, like the hiring decision, is entirely dependent upon the other factors in the model. Effects of Terminations Terminations, whether they be voluntary or involuntary, 32 have a considerable effect upon the organization. First, a termination results i n the employer losing his investment in the worker. Not only is there the cost of hiring and training a new employee, but also the new employee is likely to be less productive than the one he replaces. Second, the introduction of new employees and promotion of more senior men disrupts the established work groups and leads to increased confusion in the organization. This lowers the group's productivity and may lead to increased absenteeism1^ and turnover. 1^ Third, i f the termination is voluntary there is l i k e l y to be a considerable time-lag between the decision to quit and the actual resignation.1'''' During this time period the employee's contribution is l i k e l y to be less than that of the average worker. In summary, terminations of any kind affect the organization's costs and production. The effect on hiring and training can be easily represented in the manpower model. The effect of normal levels of terminations is reflected in the productivity and absentee coefficients that are used in 15John B. Fox and Jerome F. Scott, Absenteeism: Manage-ment Problemf (Boston, Harvard University Graduate School of Business Administration, 1957). l^Elton Mayo and George F.F. Lombard, Teamwork and  Labor Turnover in the Aircraft Industry of Southern California. (Boston, Harvard University.. Graduate School of Business Administration, 1957). 17wayne L. McNaughton, "When the Employee Decides to Quit", Personnel. XXXII, (May, 1956), pp. 525 - 532. 33 the model. Changes i n the termination rate cannot be readily-treated unless the organization has s u f f i c i e n t information to r e l a t e these changes to productivity and absenteeism. Determinants of Turnover Theoretical Indicators. A vast number of studies have been made concerning the factors that determine turnover rates. For the purposes of t h i s discussion, the research studies were sub-divided into three groups; biographical studies, psychological studies, and economic studies. The biographical studies have indicated that relationships e x i s t between turnover rates and age, sex, marital status ( r e s p o n s i b i l i t y ) , previous job history, previous wages, and so on. The fact that other studies have found no correlations between any of the above factors and turnover leads one to doubt t h e i r general a p p l i c a b i l i t y . This view Is substantiated by both Schuh 1® and H u l i n 1 9 w n o report that, while biographical factors may a f f e c t turnover i n c e r t a i n cases, general con-clusions cannot be made. Studies of the relationships between a number of psychological factors and labour turnover have been more successful. Schuh has recently reviewed a l l the published ^ A l l e n j . Schuh, "The P r e d i c t a b i l i t y of Employee Tenure: A Review of the Litera t u r e " , Personnel Psychology. XX, No. 2 , (Summer, 1 9 6 7 ) , pp. 1 3 3 - 1 5 2 . 1 9 C h a r l e s L. Hulin, "Job S a t i s f a c t i o n and Turnover i n a Female C l e r i c a l Population", Journal of Applied Psychology. L, No. 4 , (August, 1 9 6 6 ) , pp. 280 - 2 8 5 . 3^ tests on the effect of these factors on turnover. He reports that i n particular situations intelligence, aptitude, person-a l i t y and interests affect tenure. The only factors that were positively related in a l l cases were job satisfaction 20 and work group relations. It must be realized, however, that these factors only consider the forces which tend to make the worker stay with the firm. A number of other factors, such as relative wage levels and opportunity elsewhere, tend to force the worker to leave. The complexity of these economic factors have re-stricted the studies to aggregate situations. Vroom reported 21 that turnover increases as unemployment decreases. Harker found that turnover i n the United States closely followed the level of business activity in 20 out of 22 years between 22 1935 and 1957. While these economic studies provided well correlated indicators of changes in labour turnover rates in an aggregate sense, there would be d i f f i c u l t i e s in applying them to a specific organization. In summary, the factors which are good general indic-ators of turnover are d i f f i c u l t to measure and even more d i f f i c u l t to relate.to specific turnover rates. Fortunately, 2 0Schuh, op.cit.. 2 1 V i c t o r H. Vroom, Work and Motivation. (John Wiley . and Sons, Inc., New York, 1964), pp. 178. . 2 2John B. Harker, "Business Activity and Turnover", Personnel Journal. XXXVI, No. 5, pp. 183 - 184. 35 a t u r n o v e r i n d i c a t o r need not be based on t h e o r e t i c a l concepts. E m p i r i c a l i n d i c a t o r s , i f they can be found, are s a t i s f a c t o r y f o r manpower p l a n n i n g . The f o l l o w i n g s e c t i o n s d i s c u s s s e v e r a l e m p i r i c a l i n d i c a t o r s which have been used i n o t h e r manpower models. Turnover as a F u n c t i o n of Employment S t a b i l i t y . One of the b a s i c assumptions of G o t t e r e r ' s model Is t h a t the r a t e a t which employees r e s i g n i s a f u n c t i o n of the s t a b i l i t y of employment. S p e c i f i c a l l y he assumes t h a t the turnover r a t e i s two p e r c e n t when employment s t a b i l i t y i s a maximum and i n c r e a s e s i n p r o p o r t i o n to the percentage of the l a b o u r f o r c e b e i n g l a i d o f f , 2 ^ While t h i s c r i t e r i o n may be a good i n d i c a t o r i n some cases, i t cannot be recommended f o r g e n e r a l use. E m p i r i c a l evidence i n d i c a t e s that a f i r m which i s ex-panding i t s l a b o u r f o r c e f i n d s t h a t many of the men they h i r e q u i t w i t h i n a s h o r t time. Undoubtedly t h i s i s due to improper s e l e c t i o n , placement, and t r a i n i n g , but i s i s a f a c t which must be c o n s i d e r e d . A c c o r d i n g to G o t t e r e r * s d e c i s i o n r u l e the f i r m should have extremely low t u r n o v e r r a t e s i f employment i s expanding or s t a b l e . Thus, G o t t e r e r 1 s r u l e i s not a p p l i c a b l e under these c o n d i t i o n s . Even when there are l a y - o f f s the r u l e does not n e c e s s a r i l y a p p l y . S t u d i e s by Mayo2-' 23Gotterer, o p . c i t . . pp. 193. 2^Norman R. F. Maier, Psychology i n I n d u s t r y . (3rd. ed.), (Boston, Houghton M i f f l i n Co., 1965), PP- 624. 2^Mayo and Lombard, o p . c i t . . 3 6 and Fox 26 indicate that turnover i s l i k e l y to increase when a firm i s laying off workers. They found that the causes of the increased turnover and absenteeism were the uncertainty, i r r e g u l a r i t y and confusion that the l a y - o f f s produced rather than the l a y - o f f s themselves. Once these causes were i d e n t i -f i e d and p o l i c i e s implemented to minimize them, the re-searchers found that the r e l a t i o n s h i p between turnover and l a y - o f f s ceased to e x i s t . Therefore, i t appears that Gotterer's decision rule need not be applicable when the work force i s contracting and i s not applicable i f the work force i s expanding. Turnover as a Function of Length of Service. Another commonly used in d i c a t o r of turnover i s the length of service of the employee either i n t o t a l or with respect to his pre-sent p o s i t i o n . There i s strong empirical evidence to support the assumption that turnover i s a function of the worker's length of service with the firm. Maier c i t e s a study of a public service corporation where turnover rates depended upon the length of service more than i t depended upon other measur-able f a c t o r s . The B r i t i s h Columbia Telephone Company reports that the turnover of telephone operators i s well correlated to the length of service. 2® The writer's experience i n the Fox and Scott, o p . c i t . . 2 ?Maler, o p . c i t . . pp. 6 2 4 . 2 8 Personal communication with Mr. D.M. Carter, Personnel, B r i t i s h Columbia Telephone Company, Vancouver, B. C. 37 mining industry also substantiates this assumption. In contrast to this evidence, research in the armed forces shows that there is a correlation between turnover and the length of service in a particular position. 2 9 The differences between the conflicting evidence can be reconciled i f the characteristics of the groups are con-sidered. Most unskilled and semi-skilled workers are employed in positions where there are limited opportunities for advancement. In many of these jobs, advancement is based on the worker's seniority with the organization. Furthermore, alternative job opportunities are usually at the same or lower s k i l l levels and the worker cannot move to a higher job category by going to another employer. Under these conditions the worker:is unlikely to be by-passed when pro-motions are determined or to feel that he is missing out on better opportunities elsewhere. The effect of these factors on the employee's decision to quit should be minimal. The factors which are li k e l y to affect turnover are the biographical and psychological factors discussed previously. Except In times of mass unemployment the labour force available to a firm is made up of young people seeking their f i r s t job and those who have quit a previous employer^ The young worker entering the labour force probably has l i t t l e work 29W.E. D i l l , D.P. Gaver and W.L. Weber, "Models and Modelling for Manpower Planning", Management Science. XIII, No. 4 , (December, 1 9 6 6 ) , pp. 142 - 167. ~~ 38 experience and few r e s p o n s i b i l i t i e s . I f he f i n d s t h a t he doesn't l i k e the type of work he q u i t s and seeks a l t e r n a t i v e employment. The main f a c t o r a f f e c t i n g t h i s d e c i s i o n i s the time t h a t i t takes the work to d i s c o v e r t h a t he d i s l i k e s the work. Although t h i s time w i l l vary between i n d i v i d u a l s the r e l a t i o n s h i p between tu r n o v e r and t o t a l l e n g t h of s e r v i c e i s e v i d e n t . The youth now j o i n s the second group that c o n s t i t ute the l a b o u r supply, those who have q u i t t h e i r p r e v i o u s job. The worker now repeats the h i r i n g , time l a p s e , q u i t t i n g procedure u n t i l he f i n d s s a t i s f a c t o r y employment. Two items i n t h i s process are worthy of note. F i r s t , a l a r g e number of the men h i r e d by an o r g a n i z a t i o n are s u b j e c t to t i m e - o r i e n t e d l e a v i n g f o r c e s . The l e n g t h of s e r v i c e i n the f i r m w i l l measure these f o r c e s . Second, because of the tendency to q u i t s h o r t l y a f t e r h i r i n g , a f i r m may have to h i r e s e v e r a l employees b e f o r e they f i n d one t h a t stays with the f i r m . T h i s has severe i m p l i c a t i o n s upon the f i r m t h a t wants to expand i t s work f o r c e or t h a t f a i l s to p r o v i d e the necessary c o n d i t i o n s and b e n e f i t s to r e t a i n i t s s e n i o r employees. The second group of employees to be c o n s i d e r e d i n c l u d e s managerial, p r o f e s s i o n a l and m i l i t a r y p e r s o n n e l . Promotion i s based more on merit than s e n i o r i t y and the employee can move e i t h e r h o r i z o n t a l l y or upward when he takes another job. For t h i s group, the l e n g t h of s e r v i c e with the o r g a n i z a t i o n i s l i k e l y to be l e s s important than present and f u t u r e 39 o p p o r t u n i t i e s for advancement. Since an i n d i v i d u a l i s normally u n c e r t a i n of how h i s superiors rate him and what h i s o p p o r t u n i t i e s are w i t h i n the f i r m , he seeks out a c r i t e r i o n which allows him to measure t h i s . In many instances the c r i t e r i o n i s the length of s e r v i c e i n h i s present job r e l a t i v e to that of h i s reference g r o u p . i f the i n d i v i d u a l f e e l s that he i s being promoted r a p i d l y there i s a tendency f o r him to stay with the o r g a n i z a t i o n . I f , on the other hand, he f e e l s that he i s being l e f t behind, there w i l l be a tendency f o r him to seek o p p o r t u n i t i e s elsewhere. In summary, i t appears that length of s e r v i c e can be a s a t i s f a c t o r y i n d i c a t o r of turnover. I f the group i s composed of s e m i - s k i l l e d or s k i l l e d workers or low l e v e l c l e r i c a l personnel the t o t a l length of service with the f irm should be used. I f the group i s composed of p r o f e s s i o n a l personnel the length of service i n the job category should be used. In e i t h e r case the i n d i c a t o r s would have to be adjusted f o r changes i n the age and sex composition of the work f o r c e , economic c o n d i t i o n s , and job s a t i s f a c t i o n l e v e l s . Discharges Besides l e a v i n g the work force v o l u n t a r i l y a worker may be forced to leave by being discharged. Although the discharge r a t e i s u s u a l l y quite low and the d e c i s i o n i s made 3°D111, Gaver and Weber, o n . c i t . . pp. 163. 