UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Simulation modeling as a decision analysis support tool at the Vancouver Container Terminal Zhou, Aimee Zhiwei 2003

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-ubc_2003-0339.pdf [ 7.81MB ]
Metadata
JSON: 831-1.0091122.json
JSON-LD: 831-1.0091122-ld.json
RDF/XML (Pretty): 831-1.0091122-rdf.xml
RDF/JSON: 831-1.0091122-rdf.json
Turtle: 831-1.0091122-turtle.txt
N-Triples: 831-1.0091122-rdf-ntriples.txt
Original Record: 831-1.0091122-source.json
Full Text
831-1.0091122-fulltext.txt
Citation
831-1.0091122.ris

Full Text

Simulation Modeling as a Decision Analysis Support Tool at the Vancouver Container Terminal by A IMEE(ZHIWEI ) Z H O U B.Econ(World Economics), Fudan University 2000 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L M E N T OF T H E R E Q U I R E M E N T S FOR T H E D E G R E E OF M A S T E R OF SC IENCE IN BUSINESS A D M I N I S T R A T I O N in T H E F A C U L T Y OF G R A D U A T E STUDIES F A C U L T Y OF C O M M E R C E A N D BUSINESS A D M I N I S T R A T I O N We accept this thesis as conforming to the required standard T H E UN IVERS ITY OF BRITISH C O L U M B I A March 2003 © Aimee(Zhiwei) Zhou, 2003 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t 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 f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head o f my department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n permission. Department o f The U n i v e r s i t y of B r i t i s h Columbia Vancouver, Canada ABSTRACT The objective of this research is to find whether replacing tractor/trailers in Vanterm (Vancouver Container Terminal) with straddle carriers wi l l increase the productivity. The productivity is measured in lifts per hour per crane. After a significant productivity increase was demonstrated, the objective of this work was then extended to estimate the optimal number of straddle carriers and to quantify the potential o f the straddle carriers in terms of productivity increases. The results of this project wi l l be used to support the decision of purchasing and implementing new equipment for Vanterm. Two discrete-event simulation models were developed as a decision support tool in this project. The models were used to evaluate several transporter allocation scenarios. Statistical analyses were implemented to analyze the results of those scenarios. The results of the simulation gave valuable insight into the vessel operation of Vanterm and provided management at TSI with a strong tool for testing configuration changes to Vanterm without costly investment. In addition to the simulation models, further studies were conducted by testing more scenarios with modified simulation models, applying analytical models and analyzing deterministic models. i i T A B L E OF CONTENT ABSTRACT ii LIST OF TABLES iv LIST OF FIGURES v ACKNOWLEDGEMENT . vi 1. INTRODUCTION 2 2. BACKGROUND 3 2.1 Equipment Used in Vessel Operation 3 2.2 Current Strategy 4 2.3 Double Buffering Strategy 5 3. LITERATURE REVIEW 6 4. METHODOLOGY 9 4.1 Process Mapping 9 4.2 Data Collection 9 4.3 Model Development 11 4.4 Scenario Analysis 15 4.5 Sensitivity Analysis 16 5. RESULTS 18 5.1 Results from Scenario Analysis 18 5.2 Results from Sensitivity Analysis : 25 5.3 Conclusion 27 6. FURTHER STUDY 28 6.1 More Simulation 28 6.2 Jackson Closed Network 37 6.3 Deterministic Models 43 REFERENCE 53 APPENDIX A - Process Maps 54 APPENDIX B - Service Time Distributions 60 APPENDIX C - Container Operations Simulation Model - User Guide 64 APPENDIX D - Validation Details 81 APPENDIX E - Results of the Scenario Analysis using the Tractor/Trailer Model 82 APPENDIX F - Results of the Scenario Analysis using the Straddle Carrier Model 83 APPENDIX G: The Calculation of Stationery Probabilities 84 APPENDIX H: The Estimation of the Minimum Number of Exponential Distributions Required in the Approximation 85 APPENDIX I: Estimation of the Number of States in the Jackson Closed Network model 87 LIST OF TABLES Table 1: Service Time Distributions 10 Table 2: Simulation Model Essential Elements 11 Table 3: Results of Detailed Validation Analysis on Vessel A 15 Table 4: Crane productivities (lifts/hour) from the Scenario Analysis using the T/T Model 19 Table 5: Crane productivities (lifts/hour) from the Scenario Analysis using the SC Model 22 Table 6: Crane productivities (lifts/hour) from the Scenario Analysis using the SC Model with 90% Crane Service Time 23 Table 7: Crane productivities (lifts/hour) from the Scenario Analysis using the SC Model with 80% Crane Service Time 23 Table 8: Comparison of Productivities Among Different Scenarios 24 Table 9: Crane productivities (lifts/hour) from the Sensitivity Analysis using the T/T Model with 80% Crane Service Time 26 Table 10: Comparison of the Crane productivities (lifts/hour) from the Scenario Analysis using the SC Model with 80% Crane Service Time and the Results from the Sensitivity Analysis using the T/T Model with 80% Crane Service Time 26 Table 11: Comparison of Simulated Crane Productivities (Lifts/Hour) from Different Models of unloading process 29 Table 12: Comparison of Crane Productivities from Different Models of loading process (Unit: Lifts/Hour) .' 30 Table 13: Comparison of Crane Productivities from Different Models of unloading process with 20 containers (Unit: Lifts/Hour) 31 Table 14: Comparison of Crane Productivities from Different Models of loading process with 20 containers (Unit: Lifts/Hour) .32 Table 15: Comparison of Crane Productivities from Model of Unloading Process with Different Buffer Size (Unit: Lifts/Hour) 35 Table 16: Comparison of Crane Productivities from Model of Loading Process with Different Buffer Size (Unit: Lifts/Hour) '. 