40 independently of manpower requirements i t should he considered in the model. Despite the lack of published evidence, i t is reasonable to expect that newly hired employees are more li k e l y to be discharged than more senior workers. Personal traits such as incompetance, emotional instability and insubordination may not be detected before the worker Is hired but wi l l become evident shortly afterwards and cause the worker to be discharged. Other discharges are due to specific actions of the employee or to traits which develop after he is hired. In total, the rate is li k e l y to be a function of the length of service for junior employees and constant for more senior personnel. Under these conditions a constant rate independent of both the hiring rate and length of service may be satisfactory. Discharges could be treated in the model by adjusting the labour force requirement to include a discharge coefficient. Lay-offs The third way in which employees leave the work force Is by being lai d off. This decision i s also made by the organization but, in contrast to discharges, the decision depends entirely upon the future requirements of the firm. The manpower model could be built to cope with any number of policy constraints which would affect the timing of the.'.lay-offs and the number of workers affected. A time lag between the decision and the lay-off would be required since the kl • organization must inform the workers of the impending lay-off. Information is also required with regard to the decision c r i t e r i a for lay-offs. If the criterion is either total seniority or job seniority i t could be readily handled in the model. Depending on company policy, constraints might be introduced so that there would be no lay-offs i f the workers were to be recalled within a short time or i f only a few men were to be l a i d off. Since the lay-off decision is generated by the model and is not subject to the external environment any decision criterion and constraint could be introduced providing that the necessary information is available. The procedure for treating employees who are l a i d off also depends on company policy. If the workers are not subject to re-call by the employer, then they can be consid-ered to leave the work force completely when they are lai d off. If the workers are subject to r e - c a l l , then provision must be made to re-introduce the worker to the same job category without going through the training programme. Provision must also be made for the laid-off employees to sever his relations with the employer and a criterion dev-eloped to determine the probability of a l a i d off employee quitting. Although there are no published studies on the factors influencing a laid off employee to quit, a historical study would be possible i f "the organization had a pattern of 42 l a y i n g - o f f and r e c a l l i n g employees. I n a l l l i k e l i h o o d the q u i t r a t e i s r e l a t e d t o the l e n g t h o f t h e l a y - o f f , the ex-p e c t e d l e n g t h o f the l a y - o f f , o t h e r o p p o r t u n i t i e s , and the v a l u e o f the a c c r u e d b e n e f i t s f o r e g o n e . CONCLUSIONS B a s i c Requirements o f a G e n e r a l Model The i n v e s t i g a t i o n o f the r e q u i r e m e n t s i n a g e n e r a l model demonstrated t h a t the f o l l o w i n g f a c t o r s must be c o n s i d e r e d i n any manpower p l a n n i n g model; 1. A f o r e c a s t o f f u t u r e l a b o u r r e q u i r e m e n t s . 2. I n f o r m a t i o n on the p r e s e n t l a b o u r f o r c e . 3 . A h i e r a r c h i c a l o r g a n i z a t i o n s t r u c t u r e . 4. P r o v i s i o n f o r time l a g s whenever h i r i n g o r t r a i n i n g o c c u r s . 5 . A l a b o u r p o o l from which the employees a r e h i r e d . 6 . P r o v i s i o n f o r l a b o u r t u r n o v e r . 7. P r o v i s i o n f o r h i r i n g and p r o m o t i n g employees. 8. P r o v i s i o n f o r l a y i n g - o f f and demoting employees. S p e c i f i c Models The i n v e s t i g a t i o n o f the g e n e r a l r e q u i r e m e n t s i n a manpower p l a n n i n g model a l s o i n d i c a t e d t h a t s e v e r a l t y p e s o f models c o u l d be c o n s t r u c t e d . The b a s i c d i f f e r e n c e s between these t y p e s a r o s e through the e f f e c t o f t r a i n i n g on p r o d u c t i o n and the q u i t r a t e r e l a t i o n s h i p . I f the t r a i n e e s 43 d i d n ot a f f e c t p r o d u c t i o n , s i m u l a t i o n t e c h n i q u e s would be a p p l i c a b l e . A l t e r n a t i v e l y , i f p r o d u c t i o n was a f f e c t e d , dynamic programming would be r e q u i r e d . There were a l s o two b a s i c ways t o t r e a t the q u i t r a t e f u n c t i o n . I t has been h y p o t h e s i z e d t h a t the q u i t r a t e depended on the l e n g t h o f s e r v i c e w i t h the employer i f the employee c o u l d not improve h i s p o s i t i o n by c h a n g i n g j o b s . I t was a l s o h y p o t h e s i z e d t h a t t h e q u i t r a t e would be a f u n c t i o n o f the l e n g t h o f s e r v i c e i n a p a r t i c u l a r j o b i f the employee c o u l d improve h i s p o s i t i o n by c hanging employers. These f o u r t y p e s of models, t o g e t h e r w i t h an o u t l i n e o f the t y p e s o f employees the models would t r e a t , a r e i l l u s t r a t e d I n F i g u r e I I - 3 . The Type I model, (non-managerial employees, no e f f e c t on p r o d u c t i o n ) i n c l u d e s a l l p r o c e s s i n g and assembly-l i n e j o b s . Type I I ( n o n - m a n a g e r i a l employees, t r a i n e e s a f f e c t p r o d u c t i o n ) i n c l u d e s Job-shop w o r k e r s , maintenance w o r k e r s , t e l e p h o n e o p e r a t o r s and so on. Type I I I i n c l u d e s a l l t y p e s of m a n a g e r i a l and m i l i t a r y p e r s o n n e l who a r e s u b j e c t t o t r a i n i n g on the j o b . Type IV i n c l u d e s the same group but t r a i n i n g i s d i v o r c e d from the j o b . The f o r m a l manage-ment t r a i n i n g s c h o o l s o p e r a t e d by some o f the l a r g e r c o r p o r a t i o n s i l l u s t r a t e the Type IV model. I f the l a b o u r f o r c e were d i v i d e d i n t o f o u r groups a c c o r d i n g to these c r i t e r i a , the Type I and Type I I models would c o n t a i n the l a r g e s t number of w o r k e r s . The m a j o r i t y o f the models d e v e l o p e d t o date have been c o n s t r u c t e d t o 44 TYPE I - Q u i t Rate depends on l e n g t h of s e r v i c e - P r o d u c t i o n i s independent of the number of t r a i n e e s - Examples a s s e m b l y - l i n e s p r o c e s s i n g i n d u s t r i e s a p p r e n t i c e programmes TYPE III - Quit Rate depends on time i n job category - P r o d u c t i o n depends on the number of t r a i n e e s - Examples m i l i t a r y personnel most managerial jobs TYPE II - Quit Rate depends on l e n g t h of s e r v i c e - P r o d u c t i o n depends on the number of t r a i n e e s - Examples job-shops maintenance workers TYPE IV - Quit Rate depends on time i n job category - P r o d u c t i o n i s independent of the number of t r a i n e e s - Examples formal t r a i n i n g of managerial employees F i g u r e II-3 A l t e r n a t i v e Types of Models c o n s i d e r a s p e c i f i c sub-group of the Type I model or some v a r i a t i o n of i t . U n f o r t u n a t e l y , these models have not c o n s i d e r e d a l l the r e l e v a n t f a c t o r s necessary f o r t h e i r use i n most Type I s i t u a t i o n s . F o r example, F o r r e s t e r n e g l e c t e d turnover e n t i r e l y while G o t t e r e r c o n s i d e r e d t u r n -over to be r e l a t e d to the l a y - o f f r a t e . Both of them n e g l e c t e d to c o n s i d e r a h i e r a r c h i c a l s t r u c t u r e . Nemhauser 1 model f o r s c h e d u l i n g telephone operators (a Type I I sub-group), while c o r r e c t f o r telephone o p e r a t o r s , d i d not i n c l u d e a job h i e r a r c h y . In view of these l i m i t a t i o n s i t was decided to c o n s t r u c t a new model which would i n c l u d e the b a s i c requirements of the g e n e r a l model. The Type I group was s e l e c t e d as the b a s i s f o r the model f o r two reasons. F i r s t , t h i s group of non-managerial employees i s the l a r g e s t group i n most o r g a n i z a t i o n s . Second, the model can be c o n s t r u c t e d without u s i n g dynamic programming techniques. Because dynamic programming i s a c o s t - o p t i m i z i n g procedure, c o s t equations would have been r e q u i r e d f o r each r e l a t i o n s h i p i n the model. I t was not the purpose of t h i s study to i n v e s t i g a t e the s i z e , shape and i n t e r r e l a t i o n s h i p of the c o s t f u n c t i o n s i n a manpower system. A study of t h i s s o r t would have impinged upon a number of aggregate p r o d u c t i o n p l a n n i n g techniques and l e d away from the o r i g i n a l purpose of the study. CHAPTER I I I DEVELOPMENT OF THE MODEL The purpose of t h i s chapter was to develop a working model of the manpower p l a n n i n g f u n c t i o n which c o u l d be used f o r o r g a n i z a t i o n a l p l a n n i n g or f o r r e s e a r c h i n t o the e f f e c t of manpower s t r u c t u r e s on the personnel f u n c t i o n . On the b a s i s of the c o n s i d e r a t i o n s d i s c u s s e d i n Chapter I I , the model was developed to analyse the segment of the work f o r c e i n which: 1. The employee i s subjected to l e a v i n g f o r c e s t h a t can be approximated as a f u n c t i o n of t h e i r l e n g t h of s e r v i c e with the employer. 2 . The employee does not a f f e c t the o r g a n i z -a t i o n ' s p r o d u c t i v i t y while he i s being t r a i n e d . I. ASSUMPTIONS A number of assumptions were made i n order to develop a f o u n d a t i o n f o r the model. The g e n e r a l c r i t e r i a used i n making these assumptions were t h a t the model must be a r e a l i s t i c r e p r e s e n t a t i o n of the system and the i n f o r -mation r e q u i r e d must be r e a d i l y a v a i l a b l e to the o r g a n i z a t i o n . General Assumptions The f o l l o w i n g assumptions were made because 4 7 the o r g a n i z a t i o n does not normally have the i n f o r m a t i o n r e q u i r e d to t r e a t the f a c t o r s i n a d i f f e r e n t manner. The assumptions would be r e q u i r e d i n any o b j e c t i v e manpower model. 1 . Because the f o r e c a s t c o n s i d e r s workers who have y e t to be h i r e d , the workers are co n s i d e r e d as members of a group. I n d i v i d u a l c h a r a c t e r i s t i c s are n e g l e c t e d . 2. A l l employees i n a job category have equal p r o d u c t i v i t y . 3 . A l l employees have equal a b i l i t y . 4 . Worker p r o d u c t i v i t y i s known and c o n s t a n t . S i m p l i f y i n g Assumptions A number of s i m p l i f y i n g assumptions were made i n c o n s t r u c t i n g the model. The gen e r a l purpose of these assumptions was to d e l i n i a t e a s p e c i f i c model type and to remove a number of minor f a c t o r s from the model. Q u i t t i n g . The p r o b a b i l i t y of a worker q u i t t i n g d u r i n g a time p e r i o d was assumed to be a f u n c t i o n of the worker's l e n g t h of s e r v i c e i n the o r g a n i z a t i o n a t the s t a r t of the time p e r i o d . As mentioned p r e v i o u s l y , i t was thought t h a t t h i s assumption was necessary i f the model was to be used f o r manpower p l a n n i n g below the managerial l e v e l . l a b o u r Requirements. Future labou r requirements were assumed to be known with c e r t a i n t y . The reason f o r assuming d e t e r m i n i s t i c l a b o u r requirements was that the model was co n s i d e r e d as separate from p r o d u c t i o n and i n v e n t o r y 48 models. I f the model were to be combined into an aggregate model or i f optimizing techniques were being used, p r o b a b i l i -s t i c data might be desirable. This could be readily i n t r o -duced to the model by way of the Monte Carlo technique. F i r i n g . The number of workers discharged during a decision period was assumed to be n e g l i g i b l e . Since the number discharged would be considered i n either the labour requirement or the quit rate, the model was unaffected by this assumption. I l l n e s s . Accidents and Absenteeism. I t was assumed that the number of workers unavailable for work due to i l l n e s s , accidents and absenteeism was n e g l i g i b l e . In actual practice the labour requirement would be adjusted to consider the expected number of workers unavailable due to these f a c t o r s . S p e c i f i c Assumptions In addition to the simplifying assumptions which de l i n i a t e d and s i m p l i f i e d the model, a number of s p e c i f i c assumptions were made. In general these were required to provide the organizational p o l i c i e s for promotion. In a few instances assumptions were made to avoid the constraints of the computer language (FORTRAN). A l l these assumptions could be e a s i l y changed i f they were found to be inapplicable to the organization being studied. Basis for Promotion. I t was assumed that workers were 49 to be promoted on the b a s i s o f t h e i r l e n g t h of s e r v i c e w i t h the o r g a n i z a t i o n . The e f f e c t of t h i s assumption was to determine who was to be promoted and, t h e r e f o r e , to determine the c o m p o s i t i o n of the r e g u l a r work f o r c e i n the f u t u r e . The composition, i n t u r n , determined the number t h a t would q u i t a t each job category and the promotions r e q u i r e d to f i l l these v a c a n c i e s . In a c t u a l p r a c t i c e the promotion c r i t e r i o n would be a f u n c t i o n of the worker's a b i l i t y and h i s s e n i o r i t y . Because the model was a f o r e c a s t i n g d e v i c e , a b i l i t y was assumed to be equal f o r a l l workers. Under these c o n d i t i o n s s e n i o r -i t y was the prime c r i t e r i o n f o r promotion. I f a more s u b j e c t i v e c r i t e r i o n , such as a b i l i t y , was used i n p r a c t i c e t o determine who was to be promoted i t would a f f e c t the i n d i v i d u a l worker but would have l i t t l e e f f e c t on the number of men promoted. In some o r g a n i z a t i o n s the l e n g t h of s e r v i c e i n a p a r t i c u l a r job has been suggested as the c r i t e r i o n . T h i s assumption c o u l d be used i n the p r e s e n t model by keeping r e c o r d s of worker's promotions. The m o d i f i c a t i o n would only be necessary i f an e x i s t i n g o r g a n i z a t i o n wanted to i n i t i a t e manpower p l a n n i n g . I f the o r g a n i z a t i o n used the model from the time i t s t a r t e d ( I . e . , when a l l employees had zero s e r v i c e ) the end r e s u l t would be i d e n t i c a l to promoting by l e n g t h of s e r v i c e i n the f i r m . Promotion C o n s t r a i n t . I t was assumed t h a t workers must be p r e s e n t l y employed a t the next lower job category i n order to be e l i g i b l e f o r promotion. The e f f e c t o f t h i s 50 assumption was to constrain the number eligible for promotion and prevent an unrealistic number of promotions from occurring. A constraint was introduced to limit the fraction of the labour force that could be promoted in any one time period. Thus i f the decision-maker f e l t that promoting more than f i f t y percent of a group would be detrimental to the organization he could introduce a constraint of this size. When the requirements exceeded the constrained supply the difference would be reported as a shortage. The results could then be analyzed and a decision made to promote the extra workers required, to tolerate the shortage or to promote additional workers in earlier periods. Provision was made to specify the constraint for each job category. Quit Bate for Trainees. The probability of a trainee quitting was assumed to be the same as the probability for a member of the regular work force. Hiring. It was assumed that workers would only be hired for the lowest job category and that the requirements in higher categories would be met entirely by internal promotions. The assumption was made in order to avoid considering the cost implications of hiring skilled employees versus training. The assumption also c l a r i f i e d the basis for promotion. If employees were hired for higher job categories they would be eligible for promotion to the next category even though they had less seniority than other workers. With the present assumption, employees in higher job categories 51 are always more senior. The assumption that workers can only be hired for the lowest job category Is r e a l i s t i c for the type of organi-zation under consideration. In most industrial organizations the production workers are unskilled or semi-skilled. The type of work differs between plants and consequently employ-ees must receive some training within the plant In order to be able to perform their job. It is also common for those plants, whether unionized or not, to consider seniority in determining promotions. The hiring assumption is valid under these conditions. Another type of employee is the specially-trained skilled worker;" such as a journeyman trades-man. In most Instances, workers are not promoted into this group. In effect they are a separate, one-level hierarchy. The remaining group, which includes skilled production workers and c l e r i c a l personnel, may be either hired or promoted from within. The assumption of hiring only at the lowest level would not be entirely applicable unless the organization had an inviolate rule of promotion from within the organization. Training Time. It was assumed that a l l workers being promoted to or hired for a job category would receive equal training. Although this assumption would only be s t r i c t l y correct If a l l employees had equal a b i l i t y and equal experience, It was a good approximation and was consistant with the previous assumptions. 5 2 Demotions and Lay-offs. The demotion and lay-off aspects of manpower forecasting are neglected in the model. In many organizations the work force is either stable or increasing. In others, where the work force is steadily decreasing, the organization relies on natural a t t r i t i o n to decrease the force rather than suffer the costs of demotions. Under either of these circumstances a demotion or lay-off procedure Is unnecessary. Nevertheless there are organi-zations with seasonal fluctuations in their labour requirements and these groups should be considered in a general model. In contrast to the hiring and promotion procedure where the policy considerations are f a i r l y uniform, lay-off and demotion procedures are subject to a number of varied constraints. As mentioned in Chapter II, demotions could be from each category or by total seniority. Workers laid off could be subject to rehiring and a separate quit rate used. A constraint could be introduced so that lay-offs would not occur unless the number to be l a i d off exceeded a certain size. Because of the sizable intangible costs incurred by lay-offs the organization might be reluctant to lay-off or demote employees for short periods of time. None of these considerations are universally applicable. Specific organi-zations may have policies which incorporate any combination of factors. Rather than select a particular sub-set of policies for the model i t was decided to omit the demotion and lay-off aspects entirely. 53 Training Time Limitation. It was assumed that a training delay would exist In the lowest Job category. The primary reason for the assumption was that the FORTRAN computer language was unable to handle a variable with the subscript " 0 " (zero). If there were no training delay when workers were hired, the workers would have to be advanced from length of service "zero" to length of service "one" in the Labour Force Update procedure. This could only have been accomplished by making the model considerably more complex and by a r t i f i c a l l y advancing the time periods in order to treat input data at time period "zero". The training delay has been defined to include a l l time lags between the promotion decision and when the employee started work. Even i f training was not required, a delay would occur i n the lowest category due to the time consumed in recruiting and selecting new employees. Therefore the assum-ption was thought to be r e a l i s t i c for most organizations. Calculation Procedure. In order to define a specific calculation procedure i t was assumed that ( 1 ) a l l hiring, promotions and training occur at the start of the time period, ( 2 ) employees quit at an even rate throughout the time period. Thus, i f an average of 1 0 0 workers were required to meet production forecasts, and i f 10 workers were expected to quit, the labour force would be 1 0 5 men at the start of the period and 95 at the end. Hiring Constraint. A hiring constraint was Introduced 54 to limit the number that could be hired in any period. It was assumed that the size of the constraint would vary for different time periods. II. NOMENCLATURE The following terms were used in the construction and description of the model. T J I K JMAX IMAX KMAX DEL(K) P ( D HMAX(J) G(K) R(K,J) MEN(K,I,J) TR(K,I) PPSTAY(K,I) = the current decision period. = the future time period. = total length of service with the organization. = number of job categories. = time horizon of the programme. = most senior length of service group. = highest position in organization hierarchy. = training delay in category K. = probability of staying to next time period given length of service - I. = maximum number of hires allowed in period J. = fraction of employees in category K that are available for promotion. = work force required in category K at time J. = regular labour force In category K with seniority I at time J. = labour force being trained for category K. = the probability of a worker with seniority I and in job category K staying through the training period. 