36 Table 17: Long Term Crane Productivities (Unit: Lifts/Hour) Calculated from the Jackson Closed Network . Model with Exponential Service Times 39 Table 18: Estimate of the Minimum Number of Exponential Distributions Required to Approximate Each Service Time Distribution 42 Table 19: Steady State Crane Productivities (Lift/Hour) of the Tractor/Trailer Deterministic Model 47 Table 20: Steady State Crane Productivities (Lift/Hour) of the Straddle Carrier Deterministic Model 51 iv LIST O F FIGURES Figure 1: Gantry Crane 3 Figure 2: Rubber Tire Gantry 3 Figure 3: Tractor/Trailer 3 Figure 4: Straddle Carrier 3 Figure 5: Comparison of Simulation Results and Real Operation Outcome 13 Figure 6: Detailed Validation Analysis on Vessel A (In Total) 14 Figure 7: Detailed Validation Analysis on Vessel A (Discharging) 15 Figure 8: Detailed Validation Analysis on Vessel A (Loading) 15 Figure 9: Simulated "Hang Time" Using Different Numbers of Tractor/Trailers 18 Figure 10: Simulated Net Crane Productivities Using Different Numbers of Tractor/Trailers 19 Figure 11: Simulated Hang Time Using Different Numbers of Straddle Carriers 21 Figure 12: Simulated Net Crane Productivities Using Different Numbers of Straddle Carriers 21 Figure 13: Comparison of Productivities Among Different Scenarios 24 Figure 14: Comparison of Crane Productivities (Unit: lifts/hour) in the Unloading Process From Different Tractor/Trailer Models 30 Figure 15: Comparison of Crane Productivities (Unit: Lifts/Hour) in the Loading Process from Different Tractor/Trailer Models 31 Figure 16: Comparison of Crane Productivities (Unit: Lifts/Hour) in the Unloading Process from Different Tractor/Trailer Models with Different Number of Containers 31 Figure 17: Comparison of Crane Productivities (Unit: Lifts/Hour) in the Loading Process from Different Tractor/Trailer Models with Different Number of Containers 32 Figure 18: Comparison of Crane Productivities (Unit: Lifts/Hour) in the Unloading Process From Different Straddle Carrier Models 34 Figure 19: Comparison of Crane Productivities (Unit: Lifts/Hour) in the Loading Process From Different Straddle Carrier Models 35 Figure 20: Jackson Closed Network 38 Figure 21: Comparison of Crane Productivities (Unit: Lifts/Hour) from Jackson Closed Network Model and Tractor/Trailer Simulation Model 40 Figure 22: A cycle of RTG and Tractor/Trailer Operation in 3 cases 44 Figure 23: A cycle of Straddle Carrier Operation in 3 cases 48 Figure 24: Crane Productivities from the Deterministic Models 51 v A C K N O W L E D G E M E N T I would like to express my gratitude to many people who encouraged and helped me in my studies and contributed to this thesis: • Professor Maurice Queyranne, my thesis advisor and faculty advisor of my project, for his precious advices and comments on my thesis; • Professor Martin L . Puterman, for his contribution as a thesis committee member and his support of my project as the C O E director; • Mehmet A. Begen, for his leadership and help as the project manager of this project, and Justin Wong and Bailey Kluczny, for their technical support as team members; • Center for Operations Excellence (COE) at University of British Columbia, for offering me the chance to study in this Master of Science program and to work on this project, and giving me financial assistance; • Terminal System Inc. (TSI), for providing this challenging project to C O E and offering financial assistance. Specially, I want to thank Norman C. Stark, President and C.E.O, Mogens Christoffersen, Terminal Planning & Development Manager and Kelly Visscher, Computer Operations Manager; • My family, for their emotional and financial support throughout my studies; • My classmates, for their help in my studies. 1. INTRODUCTION According to the WorldCargo News, conventional rubber tire gantry (RTG) and tractor/trailer systems are increasingly perceived as unable to meet carriers' demands for the fast turnaround of their container vessels. A new operation, straddle carrier direct operation, also known as double buffering strategy, can achieve higher crane productivity and thus shorten the vessel turnaround time in some ports. TSI operates Vanterm — the largest container terminal that is located in the inner harbour of the Port of Vancouver — under a long-term lease agreement with the Vancouver Port Authority. Vanterm currently employs an R T G and Tractor/Trailer system. TSI had considered implementing straddle carriers in Vanterm to improve the crane productivity and thus increase customer satisfaction. Due to the large fixed cost investment of straddle carriers, it was necessary to find out how much efficiency could be achieved by the double buffering strategy before management made decisions. 