55 RPRO AVPRO J 1 PHIRE HIRE EXMEN RETR SHORT TMEN(K,J) TPRO(K,J) QUITS(K,J) NWORK = number of promotions required. = number of employees available for promotion. = the time period which must be considered when promoting for period J. = number of hires desired. = actual number hired at time J. = the number of workers in a regular work force that are expected to stay to the end of period J. = the extra number of workers required at the start of period J to satisfy the labour force requirement in that period. = the expected shortage in category K at time J. = the total number of workers in category K at the end of period J. = the total number of workers promoted to satisfy the requirements of category K at time J. = number of workers quitting category K in period J. = the average number of workers available for work after promotions and quits have been considered. III. BUILDING THE MODEL General Perspective The manpower model Is essentially a forecasting device based on the number of workers currently available in each Job category, future labour requirements, the quit rate and the organizations policies. Because the calculations in 56 a particular decision period affect the lower job categories the decision period must be far enough into the future to allow these adjustments to take place. The time difference between the current time and the decision period must be equal to the sum of the time lags for each category below the one being considered. For example, assume that there are two job categories with training delays of two months each. In time period T = 1, the decision period for category K = 2 Is period J = T + DEL(l) + DEL(2) = 5- When K = 1 is considered, J = T + DEL(l) = 3. This may be shown in graphical form as follows: Figure 3-1 Timing of Decisions 57 Basic Equations Before proceeding to a discussion of the movement of workers between job categories at various time periods the basic relationships in each decision node (i.e., for a particular K and J) must be discussed. The interactions at a decision node are illustrated in Figure 3 - 2 . Q U IT5CK.J) Figure 3-2 Typical Decision Node K job category number. J = decision period number. P(J) = probability of staying through period J. H(K,J) = average number of workers required. MEN(K,J-1) number of workers at the end of period J - l . X(K,J) number of workers required at the start of period J. QUITS(K,J) = number of workers quitting during period J. TE(K,J) = number of promotions required to satisfy the requirement. TPBO(K,J) = number of workers to be promoted from category K-l. 58 Assuming that the probability of staying depends on the decision period rather than worker seniority, the basic relationships may be written as follows: 3 - 1 X(K,J) = MEN(K,J-1) + TR(K,J) 3 - 2 QUITS(K,J) = (1-P(J))*X(K,J) 3 - 3 MEN(K,J) = P(J)*(X(K,J)) 3 - 4 TPRO(K,J) = TR(K,J)/F(J-DEL(K))*—*P(J-1) If employees are assumed to quit at a constant rate during the period then; 3 - 5 R(K,J) = X(K,J) + MEN(K,J)/2 Since MEN(K,J-1), P(J), AND R(K,J) are known the basic equations may be solved in the following manner: From equations 3-3 and 3-5, R(K,J) = X(K,J) + P(K)*(X(K,J))/2 Therefore X(K,J) = 2*R(K,J)/(1 + P(J)) The other equations may now be solved 3 - 1 TR(K,J) = X(K,J) - MEN(K,J-1) 3 - 2 QUITS(K,J) = (1 - P(J))*X(K,J) 3 - 3 MEN(K,J) « P(J)*X(K,J) 3 - 4 TPRO(K,J) = TR(K,J)/P(J-DEL(K)*---*P(J-l) Sample Calculation The use of these equations in a sample calculation w i l l serve to demonstrate how they are used in the manpower 59 model. Assume that there are two job categories with training delays DEL(l) = 1 and DEL(2) = 2. When T = 1, the decision nodes for the job categories are: K = 1 J = T + DEL(l) = 1 + 1 = 2 K = 2 J = T + DEL(l) + DEL(2) = 1 + 1 + 2 = 4 The decision nodes are (1,2) and ( 2 , 4 ) . Information is required for MEN(K,J-1), R(K,J) and P(J=1, JMAX) where JM/SX i s the last decision period. Let MEN(2,3) = 50 MEN(1,1) = 100 R(2,4) = 60 R(l , 2 ) = 100 P(J) = 0 . 9 0 for a l l time periods. Consider the highest job category (Decision node ( 2 , 4 ) ) , X(K,J) = 2*(R(K,J))/(1 + (P(J)) X(2,4) = 2(60)/(l + .90) X(2,4) = 63 TR(2,4) = X(2,4) - MEN(2,3) =63 - 50 6o TPRO(2,4) = TR(2 ,4)/(P(2)*P(3)) = 13 /(.9*.9) = 16 Q,UITS(2,4) = (1 - P ( 4 ) ) * X ( 2 , 4 ) = (1 - . 9 ) * 6 3 = 6 MEN(2,4) = P ( 4)*X ( 2 , 4 ) = . 9 * 6 3 = 57 Assuming that the employees quit at an even rate throughout the period the average number of men available for work i s ; NWORK = MEN(2,4) + QUITS(2,4)/2 57 + 6/2 = 60 As would be expected this is the same as R ( 2 , 4 ) , the work force required. Since 16 men were promoted from MEN(1,1) the revised number of men in MEN(1,1) is (100 - 16) or 8 4 men. The number who quit during training i s TPR0(2,4) - TR( 2 ,4 ) or 3 men. The i n i t i a l conditions together with the result of the f i r s t calculations are illustrated i n Figure 3 - 3 ' The next job category (K=l) may now be considered. X(l , 2 ) = 2(R ( 1 , 2 ) ) / ( 1 + P(2)) = 2 ( 1 0 0 ) / ( 1 + .90) = 105 K -L a b o u r Pool S O /I „\ I O O / I V y T - 5 F i g u r e 3-3 Sample C a l c u l a t i o n 62 TE(1,2) = X(l , 2 ) - MEN(1,1) = 105 - 84 = 21 Since K = 1, TPRO is the number hired TPR0(1,2) = TR(1,2)/P(1) = 2 1 / . 9 0 HIRE = 23 QUITS(1,2) = (1 - P ( 2))*(l , 2 ) = (1 - .9)*105 = 11 MEN(1,2) = P(2)*X(1,2) = .9*105 = 94 NWORK = MEN(1,2) + QUITS(l,2)/2 =94 + 11/2 = 100 This completes the calculation for T = 1. The entire procedure i s then repeated for a number of time periods as illustrated in Figure 3-k. The General Model The construction of a general manpower planning model involved the programming of the manpower calculation equat-ions with the quit rate as a function of the length of service. The policy assumptions and constraints discussed previously were introduced into the model. The model is F i g u r e 3-4 Sample C a l c u l a t i o n f o r Two Time P e r i o d s ON 6 4 described in simplified flow charts on the following pages. Detailed flow charts and a l i s t i n g of the computer programme are included in Appendix A. The FORTRAN "DO" statement was used in the flow charts to reduce the number of pages required and to simplify the drawings. Unless otherwise noted, the processing operation referred to in the "DO" statement immediately follows the statement. The traditional flow charting technique and the modified style used In this study are illustrated below. D o U4-1 - e o V e O p € C«xV l o T I , = \ , o D O 1IM-I F i g u r e 3-$ M o d i f i e d Flow C h a r t i n g Technique 65 c S T A R T I PPSTAY(K,X> Rend I M A K , K M AX , JHAX,Pf tJ ^(K,J\, G(K), T - O I D O l I T L . L E , DO U4-I I D O \ \TL\ X =- l , I K A X PPSTAVIK.X) - l . O I — P C X - H ) * -#P(X+DEL(K)) 5 C O N T I N U E I I K -K ty \Ax I ~E.Xt-V6.N ) I dt«c. IS IOm I t N f t f t L F 66 P ro-rv\ o V i o n P r o c * ol L A r e D « c \« , v o-v-i •v»odLt ^ o r Vor pro->-r>oVio->i • L E . •o 1 i \ - , J - \ -I ftV P R o = . 4-1 — A V P R O R P R o = R E T R J I AVPR.O -t> V L-De-L(l)+\ 5 P H \ R E ( R E T R / P ( I ) / P P S T A Y O . V ) H \ R E — PH I RE T R v t K . X ) _ -t>l V S t t © R T -R E T R / P C X ) -T ? R O ( « , 0 j =^  H I R E . 67 I_-X.t-\A-X IT» cj roup X ^ Z.=MENW,X,ilJ U-3 P r o - v Y - i o - V « _ o ( l Act j t A S ^ r TR ( K , x ) = ME.K(K,X,J>) PRO-- PRO-* RP RO = R P R O - X I - X - \ A A -r% cxAa - n o f m a . ! C o • » d \ Vio-n «lvj.e -Vo ro«A-n4 ->-v»oj e r r o r s T?RO(K+\,J) - PRo I S3. H - RP Ro / PPST AV(K+\,X> I I * A A W -y~LTR(K,X) *PCT*OE,UKl-uQ Q,\ -e.-v-.el o 3 ? ^ N c m A NT -R ^ M - N H A L F M « - n c t « S t r - e o l R&1R=RET^ • Y - N G t t - i A N T A c X ) u . « » \ R £ T t \ ^re>r "V \" c \ i € e S - O 4-68 R, -e. -nrt o V « f W« IO.V>O<A. r AU o r ^ « r s i * » - « r € pro-mo I D O 5«H 'tor -K>-e--ic+ I = o > H E N ( K , I , J > ) X=.\ I p-g rioet, 5 i n CTR(K,x)« V r o w p"«r«odl I 0 0 b o l 1 - l , I M A X I = MEH(K,X,J-V* P<X+l)+LTRCKX) #PPSTAy(K,X) * P C X - v i Q T M E N ( K, J ) : X=XMA* y^>en(K,i,j) I I I p » n opt,  QU ITS(K,J) D E M O T 1 0 M ujorK ? o r « - f c a u s i l <M-t v - n "5© TPRo(K,J)= o H \ R E - o SHoM- O X 69 7 Q U i T S . T P R O , R E T R, E X M E H , S H O R T , H I R E . . K - K - l T l o o L c CX.—^ o l r-e.p-eo.-V- c U DO - 5 0 \ l K \ J - DE.l_(Ni • J 1 15 1 W r i + e M E N ( K , X , J ) K= 1, KM AX X - \, I M A X T - O \ 1 D O 3<=>e. 1 K = \, K MAX J = J + DEL( K) J = J Ad. p-e r \ od. (J .L.E.J M^ X) s r o v - V V i e -v-i-a-at-V - t i - n o « p - e r i o o l . I S T O P 70 Summary The model developed In this chapter was constructed to forecast manpower requirements i n situations where the trainees did not a f f e c t the production rate. The assumptions upon which the model was based were made for one of three reasons. 1. General assumptions regarding a b i l i t y and productivity were made because the organization would not have the information to assess these factors. 2. Simplifying assumptions were made to delineate a model that would be applicable to non-managerial personnel. 3. S p e c i f i c assumptions were made to define organizational p o l i c i e s and the c r i t e r i a for h i r i n g and promotion. These assumptions were combined with the manpower equations to form a manpower forecasting model. The model was designed so that the size of the system parameters could be varied without modifying the programme. CHAPTER IV OPERATION OP THE MODEL The manpower f o r e c a s t i n g model d e s c r i b e d i n Chapter I I I was thoroughly checked out f o r p o s s i b l e e r r o r s i n l o g i c or i n programming. Once these e r r o r s were c o r r e c t e d , a number of computer runs were performed. These runs were of two t y p e s . The f i r s t type was to demonstrate how the model worked under v a r i o u s c o n d i s i o n s . The second type was d i -r e c t e d a t the i n v e s t i g a t i o n of how some paramenters, s p e c i f i c a l l y the q u i t r a t e and the t r a i n i n g time, a f f e c t e d the model. The. r e s u l t s of these s t u d i e s are d e s c r i b e d i n the f o l l o w i n g s e c t i o n s . I . SAMPLE CALCULATIONS The purpose of t h i s study was to demonstrate how the model performed a s e t of c a l c u l a t i o n s . Input Data. The g e n e r a l input data f o r t h i s s t u i y was as f o l l o w s : Number of job c a t e g o r i e s - 5. Labour Force Requirement - 2 5 0 , 2 0 0 , 1 5 0 , 1 0 0 , 5 0 , f o r job c a t e g o r i e s one to f i v e r e s p e c t i v e l y . Regular Labour Force - 2 5 0 , 2 0 0 , 1 5 0 , 1 0 0 , 50 f o r job c a t e g o r i e s one to f i v e r e s p e c t i v e l y . Labour Force s e n i o r i t y - 1 . .Promotion C o n s t r a i n t - 0 . 5 Labour F o o l S i z e - 500 per time p e r i o d . Time H o r i z o n - 24 T r a i n l n g Delay - 1 , 1 , 2 , 2 , 3 f o r job c a t e g o r i e s one to f i v e r e s p e c t i v e l y . P r o b a b i l i t y of S t a y i n g - a q u i t f u n c t i o n which peaked when the l e n g t h of s e r v i c e was s i x months and seventeen months was used. T h i s f u n c t i o n i s shown as the "medium" l e v e l q u i t r a t e i n F i g u r e 4 - 1 , page 7 8 . In order to demonstrate the a b i l i t y of the model to a d j u s t to v a r i a t i o n s i n the system, the input data was m o d i f i e d i n the f o l l o w i n g manner: 1. The l a b o u r f o r c e r e q u i r e d i n category f o u r i n time p e r i o d s e i g h t , nine and ten was Increased from 100 to 2 0 0 . 