2 2. B A C K G R O U N D 2.1 Equipment Used in Vessel Operation In TSI vessel operations, there are several pieces of equipment involved. The most important equipment is the gantry crane (Figure 1). It unloads containers from the vessel to the dockside and loads containers from the dockside to the vessel. The productivity of the Dockside Gantry Cranes is the most important performance measure used by TSI and its clients. It is measured by lifts/hour, which is how many containers are loaded or unloaded per hour. The higher the crane productivity, the better the performance of the TSI operation. In the yard, a Rubber Tire Gantry (RTG) (Figure 2), picks up and drops off containers. In current operations, RTGs are responsible for moving containers between the stacks and the tractor-trailers. If straddle carriers are implemented, RTGs will move containers between the stacks and the ground instead of tractor-trailers. Figure 2: Rubber Tire Gantry In RTG and Tractor/Trailer systems, tractor/trailers (Figure 3) are used to transport containers between the dockside and the yard. Tractor/trailers can only carry containers but not pick up or drop off them, so tractor/trailers have to wait for a crane or an RTG to serve them. P Figure 3: Tractor/Trailer Unlike tractor/trailers, straddle carriers (Figure 4) can pick up or drop off containers as well as move them around. The newly designed 1 over 1 straddle carriers can travel as least as fast as tractor/trailers and they are very stable, compared to old designs. (1 over 1 means that the straddle carrier can travel across a container when it is carrying another container.) Figure 4: Straddle Carrier 3 There are also other pieces of equipment used in the operation. Top lifters and side loaders are similar to straddle carriers, which can pick up and drop off containers by themselves. However, their travelling speed is very slow, compared to straddle carriers and tractor/trailers. Side loaders are only used to handle empty containers. Top lifters are usually used to handle the containers on the ground and on rail carts. 2.2 Current Strategy Current operations assign tractor/trailers to transport containers between the dockside and the yard. To unload a vessel, cranes pick up containers from certain bays of the vessel and then drop them onto tractor/trailers. The tractor/trailers then carry the containers near the yard locations they are assigned to. When tractor/trailers arrive, RTGs remove the containers and then stack them while tractor/trailers go back to the dockside. To load a vessel, crane operators dispatch tractor/trailers to retrieve certain containers from specific yard locations and then load them onto the vessel. R T G operators are also informed to pick up the assigned containers from stacks and then drop them off on the tractor/trailers. In both processes, cranes have to wait for tractor/trailers to collect or present containers, which creates so-called "Hang Time", the time crane spent on waiting for tractor/trailers to present or collect containers. When a crane is waiting, it is not productive, so reducing the "Hang Time" can increase the crane productivity. That also happens to RTGs. However, as far as we know, cranes are the main bottlenecks and their productivity is the most important performance measure for a container terminal, so this study only focuses on improving the crane productivity. The idea of reducing the "Hang Time" leads to a straddle carrier direct operation with a double buffering strategy. 4 2.3 Double Buffering Strategy The double buffering strategy is designed to reduce the crane "Hang Time" and thus increase the efficiency of the dockside gantry cranes. This strategy depends on the implementation of straddle carriers. Because straddle carriers can handle the containers by themselves, there is no need for cranes or RTGs to wait for straddle carriers to collect or present containers. Instead, cranes and RTGs can pick up containers from the ground and drop off containers on the ground. By using straddle carriers, two types of buffers are created, a dockside buffer under each crane and a yard buffer near each RTG . This is why this strategy is called double buffering. In the unloading process, cranes can keep moving containers from the vessel to the dockside ground buffer until there is no more room left on the ground for another container. In the mean time, straddle carriers pick up the containers in the dockside buffer, carry them to the yard buffer and then drop them off there. RTGs pick up containers from the yard buffer and then stack them. In the loading process, unless the yard buffer is full, RTGs ground those containers needed to be loaded, and straddle carriers transport them to the dockside buffer. Cranes can keep loading the vessel unless there is no container in the dockside buffer waiting to be loaded. In summary, the double buffering strategy wi l l allow the dockside cranes and RTGs to operate with less blocking ("hanging" a container) or starving (waiting for a container) during the entire import/export period. As a result, crane productivity can be increased. However, the capital investment for this double buffering strategy is huge, which made it important to quantify the efficiency that straddle carriers can bring to TSI Vanterm. The result of this project is going to be used to support TSI management in this investment and operation decision. 5 3. LITERATURE REVIEW We first looked for theoretical solutions. Container Terminal Planning - A Theoretical Approach (Watanabe, 2001), introduces a theoretical approach to design a container terminal based on annual container handling capability, storage capacity and some other factors. In section 6.2.3, it presents the selection of container handling systems, which include the system currently employed by Vanterm and a straddle carrier system without RTGs. It also gives the required sizes of the tractor/trailer fleet and straddle carrier fleet. However, it does not present how those sizes are calculated. Furthermore, it does not include a straddle carrier system with RTGs. The operation at container terminals is a Jackson closed queuing network. In Jackson closed networks (Chen and Yao, 2001), the work in process (WIP) level is a constant value. A n R T G and Tractor/Trailer system can be considered as a closed network i f the buffer under the crane is ignored, because the number of tractor/trailers dictates the WIP level. In an R T G and Tractor/Trailer system, there is