2 . The maximum number of workers t h a t could be h i r e d i n time p e r i o d two was reduced from 500 to 2 0 . The c a l c u l a t i o n s produced by the model i n the f i r s t f o u r time p e r i o d s are shown i n Table 1 . P e r i o d One. I n s p e c t i o n of Table I r e v e a l s t h a t the model a d j u s t e d the work f o r c e so that the average number of p r o d u c t i o n workers (NVJORK) e q u a l l e d the l a b o u r f o r c e r e q u i r e -ments (R(K,J)) f o r the time p e r i o d . Because i t was assumed that employees would only be h i r e d and promoted at the s t a r t of the p e r i o d w hile employees q u i t a t an even r a t e , the number of workers at the end of the p e r i o d (EXMEN) i s l e s s than the i n i t i a l l a b o u r f o r c e . T h i s decrease i n the work f o r c e i s TABLE I SAMPLE CALCULATION OUTPUT DATA DECISION JOB TIME REQ. NWORK TMEN QUIT TPRO RETR SHORT HIRE PERIOD CAT. PER 1 5 10 50 51 50 1 1 1 0 0 1 4 7 100 100 99 2 2 2 0 0 1 3 5 150 151 149 3 4 4 0 0 1 2 3 200 200 198 4 6 6 0 0 1 1 2 250 251 248 5 9 9 0 9 2 5 11 50 50 49 2 1 1 0 0 2 4 8 200 162 158 7 74 104 37 0 2 3 6 150 154 151 6 91 82 0 0 2 2 4 210 208 203 9 109 105 0 0 2 1 3 250 156 152 7 20 116 96 20 3 5 12 50 51 49 3 4 3 0 0 3 4 9 200 199 193 12 59 51 0 0 3 3 7 150 149 144 9 71 61 0 0 3 2 5 200 198 192 12 77 72 0 0 3 1 4 250 253 249 7 185 181 0 185 5 13 50 50 48 4 4 3 0 0 4 10 200 200 191 17 23 19 0 0 4 3 8 150 149 143 12 41 34 0 0 4 2 6 200 197 189 16 59 55 0 0 4 1 5 250 250 245 10 66 65 0 66 5 5 14 50 51 48 5 7 5 0 0 ** REQUIRE DEMOTION PROCEDURE**** 5 4 11 100 175 166 18 0 -75 0 0 5 3 9 150 150 142 15 18 14 0 0 5 2 7 200 200 190 19 4l 38 0 0 5 1 6 250 251 245 12 54 53 0 54 8 5 17 50 50 48 4 5 4 0 0 -*# **REQUIRE DEMOTION PROCEDURE*** 8 4 14 100 110 105 9 0 -9 0 0 8 3 12 150 150 143 13 16 .14 0 0 8 2 10 200 199 188 21 42 37 0 0 8 1 9 250 251 244 14 57 56 .0 57 9 5 18 50 51 49 3 5 4 0 0 9 4 15 100 100 97 6 3 3 0 0 9 3 13 150 150 145 9 16 14 0 0 9 2 11 200 197 187 20 40 36 0 0 9 1 10 250 251 244 14 55 54 0 55 74 reflected In the number of hires required and the number of quits. A total of fifteen workers quit in the time periods under consideration while only nine were hired. Nevertheless the work force requirements in each job category were met. (In most cases the workers available (NWORK) do not exactly equal the requirement due to rounding off errors in the programme.) Period Two. The calculations' for the second time period were upset due to several factors. The work force required in job category four was increased from one hundred to two hundred men. The promotion constraint on category three restricted the number available for promotion to half the 149 men in category three at the end of period five. Seventy-four men were promoted from category three to category four. These promotions were insufficient to meet the require-ment and the labour force shortage was calculated. It should be noted that although seventy-four men were promoted out of category three the two month training time resulted in eleven of the seventy-four quitting during training. The actual shortage that occurred in category four at time period eight was thirty-seven men. The model then proceeded to the next category (three) and promoted the necessary men to satisfy the requirement. Rounding off errors resulted in there being a difference of four between the requirement and the number at work. (1.50 versus 154). 75 I n category two the l a b o u r f o r c e requirement was i n c r e a s e d to 210 men. Because of the l a r g e number promoted from c a t e g o r y two to category three, 109 men had to be promoted i n t o category two to meet the requirement. A c o n s t r a i n t had been p l a c e d on the system so t h a t no more than twenty men co u l d be h i r e d i n p e r i o d two. As i l l u s t r a t e d i n the l a s t l i n e of the p e r i o d two data, twenty men were h i r e d but t h i s was i n s u f f i c i e n t to f i l l the vacancies caused by the promotions and a n i n e t y - s i x man shortage r e s u l t e d . In summary, the r e s u l t s are what one would expect. I f an attempt i s made to i n c r e a s e the la b o u r f o r c e by 110 men when only 20 can be h i r e d , a shortage w i l l r e s u l t . The i n t e r e s t i n g p o i n t i s that, due to the t r a i n i n g d e l a y s f o r the v a r i o u s job c a t e g o r i e s , a work f o r c e i n c r e a s e a t category f o u r i n time p e r i o d e i g h t causes a shortage to develop a t category one i n time p e r i o d t h r e e . P e r i o d s Three and Four. The next s e t of c a l c u l a t i o n s i n d i c a t e the d e c i s i o n s made i n p e r i o d t h r e e . The h i r i n g c o n s t r a i n t was r e l a x e d and a s u f f i c i e n t number were h i r e d and promoted to a l l e v i a t e the shortages. The work f o r c e r e q u i r e d and the f o r c e a v a i l a b l e are a g a i n i n balance. The d e c i s i o n s made i n p e r i o d f o u r a l s o h o l d the work f o r c e i n balance. P e r i o d F i v e . The l a b o u r f o r c e r e q u i r e d i n category f o u r a t time p e r i o d e l e v e n was reduced from two hundred workers to one hundred. T h i s meant t h a t there was an excess i n 76 category f o u r and the demotion procedure would be r e q u i r e d to a d j u s t the work f o r c e . P e r i o d s E i g h t and Nine. I t can be seen from Table I that there was s t i l l an excess of men i n category f o u r . T h i s excess was g r a d u a l l y being reduced as the workers were pro-moted to category f i v e and as the workers i n category f o u r q u i t . P e r i o d nine demonstrates a r e t u r n to the normal s i t u a t i o n once the excess i s used up. I I . EFFECT OF PARAMETERS ON THE MODEL The e f f e c t of changing some of the model parameters was a l s o i n v e s t i g a t e d . The f i r s t group of s t u d i e s c o n s i d e r e d the e f f e c t of d i f f e r e n t q u i t r a t e s on the number of workers h i r e d , the number promoted, the number t h a t q u i t and the work f o r c e s t r u c t u r e . The second group of s t u d i e s c o n s i d e r e d the e f f e c t of t r a i n i n g time on the same f a c t o r s . E f f e c t of Q.ult Rate The e f f e c t of the q u i t r a t e on the manpower system was i n v e s t i g a t e d by running the model with three d i f f e r e n t q u i t r a t e s while the other f a c t o r s remained constant. Input Data. The input data f o r these s t u d i e s was the same as i n the p r e v i o u s study except t h a t a''one month t r a i n i n g d elay was used f o r a l l job c a t e g o r i e s and the promotion c o n s t r a i n t was removed, i . e . , G(K) = 1.0. The three q u i t r a t e s were s p e c i f i e d as "low", "medium" 77 and "high". The "medium" r a t e was twice the "low" r a t e and the "high" was twice the "medium" r a t e . The shape of the q u i t f u n c t i o n and the ab s o l u t e s i z e of the three r a t e s are i l l u s t r a t e d i n F i g u r e 4-1. Output Data and A n a l y s i s . The computed r e s u l t s from the three runs were analyzed by t o t a l l i n g the number of promotions determined i n each time p e r i o d . I t must be noted t h a t , because the imodel c o n s i d e r s a f u t u r e d e c i s i o n p e r i o d i n making the c a l c u l a t i o n , t h i s i s not the t o t a l number t h a t would a c t u a l l y be promoted i n the time p e r i o d . The promotions were p l o t t e d a g a i n s t time f o r each of the three q u i t r a t e s as shown i n F i g u r e 4 - 2 . The t o t a l number of h i r e s and q u i t s were p l o t t e d i n a s i m i l a r manner as shown i n F i g u r e s 4 - 3 and 4 - 4 r e s p e c t i v e l y . A l l three graphs show a ge n e r a l trend f o r the number of promotions, q u i t s and h i r e s to vary with the p r o b a b i l i t y of the worker, q u i t t i n g . T h i s trend i s due to the f a c t t h at the work f o r c e s t a r t e d out with one month's s e n i o r i t y . I f the worker's s e n i o r i t y had been d i f f e r e n t or i f they had been i n a number of s e n i o r i t y groups the tendency to f o l l o w the q u i t r a t e p r o b a b i l i t y would have been l e s s pronounced. In s p i t e of t h i s l i m i t a t i o n , which mainly a f f e c t s the e a r l i e r time p e r i o d s , the e f f e c t of the d i f f e r e n t q u i t r a t e s i s q u i t e n o t i c a b l e . The graphs a l l show t h a t the number of workers h i r e d or promoted i n c r e a s e s more than the q u i t r a t e . For example, i n time p e r i o d e i g h t e e n , changing the q u i t r a t e 82 from the "low" to the "medium" level ( a two-fold increase) increases the number hired from 13 to 38, the number promoted from 25 to 73 and the quits from 10 to 34. Doubling the quit rate from the "medium" to the "high" level produces the same relative increase in the hires and quits but an even larger increase in the number promoted. The affect of the quit rate on these factors is shown i n Figure 4-5. From this graph i t can be seen that as the quit rate increases the number of quits increases linearly, the number hired increases slightly faster and the number of promotions increase exponentially. Effect of Training Time The effect of training time on the manpower system was Investigated by varying the training delay while other factors were held constant. Input Data. The input data for this study was the same as in the previous studies except that (1) the "medium" level quit rate was used, (2) the labour force seniority was one month for category one, two months for category two and so on. The training delays were specified as one month and two months in the f i r s t and second runs respectively. It was assumed that the delay would be the same for each job category. Output Data and Analysis. The total number of hires, quits and promotions were determined as the previous investigation and are shown in Figures 4-6, 4-7, and 4-8 87 respectively. On the basis of this information i t would appear that the size of the training delay has l i t t l e effect on the number that quit. The effect of the training delay on the number promoted and hired was more noticable. As would be expected, a longer training time meant that more employees would be in training at any one time. The reason for the higher rates of change, both when promotions were increasing and decreasing, was not clear but It appeared to be related to the seniority distribution of the i n i t i a l labour force. The variation in the number hired is due to the variation in the number of workers being trained. Conclusions The test runs indicated that the model had been properly constructed to simulate the assumed conditions and policies. Preliminary investigations indicated that the size of the quit rate function had a much greater effect on the number of promotions than on the other factors. CHAPTER V AREAS FOR FUTURE DEVELOPMENT The areas requiring further development were divided into three groups. 1 . Developments which could be incorporated into the existing model. 2. Construction of a cost-optimizing manpower model. 