significant job travelling time, which does not exist in Jackson Closed Network. In order to handle this difference, tractor/trailers are considered as servers. However, Jackson Closed Network cannot be directly applied in this case, because the service times of Crane, R T G and tractor/trailers are not exponentially distributed. Generalized Jackson closed networks (Chen and Yao, 2001) cannot be directly applied either, because the service time of tractor/trailers as a station is dependent on the number of tractor/trailers, which violates one of the assumptions. Due to the limited space constraints, the queue of containers waiting to be served is finite. Onvural(1990) gave a systematic presentation of the literature related to closed queuing networks with finite queues. This paper introduces different types of queuing networks and techniques used to analyze the queuing networks. First, it discusses why it is difficult to obtain exact closed form solutions. Second, it illustrates different types of blocking. Third, it presents some conjectures, Lemmas and algorithms to approximate the mean queue length and throughput of queuing networks. Since this paper assumes only one server at each station with one stage of service while there are many tractor/trailers and 6 straddle carriers as servers for one station, applying the approximation method in the paper may not bring accurate results. In addition, the approximation method in this paper is quite complex and time-consuming, so it is not considered in this study. This paper also mentions simulation as a good way to approximate the queuing networks. In addition to queuing networks, straddle carrier operations can be viewed as tandem queues, since limited numbers of straddle carriers connect several queues, a few under the cranes, the rest under the RTGs. There is significant backhaul time for straddle carriers, which creates blocking. Boulis and Ing(2000) present exact analysis for the M/M/2 case by studying the Markov Chain and simulated M/M/2, U/U/2 and D/D/2 cases. However, the behaviour of the tandem system with more servers or general service times was not studied. Tractor/trailers and straddle carriers can also be viewed as servers in tandem queues. The backhaul time for straddle carriers can be viewed as the delay of the server release. Also, in the current operations, since tractor/trailers (T/Ts) have to wait until the completion of crane or R T G service, their releases are also delayed. Nawijn(2000) first studied the M/M/s-M/1 model using the matrix-geometric method then the M/M/2-G/1 model. In the M/M/s-M/1 model, there are two stations, multiple servers in the first station, 1 server in the second station. However, the paper concluded that increasing the number of servers or involving general service time distributions wi l l lead to the technical difficulties and numerical problems inherent to solution methods based on generating functions in the complex plane. Since the variations of the transporter travelling times and R T G and Crane service times are relatively small, the operations could be modeled as tandem queues with deterministic input i f the straddle carriers are viewed as input to the systems and the fleet size is large enough to keep Crane and R T G busy. B6hm(2000) gives a formula for zero-avoiding transition probabilities of a multiple node tandem queue with exponential service times and deterministic input. However, in our study, the service times are not exponentially distributed, so the formula may not be well applied. Furthermore, the target of our study 7 is to find a practical optimum number of straddle carriers, which is not necessarily large enough to keep cranes and RTGs busy. Besides the theoretical approach, there are other approaches to study the operation of container terminals. Shabayek and Yeung(2002) mention that many post studies use queuing theory, but all of these studies simplify the real situation. These authors also note that the operations of container terminals are actually queuing networks, which was usually so complicated that no theoretical solution can be obtained. In that paper, a simulation model is developed to evaluate the performance of Kwa i Chung container terminals. The model simulates the whole service process of vessels, from their arrival to their departure, and provides two summary measures, the average system time and the degree of utilization of container terminals. That paper does not focus on the operation at the container terminal. However, in our study, we only simulate the loading and unloading operation on the vessels. Their model is validated by comparing the simulation results with the observed system time. In our study, we use the same idea to validate one of the simulation models. Simulation is also used to examine the key ideas of Automated Storage and Retrieval Systems (ASRS) and Automated Guided Vehicle Systems (AGVS) in maritime container terminals by Asef-Vazir i and Khoshnevis(2002). The results of simulation are straightforward and easy to understand, so we think that interpreting simulation results to TSI management is preferable to explaining theoretical solutions. 8 4. M E T H O D O L O G Y According to the literature on closed queuing networks, exact closed form solutions are very hard to obtain, so simulation, an approximation method, seems to be a better choice, although it's time consuming. In addition, there are a few other reasons to choose simulation: first, it can communicate our understanding of the operations to the management and get feedback; second, it helps management look at the operations from different perspectives; third, it is easy to explain the results from a simulation to management. For these reasons, we chose simulation as the methodology for this project to evaluate the crane productivity efficiency. In order to build the simulation models, we observed the current operations on several occasions. Process maps were drawn to represent our understanding of the operation. Data was collected. After the simulation models were built, several scenarios were tested and the results were analyzed. 4.1 Process Mapping Our understanding of the operations is reflected in the process maps. There are six process maps in total, three for the current operations and three for straddle carrier direct operations. For each operation, these maps describe the unloading and loading processes for each type of equipment involved and the container movement process for both unloading and loading. The process maps are attached as Appendix A . 4.2 Data Collection The data required to run the simulation models are mainly the service time distributions of all the equipment. Data were collected during the site visits and then modeled. The distributions are obtained from A R E N A 6.0 Input Analyzer output (See Appendix B for Detail). The distributions are listed in Table 1. As we can see, for all the equipment, performing any of the tasks requires at least a fixed amount of time. In addition, the variations of the service times are fairly small, which precludes the direct use of exponential distributions. 9 Table 1: Service T ime Distr ibutions Equipment Distribution Unit Mean (seconds) SD1 SCV 2 NB 3 SE 4 Crane (vessel to TT) 5 30 + WEIBULL(30, 1.14) Second 58.7 26 0.12 112 0.020 Crane (TT to vessel) 12.5 + ERLANG(7.39, 4) Second 42.1 15 0.13 112 0.007 RTG (pickup) 31.5 + 47*BETA(0.719, 0.961) Second 50.2 15 0.08 17 0.035 RTG (stacking) 30.5 + WEIBULL(32.1, 1.25) Second 60.4 24 0.16 37 0.026 Top Lifter, Side Loader & SC (pickup)6 2.5 + ERLANG(3.14, 3) Second 11.9 5.4 0.21 20 0.038 Top Lifter, Side Loader & SC (dropoff)7 7.5 + LOGNORMAL(10.5, 15.5) Second 17.1 9.1 0.28 40 0.023 Stacker 14.5 + WEIBULL(15.8, 1.71) Second 28.6 8.5 0.09 36 0.030 Distance 300-600 Meter Top Lifter speed 9 Km/hour Tractor/Trailer & SC speed8 18 Km/hour 1: SD is abbreviation for standard deviation. Unit of SD is one second. 2: SCV is the abbreviation for the squared coefficient of variation. SCV = -Mean 3: NB is the abbreviation for the number of observations. 4: SE is the abbreviation for the standard error in fitting the distributions to the data collected. 5: This distribution has been adjusted in simulation models for TSI in order to accommodate some delays caused by twin lifts or other factors we did not observe. Twin lifts, which means that a crane lifts two 20ft containers at the same time, usually take longer time than single lifts. We only observed single lifts, so we don't have service time distribution for twin lifts. In addition, simulation models did not capture the difference between single lifts and twin lifts because of lack of data and logic complexity. In order to accommodate the delays, we increased the mean crane service time. After testing several increments, 15 seconds was chosen as a best fit, which produced best validation results. 6, 7, 8: No data for straddle carrier service times are available. According to a former operations manager's experience, the pickup and dropoff service times are close to those of top lifters and the traveling speed is close to that of tractor/trailers, so we used those service times as straddle carrier service times. In addition, there are not many observations of the R T G service times, top lifter service times and time to handle stackers on containers. And for the travelling speed of the top lifters and tractor/trailers, we used the estimate given by a former operations manager. It was very hard to observe those activities, because the containers in the yard blocked our view and we did not have enough human resource and equipment to track the movements of the transporters. We tested the quality o f the service times by comparing the simulation results of the tractor/trailer model with those service time distributions and the recorded operation results, which wi l l be discussed in the model validation. The results of the 10 statistical analysis showed that the difference between our simulation results and the recorded ones of four vessels out of ten were in ± 5% range. The service time data were actually collected when the Vancouver Container Terminal was operating on two of those four vessels. We believed that those service time distributions fit those four vessels best and then accepted the distributions. Instead of having a fixed value, the distances between any two locations are within a certain range. The locations are mainly places on the dockside or places in the yard. The distances between the locations are important and must be specific, because they are used to calculate the time transporters wi l l spend between locations. The travelling time wi l l affect the crane productivity efficiency, as wi l l be discussed later in the interpretation of simulation results. Ship plan and yard plan also affect the results of the simulation. Since their design is not in our scope, they are inputs to the simulation model in order to reflect the reality. The explanation of all simulation inputs is in Appendix C, the Simulation Manual. 4.3 Model Development 4.3.1 Simulation Software Arena 6.0 was chosen as the simulation software, because the project team was familiar with it and it has powerful animation. A screenshot of R T G and Tractor/Trailer model animation is in Appendix C, the Simulation Manual. 