3. Integration of the manpower model into aggregate production planning techniques. I. DEVELOPMENT OF THE EXISTING MODEL The manpower forecasting model developed in this study-was a simple model of the manpower function based on the most probable relationships for personnel below the managerial level. These relationships, and the reasons for them, have been discussed in Chapter III under the heading "Specific Assumptions". In several cases, alternative assumptions could have been made and would have produced a more complex model. The primary benefit of including some of these alternatives in the model would be to describe the policies of specific organizations. The inclusion of alternatives would also enable the organization to investigate the effects of various policies on i t s personnel structure. A number of alternate policies, which could be included in the model, 89 w i l l now be considered. Q.ult Bate. The probability of an employee quitting was assumed to be a function of the total length of service and independent of whether an individual was working or being trained. If the quit rate was a function of the length of service In a particular position,the model would have to be modified so that the "I" subscript in MEN(K,I,J) referred to the elapsed time since the worker was promoted. A different quit rate for trainees could be introduced by specifying another P(I) function in the PPSTAY(K,I) calcu-lation. The quit rate could also be related to the different job categories or to seasonal factors by adding additional subscripts. Hiring. It was assumed that workers were hired for the lowest job category and that the hiring constraint was a function of time. In order to hire workers for job cate-gories other than K = 1 , a criterion for hiring and promoting workers would be required. For example, the criterion might be that workers would be promoted i f they were available and that the extra workers required would be hired from outside the organization. The hiring constraint would have to be specified for both the job category and the time period. The training delay for the new hires would have to be stipulated and an additional PPSTAY(K,I) calculated for this group. The hiring constraint could be altered independently of the hiring procedure. Besides being specified for each 90 job category, It could be made a function of the hiring rate i n past periods by subscripting the HIRES figure. An equation to weight HMAX over a number of periods would also be required. Promotions. Promotions were assumed to depend upon plant seniority. If i t was desirable to promote according to job category seniority while maintaining the quit rate as a function of total seniority an additional subscript would be required. Because FORTRAN names can only have three subscribed variables, the MEN(K,I,J) name would have to' be changed. This could be accomplished by specifying a name, such as MEN 1 , etc., which would indicate the job category that the men were in. An additional subscript, such as job category seniority, could then be added to the regular labour force. Training Delay. A training delay in the f i r s t job category was assumed to occur due to the time lag between the decision to hire and the time when the new employees started to work. Although i t is improbable that this assumption would need to be changed, i t could be avoided by a r t i f i c a l l y advancing the time periods and seniority records by one time period. Labour Requirement. The organization was assumed to be flexible enough to permit i t to hire and promote employees at the start of each time period. As employees quit, the size of the labour force would decrease and the force would 91 be adjusted at the start of the following period to maintain an average production rate. This procedure would not be entirely suitable for organizations who wished to maintain a steady labour force throughout the period. The employees would have to be hired, promoted and trained so that the change in labour force (NCHANG) was satisfied at the start of the period and the number to compensate for terminations were introduced during the period. An i l l u s t r a t i o n of the promotion and quit patterns and their effect on the size of the labour force is shown in Figure 5-1• The diagram shows that the total number of promotions and quits is not affected by the desired labour force so long as the same average number of workers are employed during the period. The constant labour force case could be introduced into the model by specifying the number of trainees required (BETE) as being equal to (NCHANG + NLEAVE) and by specifying the average number of workers (NWOB.K) as being equal to the labour force at the end of the period (TMEN(K,J)). Demotions and Lay-offs. The procedure for demoting and laying-off workers in the model is essentially the reverse of the procedure for hiring and promoting. The demotion decision occurs when the number of workers available exceeds the requirement in a particular period. The workers are demoted by removing them from the regular labour force in 92 V A R Y I N G L A B o n ft F O R C E C A S E B . O \ o OH +• 5 R(K,J) Pro -i-v^o -V i R-e OJIA. \ c LexV)otA.r F o r c e C O N S T A N T LA6001R F O R C E C A S E * © 1 R(K,J) T = o T i V L a . V o u . f F o r c e T=0 T i l F i g u r e 5-1 E f f e c t o f A l t e r n a t i v e P r o m o t i o n P a t t e r n s on t h e R e g u l a r Work F o r c e 93 accordance with the organization's policy. For example, i f demotions are based on seniority, the least senior employees would be demoted f i r s t . A record of the number of workers demoted, their job category, their seniority and the time period must be kept so that the workers can be introduced into a lower job category at the proper time period. The decision to lay off workers requires an additional step i f these workers must be re-hired before new employees are hired. In this case, the workers must be stored in. a "lay-off pool" and recalled from this pool in preference to hiring new employees. Provision should also be made for the laid-off worker to sever his relationship with the firm. In summary, modifying the model to include provision for demoting and laying-off workers does not present any real problems. These procedures were not included in the original model because the policies and c r i t e r i a for the decisions vary between different organizations. Productivity and Labour Requirements. The decision-maker was assumed to be able to forecast the organization's : labour requirements. In order to make this forecast the decision-maker must make an implicit assumption regarding the productivity of the individuals in the work force. The model developed in the study assumed that experienced and trained, inexperienced workers were equally productive. This would not occur unless the worker had been trained until he attained his maximum contribution to production. 94 The e f f e c t of i n c r e a s i n g p r o d u c t i v i t y w i t h experience c o u l d be represented i n the model by s p e c i f y i n g the l a b o u r f o r c e requirement i n terms of "worker e q u i v a l e n t s " . Records would have to be kept f o r the l e n g t h of s e r v i c e i n each job cate g o r y . Promotions would be based upon the number of "worker e q u i v a l e n t s " r e q u i r e d i n each p e r i o d . One of the problems i n adding v a r i a b l e p r o d u c t i v i t y to the p r e s e n t model i s t h a t , as the workers become more experienced, there i s a p o s s i b i l i t y t h a t t h e i r p r o d u c t i v i t y w i l l i n c r e a s e f a s t e r than the workers q u i t o r are promoted. T h i s would l e a d to an excess of "workers e q u i v a l e n t s " and some employees would be demoted or l a i d o f f . A model c o u l d be c o n s t r u c t e d to a v o i d demotions by c o n s i d e r i n g present and f u t u r e d e c i s i o n s s i m u l t a n e o u s l y . The model would r e q u i r e a s e t of c o s t f u n c t i o n s and a dynamic programming f o r m u l a t i o n o f the manpower equations. I I . A COST-ORIENTED MODEL The next step i n i n c r e a s i n g the s o p h i s t i c a t i o n o f the model i s to i n c l u d e c o s t I n f o r m a t i o n . The a d d i t i o n of co s t equations to the presen t model would p r o v i d e a u s e f u l t o o l f o r a n a l y z i n g the r e l a t i v e importance of h i r i n g and t r a i n i n g c o s t s under v a r i o u s c o n d i t i o n s . The model c o u l d a l s o be used f o r a s s e s s i n g c o s t f l u c t u a t i o n s as the s i z e of the l a b o u r f o r c e changed and f o r f o r e c a s t i n g o p e r a t i n g budgets. I f the model was expanded to i n c l u d e the oth e r p o l i c y v a r i a b l e s mentioned i n the pr e c e e d i n g s e c t i o n the e f f e c t o f 95 various sets of policies could be evaluated in terms of dollars rather than men. Cost Optimization. The inclusion of cost equations would also make the model amenable to a number of optimizing techniques. Hanssmann and Hess have applied linear program-ming to manpower planning.^ Holt and his co-workers developed a procedure for optimal planning when costs were quadratic 2 rather than linear functions. Both reports assumed a homogeneous, one job category work force and that employees could only leave the work force by being l a i d off. Never-theless, the fundamentals of the techniques should be applicable to more complex manpower models. The most promising optimizing technique for manpower planning appears to be dynamic programming. In addition to cost optimization, the technique, can solve sequential decision problems.3 This would permit a considerably more elaborate model to be constructed because i t would allow present and future conditions to be evaluated simultaneously. Trainee !Fred Hanssmann and Sidney W. Hess, "A Linear Program-ming Approach to Production and Employment Scheduling," Management Technology, I, (January, i960), pp. 46 - 51. 2Charles C. Holt, Franco Modiglianl and Herbert A. Simon, "A Linear Decision Rule for Production and Employment Scheduling", Analyses of Industrial Operations, Edward H. Bowman and Robert B. Fetter, editors. (Homewood, I l l i n o i s , Richard D. Irwin, Inc., 1959), P P « 169 - 199• 3Q. Hadley, Nonlinear and Dynamic Programming;. (Reading, Massachusetts, Add!son-Wesley Publishing Company, Inc., i960), P P . 375. 96 productivity and the effect of experience on production rates could be included in the model. An additional advantage to a dynamic programming formulation of the model l i e s in the use of the model in a number of investigations. Optimal scheduling of the work force would lead to lower labour costs, The analysis of policy considerations would be improved because the model would determine the optimal schedule for each set of policies. Cost Equations. The main d i f f i c u l t y in developing a cost oriented manpower model is the identification and measurement of relevant costs. Gaudet has published a com-prehensive report concerning the determination of recruitment, h selection, indoctrination, and severance costs. The major problem in these areas is to separate the relevant costs from the total costs of the personnel department. Gaudet dis-cusses some of the procedures which might be used to determine the average cost per employee and the use of a "selection ratio" procedure for determining total costs. The selection ratio procedure is actually of limited usefulness because different recruitment methods and different numbers of appli-cants for various Jobs cause the ratios to vary.-* The advent of high speed data processing has led to the development of h Frederick J. Gaudet, Labour Turnover: Calculation  and Cost. (New York, American Management Association, i 9 6 0 ) . 5 l b l d . . pp. 42. 97 procedures for keeping accurate records on the number of applicants at various stages in the hiring process.6 The use of these procedures by an organization would enable i t to keep accurate records of the tangible costs in the hiring and severance processes. The manpower model must also consider the effect of i turnover on the production departments. Inexperienced personnel w i l l generally affect the quantity and quality of the product, cause increased scrap losses, require increased supervision, increase maintenance costs, and Increase the number of accidents. The tangible portions of these costs are not separated from total production costs in most accounting systems. The intangible portions of these costs together with the effect which turnover has on other employees and on the company's public image are even more d i f f i c u l t to estimate. To complicate matters s t i l l further, the costs must be estimated over various production levels in order to formulate:the cost equations. A major consideration i s the relative importance of accurate costs. Bock has suggested that many of the intang-ible costs are l i k e l y to be negligible within the normal ^International Business Machines Ltd., General Inform- ation Manual - Personnel Records. (Manual No. E20-8032. 'Endicott, New York, International Business Machines Ltd., 1966). ^Robert H. Bock, "Measuring'Cost Parameters In Inventory Models," Management Technology. IV, (June, 1964) pp. 59 - 71. 98 operating range and that others can be subjectively estimated by management.'7 In some instances the estimation of tangible costs may be s l i g h t l y less stringent than accounting practice would d i c t a t e . Kriebel's study of the empirical problems i n obtaining costs indicated that various s t a t i s t i c a l techniques could be used to estimate, the l i n e a r decision rule cost co-efficients.® He also suggested that, i n many cases, i t might be easier to increase the number of cost equations rather than attempt to f i t poorly correlated costs to standardized equations. 9 A number of investigators have found that accurate cost estimation was not required for aggregate planning problems because the t o t a l cost curve was r e l a t i v e l y f l a t near the optimal s o l u t i o n . 1 0 In summary, i t i s apparent that the I d e n t i f i c a t i o n and measurement of manpower costs i s the most d i f f i c u l t problem i n developing a cost oriented manpower model. There are indications that accurate costs may not be mandatory. The shape of the cost functions and the r e l a t i v e importance of these functions should be investigated when a post oriented model i s constructed. °Charles H. Krlebel, "Coefficient Estimation i n Quadratic Programming Models," Management Science. XIII, No. 8, ( A p r i l , 1967), pp. 473 - 486. 9 l b i d . . pp. 485 1 0These investigations are discussed i n the following Section. 9 9 I I I . AGGREGATE PRODUCTION PLANNING The present model, e i t h e r with or without the cost o p t i m i z i n g aspects , i s a useful planning t o o l . Organizations such as government bodies, are e s s e n t i a l l y service o r g a n i -zations and are capable of doing t h e i r aggregate planning with a manpower model. I n d u s t r i a l o r g a n i z a t i o n s , on the other hand, must consider sales l e v e l s , i n v e n t o r i e s and the work force i n t h e i r aggregate p l a n s . For t h i s type of o r g a n i z a t i o n the manpower model i s a component of the o v e r a l l system and must be integrated with production and Inventory models. The purpose of t h i s s e c t i o n i s to b r i e f l y discuss a number of techniques which are a p p l i c a b l e to t h i s problem of aggregate planning i n i n d u s t r i a l o r g a n i z a t i o n s . Simulation The s i m u l a t i o n approach to aggregate planning involves the determination and formulation of inventory, production and work force p o l i c i e s i n the same manner as the manpower model was developed i n t h i s study. A simple model may c o n t a i n a dozen or so equations r e l a t i n g the various l e v e l s , r a t e s , and d e l a y s . 1 1 On the other hand, a d e t a i l e d study may require hundreds of equations to describe the i n t r i c a t e i n t e r a c t i o n s 1 1 S e e Stanford L . Optner, Systems A n a l y s i s for Business  and I n d u s t r i a l Problem S o l v i n g . (Englewood C l i f f s , N . J . , P r e n t i c e - h a l l , I n c . , 1 9 6 5 ) , PP- 3 7 2 - 3 9 ^ -100 i n the f i r m . 1 2 The basic objective of the simulation approach i s to develop empirical relations which represent the system being studied. Once these relations have been determined, the ef f e c t of various rates, delays and p o l i c i e s ean be . i n v e s t i -gated and the system Improved by selecting factors which reduce costs. The advantage of simulation i s that almost any s i t u a t i o n may be represented i n the model. The disadvantage i s that the r e l a t i o n s which represent the system under one set of conditions may not be the true r e l a t i o n s . Changing the conditions may y i e l d one set of resu l t s i n the model and quite another i n the actual system. A n a l y t i c a l Techniques A number of a n a l y t i c a l and h e u r i s t i c techniques have been adapted to or developed f o r the aggregate planning problem. The common advantage of these approaches i s that they produce optimal or near-optimal r e s u l t s . The common disadvantage i s that the models are considerably more r e s t r i c -ted than they are with simulation procedures. Before discussing the s p e c i f i c techniques, t h e i r common l i m i t a t i o n s must be considered. Limitations. The a n a l y t i c a l techniques currently 1 2 J a y W. Forrester, Industrial Dynamics. "(Cambridge, Massachusetts, M.I.T. Press, 1 9 6 1 ) , pp. 208 - 2 5 1 . 101 a v a i l a b l e consider a two variable system. The two variables, whose scheduling constitutes the problem, are the aggregate production rate and the work force. Because production i s only considered i n the aggregate sense, a common production unit must be determined. Furthermore, l i m i t i n g the system to a two variable decision rules out the consideration of changes i n product mix, labour mix or production sequences. The e f f e c t of these l i m i t a t i o n s i s to r e s t r i c t the use of the techniques to r e l a t i v e l y simple i n d u s t r i a l plants.where a common denominator for production can be found and where the i n t e r a c t i o n of product mix i s r e l a t i v e l y unimportant. Algorithmic Techniques. Linear programming has been successfully applied to the aggregate planning problem. The basic technique has been described by Hanssmann and Hess and involved the modification of the cost functions from a piece wise l i n e a r r e l a t i o n s h i p to true l i n e a r form.1-^ j n a recent a r t i c l e , Orrbeck carried the problem a step further by adjusting the production function to include variable productivity as the worker's experience increased. 1** Linear programming has two basic weaknesses as an aggregate planning t o o l . F i r s t , the costs must be spe c i f i e d as l i n e a r r e l a t i o n s . Second, optimal r e s u l t s can only be 13Hanssmann and Hess, op. c i t . . pp. 48 - 49. lZ*M.G. Orrbeck, D.R. Schuette, and H.E. Thompson, "The E f f e c t of Worker Productivity on Production Smoothing," Management Science. XIV, No. 6 , (February,'1 9 6 8 ), pp. 332 - 342. 102 o b t a i n e d i f the f o r e c a s t s are made with c e r t a i n t y . Hanssmann and Hess s t a t e t h a t the d e v i a t i o n s should not be s i g n i f i c a n t f o r reasonably good f o r e c a s t s . 1 - ' They a l s o suggest t h a t i n v e n t o r y c o s t s are the only c o s t s a f f e c t e d by u n c e r t a i n t y and t h a t the "cost o f u n c e r t a i n t y " can be obtained by comparing expected i n v e n t o r y c o s t s to the c o s t s under i 6 d e t e r m i n i s t i c c o n d i t i o n s . A second technique, the l i n e a r d e c i s i o n r u l e , was developed s p e c i f i c a l l y f o r the aggregate p r o d u c t i o n p l a n n i n g problem. 1? The b a s i c assumption of the l i n e a r d e c i s i o n r u l e technique was t h a t a l l c o s t f u n c t i o n s c o u l d be approximated by q u a d r a t i c e q u a t i o n s . The optimal s o l u t i o n was obtained by s o l v i n g the set of l i n e a r equations obtained when the p a r t i a l d e r i v a t i v e s of t o t a l c o s t with r e s p e c t to each p e r i o d work f o r c e and Inventory were s e t equal to ze r o . The use of q u a d r a t i c c o s t f u n c t i o n s was j u s t i f i e d by two reasons. F i r s t , i t was suggested t h a t i n many Instances the co s t r e l a t i o n s were probably n o n - l i n e a r and i n c r e a s e d r a p i d l y o u t s i d e the normal o p e r a t i n g range. The second reason f o r q u a d r a t i c equations was th a t an optimal s o l u t i o n could be obtained from u n c e r t a i n p r o d u c t i o n f o r e c a s t s . A major f a c t o r i n the use of the l i n e a r d e c i s i o n r u l e ^Hanssmann and Hess, o p . c i t . . pp. 50. l 6 I b i d . . pp. 50 - 51. -'-'Holt, M o d i g l i a n l and Simon, o p . c i t . . pp. 170. 103 was the effect of inaccurate costs on the f i n a l solution. A number of investigators have found that the total cost curve for a system is relatively f l a t near the optimal solution. 1 8 Holt's I n i t i a l studies indicated that i f the decision rule coefficient were incorrect by a factor of two, i.e., 100 percent over or 50 percent under, total costs 19 increased by 11 percent. 7 The theory behind the accuracy problem was subjected to rigorous analysis by VanDePanne and Bosje. 2 0 The analysis showed that small errors in the cost coefficients had l i t t l e effect in the short term but the errors were cumulative and produced severe distortions i f an i n f i n i t e planning horizon was considered. Thus i t would appear that accurate coef-ficient estimation was not mandatory and that a rigorous analysis of the cost components was not required with the linear decision rule. Heuristic Techniques. A number of heuristic techniques have been developed to solve aggregate planning problems. The basic premise behind these techniques was that, i f the total cost curve was relatively f l a t , a "good" solution could -•-^Charles C. Holt, et.al., Planning Production. Invent- ories and Work Force. (Englewood C l i f f s , N.J., Prentice-Hall, Inc., i960), pp. 65 - 66. 1 9 H o l t , Modigliani and Simon, op.cit.. pp. 184. 2 0C. Van DePanne and J. Bosje, "Sensitivity Analysis of Cost Coefficient Estimates: The Case of Linear Decision Rules for Employment and Production," Management Science. IX, No. 1, (October, 1962), pp. 82 - 10?. 104 which was close to the "optimal" solution. Bowman suggested that the cost coefficients for the decision rules be derived from management's past decisions rather than from the cost model. 2 1 Bowman based this decision on the premise that management subjectively estimates coefficients in their normal decisions. He suggested that experienced managers were probably good coefficient estimators and that their costs fluctuated due to variance in decision making rather than 22 biased estimates. He found that formal estimation of the coefficients produced improved performance but that the results were not as good as those obtained by the linear decision r u l e . 2 ^ A slightly different approach to coefficient estimation was taken by Jones In the development of the 2U parametric production planning technique. Rather than estimate the coefficients, Jones developed the production and work force decision rules with parameters for the desired change and relative weighting of future periods. The solution was obtained by searching the four dimensional universe of 2 1Edward H. Bowman, "Consistancy and Optimality in Management Decision Making," Management Science. IX, No. 5 , (January, 19^3), pp. 310 - 321. 2 2 I b i d . . pp. 320. 2 3 l b l d . . pp. 3 1 6 . 24curtis H. Jones, "Parametric Production Planning," Management Science. XII, No. 11, (July, 1 9 6 7 ) , pp. 843 - 8 6 5 . 