4.3.2 Simulation Essential Elements The simulation models are all event driven. Time unit is one second. Distance unit is meter. Some other essential details are listed in Table 2. Table 2: Simulation Model Essential Elements Simulation Model Entities Servers Transporters Current Operations Three Cranes, Six Tractor/Trailers and One Top Lifter Containers RTGs and SC direct operations One Side Loader Straddle Carriers 11 4.3.3 Assumptions Before building our simulation models, some assumptions are made to simplify the work: • A l l the entities are identical. • A l l the servers and transporters are identical. • Transporters only use fixed routes among locations and there is no variance in travelling speed. • There is no traffic congestion. 4.3.4 Models Two models were developed, one for straddle carrier operations, another for the current operations. The reasons why we developed two models are: first, the logics of the two systems are different, so building two models is much easier than developing only one model to accommodate two different logics; second, since not all data for Straddle Carrier Operation were available, a model for the current operations is necessary for model validation. Both models are designed to output some statistics. During the running of the simulation, some dynamic statistics are shown on the screen to help observe the performance. A screenshot of the dynamic statistics is in Appendix C, the Simulation Manual. In addition, some statistics are exported to files for further study. Examples of output files are also in Appendix C, the Simulation Manual. 4.3.5 Model Validation The R T G and Tractor/Trailer model was validated from the logic and the performance perspectives. The real outcomes of operations on ten different vessels were given by TSI. After verifying the model logic, the simulation results of the R T G and Tractor/Trailer model were compared to the real outcome of the operations. (See Figure 5. Details in Appendix D.) Since there was no data for the straddle carrier operations, we only verified the model logic. 12 For four out of ten vessels, the differences between the mean simulated crane productivities and the real ones are in the ± 5% range, which is small. The larger differences between the simulation results and the real outcome of the other vessels may have various explanations, for example, containers on a specific type of vessel may be easier to handle than the ones on some other types of vessels. Since the service time data were collected when there were two specific vessels on berth, the distributions obtained from the data might not suit some other types of vessels. For those four vessels with small difference, it is reasonable to say that the service time distributions used in the model are good approximations. Since there is no data available for Straddle Carrier Operation, we only verified the model logic. The simulation was observed to check i f the model logic complied with the one on the process maps. Several parameters were tested to observe more scenarios. Extreme cases were also tested, for example, assigning a buffer large enough to place all containers to be handled. The model logic passed all the tests. Comparison of Simulation Results and Real Operation Outcome •—Simulated Productivity • — Actual Productivity A B C D E F G H I J Vessels Figure 5: Comparison of Simulation Results and Real Operation Outcome More detailed analyses were carried to compare details of the simulation results and the real operations. 13 For each vessel we were given data of, the cranes worked on a set of batches of containers. A batch of containers is the containers on the same bay or hatch of one vessel, assigned to be loaded or unloaded in sequence before the crane is switched to another duty. Since the operations were not repeated, we only have one recorded time for each batch of containers in each set. The mean simulated times are from 20 replications of simulation. We used means to reduce the impact of randomness. The mean simulated times and the recorded times were then paired by each batch and then grouped by each set. A two-sample paired-t test was carried to test whether the mean simulated times spent on batches of containers of a specific vessel were different from the recorded times spent in real operation or not. If p-value returned from the test is smaller than 0.05, then we can conclude that there is significant difference between those two groups, otherwise, we conclude that there is no significant difference. After the times were proved not different, they were separated into two categories, depending on whether they were spent on loading or unloading. Then for each category, a two-sample paired-t test was carried to test whether or not there is difference between the mean simulated times and the actual ones. These analyses were applied to all ten vessels. The results of all three analyses for the four vessels with ± 5% difference between simulated and actual crane productivity show that the mean simulated times spent on bays or hatches of each of those four vessels are not significantly different from the real ones. (See Figure 6 to 8 and Table 3 for examples) Validation (Vessel A) O 20 40 60 80 100 Actual time spent on each bay Figure 6: Detailed Validation Analysis on Vessel A (In Total) 14 Validation (Vessel A Discharging) 10 20 30 40 50 60 Actual time spent on each bay Figure 7: Detailed Validation Analysis on Vessel A (Discharging) Validation (Vessel A Loading) 20 40 60 80 100 Actual time spent on each bay Figure 8: Detailed Validation Analysis on Vessel A (Loading) Table 3: Results of Detailed Validation Analysis on Vessel A t-Test: Paired Two Sample for Means (Vessel A) Total Unloading ' Loading Actual Simulated ' Actual Simulated >* Actual. Simulated j Mean 22.84 22.39 20.53 19.91 24.62 24.29 Variance 318.12 301.33 206.45 199.74 400.80 374.98 Observations 122 122 53 53 69 69 P(T<=t) two-tail- ' 0.44 0.47 0.68 Those four specific vessels were chosen for scenario analysis, because the differences between the simulation results and the real outcome of these four vessels are small enough for us to believe that the models can simulate well the operations on those vessels. We did not run scenario analysis on the other six vessels, because we believed that our model could not simulate the operations on those vessels very wel l and thus could not produce reliable outcomes. 4.4 Scenario Analysis First, different numbers of tractor/trailers per crane were compared using the Tractor/Trailer Model. The simulated crane productivities of those scenarios were compared to determine the "practical optimal number" of tractor/trailers per crane. The practical optimal number of tractor/trailers per crane is not the theoretical optimal number. In theory, adding more resource may increase productivity. However, the operation cost wi l l also increase i f the number of transporters per crane increases. The practical optimal number is the result of a tradeoff between the productivity increase and the cost increase. 15 We decided that i f after assigning a certain number (x) of tractor/trailers or straddle carriers to each crane, increasing one more tractor/trailer or straddle carrier per crane could only bring less than 2% crane productivity increase (less than 1 lift/hour), we would claim that x was the practical optimal number of transporters per crane. Second, different numbers of straddle carriers per crane were compared using the straddle carrier model. The practical optimal number of straddle carriers per crane was also determined. The simulated crane productivities were compared to those from the tractor/trailer model with five tractor/trailers per crane, which reflected the real operations, in order to quantify the efficiency gains expected from the double buffering strategy. Third, the assumption that using straddle carriers can shorten the crane service time was examined. As a TSI former operations manager said, a crane might work faster to discharge a container from a vessel to a buffer than to a tractor/trailer, and also work faster to load a container from a buffer than from a tractor/trailer to a vessel. Because of that, crane productivity could be higher than the results from our simulation models. Straddles may thus allow crane operators to speed up the crane operations to achieve higher productivity. To explore the limits of this potential and to investigate the effect of changes in the crane service time, we have run additional scenarios. Different numbers of straddle carriers per crane were tested while the crane service time was decreased to 80% or 90% of the original service time. Since the upper limit of crane service rate is estimated to be 40 lifts per hour, a further reduction of crane service time is not realistic and thus not considered in this study. It was shown that the optimal number of straddle carriers per crane still held even when the crane service time was reduced. 4.5 Sensitivity Analysis Crane service time is the most critical technical parameter of the dockside operations. Therefore, it would be useful to know how changes of this technical parameter affected the result. Sensitivity analysis was carried out with respect to crane service time to ensure the accuracy and robustness of the simulation results. This was a useful step 16 allowing us to increase our confidence in the recommendations made based on the results of the scenario analyses. We did not consider the case that cranes worked slower than at the time we collected service time data. The reason is that the crane is the bottleneck. If a crane works slower, then with the practical optimal number of transporters, the chance of crane blocking or starving is smaller, which means that the number is still the practical optimal. Different tests were done using the T/T model and SC model with faster cranes. In those tests, service times were reduced to 80% of observed levels. Again, since the limit of the crane service rate is 40 lifts per hour, a further reduction of crane service time is not considered. The results from both models with same reduced crane service times were compared to examine whether the recommended number of straddle carriers could finish the jobs as fast as the tractor/trailers in the current operations. 17 5. R E S U L T S 5.1 Results from Scenario Analysis In order to evaluate the efficiency of the double buffering strategy, the results from scenarios were analyzed to figure out: whether a double buffering strategy can increase crane productivity or not; how many straddle carriers are needed to achieve a target crane productivity. For every scenario, we ran 20 replications of the simulation and used mean crane productivities for comparison. The variations were less than 1%. First, the performance of the current operations was studied to obtain the figures for comparison to the Straddle Carrier Operation. Different numbers of tractor/trailers per crane were tested. Some results are listed in Table 4. Complete results are in Appendix E. H a n g T i m e 3000-1 Number of T/Ts Figure 9: Simulated "Hang Time" Using Different Numbers of Tractor/Trailers 18 Table 4: Crane productivities (lifts/hour) from the Scenario Analysis using the T/T Model Vessel Crane 6T/Ts Difference 5 T/Ts Ideal Productivity 4T/Ts Difference A i 1 29.11- ' 0.00% 29.11 33.35 28.41 -2.42% 2 27 - 0.99% 26.73 29.41 26.22v -1.91% 28.05 0.49% 27.91 , 31.32 2731 ; -2.16% ^ t if i • t { B 1 26.4 1.38% 26.04 29.38 24.73; -5.04% 2' 28.3 0.22% 28.24 31.52 26.56 -5.94% 27.5 ' 0.71% 27.31'- / 30.62 25-.79V > -5.56% ( 1 24.54 T 0.20% 24.49 i l 30.81 23:71 , -3.21% 2 25^ 53 > 0.00% 25:53 * 29.63 24.61; . -3.62% 3 26.78. 