105 p o s s i b l e parameters to s e l e c t a s e t of parameters which gave the lowest c o s t s . When the approach was a p p l i e d to a number of s i t u a t i o n s i t was found to y i e l d r e s u l t s which were comparable to H o l t ' s l i n e a r d e c i s i o n r u l e and to l i n e a r programming w i t h c e r t a i n f o r e c a s t s . Jones a l s o found t h a t the approach was d e c i d e d l y s u p e r i o r to l i n e a r programming i f u n c e r t a i n f o r e c a s t s were Inc l u d e d . The r e s u l t of t h i s i n v e s t i g a t i o n a l s o supported Bowman's hyp o t h e s i s t h a t the c o n s i s t e n c y w i t h which c o e f f i c i e n t s were used was an important 25 determinant o f the r e l a t i v e o p t l m a l l t y o f the r e s u l t s . Taubert has r e c e n t l y i n v e s t i g a t e d the a p p l i c a b i l i t y of a number of search techniques to the aggregate s c h e d u l i n g 26 problem. The b a s i c approach was to convert H o l t ' s l i n e a r d e c i s i o n r u l e s i n t o a twenty dimension response s u r f a c e . The s u r f a c e was explo r e d by conjugate g r a d i e n t , v a r i a b l e m e t r i c and p a t t e r n search methods. Taubert r e p o r t e d t h a t the methods sought out a minimum p o i n t on the s u r f a c e which approximated the r e s u l t s o f the l i n e a r d e c i s i o n r u l e . Comparison of Techniques. A comparison between s i m u l a t i o n and a n a l y t i c a l techniques was not p o s s i b l e because the same f i r m s have not been s t u d i e d . The a n a l y t i c a l techniques, however, were compared to each o t h e r . Bowman ^^jones, o p . c i t . . pp. 8 5 6 . 26willlam H. Taubert, "A Search D e c i s i o n Rule f o r the Aggregate S c h e d u l i n g Problem," Management Science. XIV, No. 6 , (February, 1 9 6 8 ) , pp. 3^3 - 3 5 9 -io6 compared the costs obtained by his "managerial coefficients" procedure to the results obtained by Holt. In three cases, where the cost reductions were relatively small, Bowman's procedure produced comparable results. In a fourth case, a paint factory, Bowman did not obtain the large cost reduction obtained by Holt. 2? The parametric production planning tech-nique was applied to the paint factory and produced results which differed from the linear decision rule by $933 on a two million dollar cost base. Jones also compared the technique to a linear programming solution for a hypothetical firm. He found that parametric planning produced eight percent higher than linear programming with certain forecasts and eight percent lower than linear programming with uncertain forecasts. 2 9 In summary, i t would appear that the heuristic tech-niques yield results which are not appreciably different from algorithmic techniques with complete certainty. The time savings obtained by u t i l i z i n g a heuristic approach, together with the ab i l i t y of Jones' technique to consider uncertainty and r e a l i s t i c cost functions would indicate that parametric production planning may be the best approach to future planning problems. 27Bowman, op.cit.. pp. 316. 2®Jones, op.cit.. pp. 852. 2 9 I b l d . . pp. 852. CHAPTER VI CONCLUSIONS The study showed t h a t a number o f i n v e s t i g a t o r s have c o n s t r u c t e d manpower f o r e c a s t i n g models. S e v e r a l models were d e v e l o p e d s o l e l y f o r manpower p l a n n i n g p u r p o s e s . Other models, the m a j o r i t y o f the ones i n v e s t i g a t e d , were d e v e l o p e d t o c o n s i d e r manpower p l a n n i n g as p a r t o f t h e aggregate p r o d u c t i o n p l a n n i n g d e c i s i o n . The d i v e r s i t y o f model t y p e s and the wide range o f assumptions made i n p r e v i o u s s t u d i e s s u g g e s t e d t h a t the f a c t o r s t o be C o n s i d e r e d i n a g e n e r a l model r e q u i r e d I n v e s t i g a t i o n . The i n v e s t i g a t i o n demonstrated t h a t t h e f o l l o v i i n g f a c t o r s s h o u l d be i n c l u d e d i n a g e n e r a l manpower p l a n n i n g model. 1. A f o r e c a s t o f f u t u r e l a b o u r r e q u i r e m e n t s . 2. I n f o r m a t i o n on the p r e s e n t l a b o u r f o r c e . 3 . A h i e r a r c h i c a l o r g a n i z a t i o n s t r u c t u r e . 4. P r o v i s i o n f o r time l a g s whenever h i r i n g o r t r a i n i n g o c c u r s . 5. A l a b o u r p o o l from w h i c h the employees a r e h i r e d . 6. P r o v i s i o n f o r l a b o u r t u r n o v e r . 7. P r o v i s i o n f o r h i r i n g and p r o m o t i n g employees. 8. P r o v i s i o n f o r l a y i n g - o f f and demoting employees. When these c o n s i d e r a t i o n s were compared t o the e x i s t i n g 108 models i t was found t h a t none of the models Included a h i e r a r c h i c a l o r g a n i z a t i o n s t r u c t u r e and th a t many d i d not adequately c o n s i d e r time d e l a y s o r the la b o u r turnover r e l a t -i o n s h i p . A d e c i s i o n was made to c o n s t r u c t a f o r e c a s t i n g model which would i n c l u d e the r e l e v a n t f a c t o r s , p a r t i c u l a r l y a h i e r a r c h i c a l s t r u c t u r e . The i n v e s t i g a t i o n showed t h a t two types o f f o r e c a s t i n g models c o u l d be b u i l t . A s i m u l a t i o n model would be a p p l i c a b l e i f the f o r e c a s t i n g d e c i s i o n was based on i n f o r m a t i o n p e r t a i n i n g to the c u r r e n t p e r i o d . A dynamic programming model would be necessary i f the f o r e -c a s t i n g d e c i s i o n depended ypon a b a l a n c i n g of present and f u t u r e d e c i s i o n s . A dynamic programming f o r m u l a t i o n o f the model would have r e q u i r e d the development of c o s t r e l a t i o n -s h i p s so t h a t optimal d e c i s i o n s c o u l d be obtained. Because the study had been r e s t r i c t e d to the i n v e s t i g a t i o n and development of the I n d u s t r i a l R e l a t i o n s aspects of the model, the c o s t aspects were beyond the scope of the study. Rather than c o n s t r u c t a model based upon inadequately i n v e s t i g a t e d c o s t equations, the d e c i s i o n was made to c o n s t r u c t a simu-l a t i o n model. The e f f e c t o f t h i s d e c i s i o n was to r e s t r i c t the model to o r g a n i z a t i o n s where the number of t r a i n e e s d i d not a p p r e c i a b l y a f f e c t p r o d u c t i o n . In o r d e r t o f u r t h e r d e l l n l a t e the model a number of assumptions were made to s p e c i f y the o r g a n i z a t i o n ' s h i r i n g , promotion...and t r a i n i n g p o l i c i e s . A s e t of equations were developed to demonstrate the fundamental c a l c u l a t i o n which 109 determined the number of promotions and q u i t s i n each time p e r i o d . The equations were then i n c l u d e d i n the model and the model was programmed f o r s o l u t i o n by computer. Test c a l c u l a t i o n s were made to demonstrate how the model worked and to i n v e s t i g a t e how d i f f e r e n t q u i t r a t e s and t r a i n i n g times a f f e c t e d the number of workers h i r e d and promoted. The model showed t h a t as the q u i t r a t e i n c r e a s e d the number of q u i t s i n c r e a s e d l i n e a r l y , the number h i r e d i n c r e a s e d s l i g h t l y f a s t e r and the number promoted i n c r e a s e d exponent-i a l l y . I n c r e a s i n g the t r a i n i n g time i n c r e a s e d the number of promotions but d i d not a f f e c t the number of h i r e s or q u i t s . Because the model was developed and programmed to c o n s i d e r a set of the more probable p o l i c y assumptions i t was l a c k i n g the f l e x i b i l i t y to t r e a t o t h e r p o l i c y c o n d i t i o n s . The nature of these p o l i c y a l t e r n a t i v e s were i n v e s t i g a t e d and the procedures f o r changing the model to i n c l u d e them were d e s c r i b e d . The most f e r t i l e area f o r f u t u r e developments i n manpower f o r e c a s t i n g appeared to be i n the c o n s t r u c t i o n of a dynamic programming model. In a d d i t i o n to removing the r e s t r i c t i o n on t r a i n e e p r o d u c t i v i t y , dynamic programming would produce a c o s t - o p t i m i z i n g model t h a t c o u l d e i t h e r be used by i t s e l f or i n t e g r a t e d i n t o a l a r g e aggregate p l a n n i n g model. Despite the i n d i c a t i o n t h a t approximate c o s t i n f o r -mation would y i e l d near o p t i m a l r e s u l t s the i n t e r r e l a t i o n s h i p o f c o s t s w i t h the manpower f u n c t i o n wouvld appear to warrant 110 i n v e s t i g a t i o n before or d u r i n g the c o n s t r u c t i o n of a c o s t -o p t i m i z i n g model. The i n v e s t i g a t i o n of the f a c t o r s which should be i n c l u d e d i n a g e n e r a l model r e v e a l e d that there were s e v e r a l areas that r e q u i r e f u r t h e r r e s e a r c h . The s i z e of the l a b o u r supply a v a i l a b l e to the o r g a n i z a t i o n can only be s u b j e c t i v e l y e stimated. In view of the l a b o u r shortage i n c e r t a i n i n d u s t r i e s and r e g i o n s a study might be i n i t i a t e d to determine the f a c t o r s a f f e c t i n g the supply of l a b o u r to the f i r m . Another area i n the h i r i n g process that should be i n v e s t i g a t e d i s the e f f e c t of the h i r i n g r a t e on the a b i l i t y of the workers h i r e d . A number of p s y c h o l o g i c a l t e s t s are a v a i l a b l e to measure worker a p t i t u d e s , but as f a r as c o u l d be determined, they have not been used i n t h i s type of study. BIBLIOGRAPHY 1. Books D e P h i l i p s , Prank A.., W i l l i a m A.M. B e r l i n e r , and James J . C r l b b i n , Management of T r a i n i n g Programs. Homewood: Ric h a r d D. Irwin, Inc., i 9 6 0 . F o r r e s t e r , Jay W. I n d u s t r i a l Dynamics. Cambridge: M.I.T. Pre s s , 1961. Fox, John B. and Jerome F. S c o t t . Absenteeism: Management  Problem. Boston: Harvard U n i v e r s i t y Graduate School o f Business A d m i n i s t r a t i o n , 1957-Gaudet, F r e d e r i c k J . Labour Turnover: C a l c u l a t i o n and Cost. American Management A s s o c i a t i o n , Inc., i 9 6 0 . 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L _ / X . = - X V \ A X - \ ~~T~ T - T v l Z I Z i z z z IZEZ Z I Z ZLZZ ZIEZ O o £j o \ z z z 11? ^4. S T O R E - C\ I I x * \, xxx I I I I K C, VV /-V N Cr - ? s ( K , J ) -T T R : ^ A L P •V U C.ViAv\ Cr 3. 1 <3cf H J V A- V V A T * S I f<3-119 I 1 O o "e .cH o I PP V? A-^  I G - ( K ) ^ , S T O V E S T X - X W A X I 2 : - M ^ U I K , X , . . . ± > . 5 . G r S . . I f \ P R o -- Z . X = 1 - \ - ? ? s O -120 V - Y L_ A ~ Z - X 4 K - K + \ ! T P R O ( K , J ) "| = P R O r Y L AT a > \ f t x - D £ L ( K ) -1 o o 4 ^ C M X - \ j i — A T 1 • 1_- X -v \7 A P P R - TPvCK, ,r.) *- p<u) A -t- A ? P R r. 3 - -1 - L A T -v \ V 4 - i V \_ ~ T VA A X X ) * P ( u ) 5V PPS-\Ai ( K , T ) K\ A S = A P P R •t-APPKA t. "5 M A\* BP . - - }A A V M Q u. A v-\ T ^ ( W . i ^ - M ^ A L P V y M A V B £ . G £ V H Q u A U x ^ Nor - t i Q u A W T r'.'i.T vc "v. R-H Vv -v N o x V \< -- K -1 . . y K - K - \ ZIEZ ~Z - VVEVUV^V^O-S' V - o r 4 _ oo s^-e. t hen (K,x z z z CI K - K .v \ p o fc,o>© 1 2.ME.W -^-MEvI T Z I , t _ zz:' rzzz 1=.J*AA*- \ 122 V L=.XVA Att--2. I X . . A - o J r =. v, x v~\ A v l i T o l i V. T O T T VJ V U O p> \< =. N\ CrOVlPj . l_T. 123 AH 1^ . \, r n A x T -~. o X. MOO | K r -p-e. r \o d V 1 _ 1> 9o U GET cS o ?^ 

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