0.10% 26.75 31.65 25.89 -3.20% 25.6 0.11% 25 57 30.78 24.72 -3.32% V • , ! r < D- 1 27197 .„ 0.53% 27.83"' / 30.52 25.45 \- -8.55% 2 26.89 0.00% 26.89 29.46 24-85 , ' -7.58% 27.44 - * 0.27% 27.36~ i 1 30 25-. 15" * -8.08% *: Crane Numbers are not the numbers painted on the cranes, but the ones used in the simulation. **:The Difference columns show the differences between the results of the tractor/trailer model using different number of tractor/trailers per crane and the results of the tractor/trailer model using 5 tractor/trailers. ***: Ideal Productivities are calculated by subtracting the "hang time" from the total time spent on the corresponding vessel with 5 tractor/trailers per crane. N e t P r o d u c t i v i t y 5 -0 "I 1 1 1 ! i 1 1 0 1 2 3 4 5 6 7 8 Number of T/Ts Figure 10: Simulated Net Crane Productivities Using Different Numbers of Tractor/Trailers 19 According to Figure 9, increasing the number of tractor/trailers per crane can decrease the hang time. We don't have the actual hang time data, so we could not compare the simulated hang time with the actual ones. By decreasing the hang time, there are fewer chances of crane blocking or starving, so crane productivity is increased. However, hang time cannot be eliminated completed, since in the loading process, cranes have to wait for the arrival of export containers, which must be retrieved from the yard. The ideal productivities listed in Table 4 are not achievable because of crane starving. According to Figure 10, it is clear that increasing the number of tractor/trailers per crane can increase crane productivity. However, after assigning a certain number of tractor/trailers per crane, adding one more tractor/trailer per crane cannot bring a significant increase in crane productivity. In other words, the marginal increase in crane productivity is positive but decreasing while the number of tractor/trailers per crane increases. According to our definition of practical optimal number of transporters, assigning 5 tractor/trailers per crane is the optimal solution for the current operations. This solution is exactly what TSI management implemented for more than ten years. Reducing the number of tractor/trailers per crane from 5 to 4, there wi l l be a more than 4% productivity loss. Second, the performance of Straddle Carrier Operation was studied and compared to that of the current operations. Different numbers of straddle carriers per crane were tested. Some results are listed in Table 5. Complete results are in Appendix F. According to Figure 11 and similarly to the Tractor/Trailer Model, increasing the number of straddle carriers per crane can decrease hang time and thus increase crane productivity. However, assigning more than 3 straddle carriers per crane does not reduce hang time significantly. Another observation is that since cranes put containers directly into the buffers there is less hang time compared to the tractor/trailer model. According to Figure 12, assigning more than 3 straddles per crane to the dockside operation does not improve the productivity further. Also, decreasing the number of straddles per crane from 3 to 2 may result in considerable productivity loss. In most 20 cases, 3 straddle carriers can clean up the buffer quickly enough to ensure sufficient buffer space for the cranes. This tells us that assigning 3 straddle carriers to each crane would be the optimal configuration, taking in account the cost. Hang Time (Minutes) 500 -, _ 0 -I , , , , , , , 1 0 1 2 3 4 5 6 7 8 Number of SCs Figure 11: Simulated Hang Time Using Different Numbers of Straddle Carriers Net Productivity (Lifts/Hour) 29.5 -, — — 28.5 J 1 2 3 4 5 6 7 8 Number of SCs Figure 12: Simulated Net Crane Productivities Using Different Numbers of Straddle Carriers 21 Table 5: Crane productivities (lifts/hour) from the Scenario Analysis using the SC Model Vessel name Crane 5 T/T 4 SCs Difference 3 SCs Difference 2 SCs Differenc e A 1 29.11 30:15 * 3.59% 30.15, ' 3.59% 29'.551 . 1.51% 2 26.73 27.82 4.06% 28.01 ' 4.77% 27.91 :* 4.41% 27.91 28.98 3.83% 29 08 4.18% 28.74 2.95% ' •» • „ 5 V ! ' * 5 B 1 26.04 27.02 3.78% 26.94 . 3.45% 26.16 0.46% 2 28.24 28.56 1.12% 28.46 i 0.78% 26.67 -5.54% 27.31 27.92 v' 1 2.23% 27.83 1.89% 26.46; s -3.10% • '< 1 24.49 25.59 4.49% 25.49 , 4.07% 24.3 1 -0.78% 2, 25.53 26.42- ... 3.47% 26.49 * 3.76% 25.77, ' 0.95% 3 26.75 27.08, 1.25% 27.2 1.68% 26 16 -2.22% 25.57 26.35 3.05% 26.3If' 3.13% 25.36. > -0.83% D 1 27.83 28.81 \« 3.55% 28.58 - 2.71% 28.12' 1 1.07% 2 26.89 27.33- 1.67% 27.26 1.39% 27.18 1.10% 27.36 28.08' 2.62% 27 93 • 2.05% 27.66* ; 1.08% *: Crane Numbers are not the numbers painted on the cranes but the one used in the simulation. **: The Difference columns show the differences between the results of straddle model using different number of straddles per crane and the results of the tractor/trailer model using five tractor/trailers. Third, after running the scenarios above, it was determined that straddle carrier operations could potentially replace the current operations. To gain confidence in this result, scenarios with different numbers of straddle carriers per crane were ran again with different crane service times. This allowed us to test whether or not the result would hold i f the cranes were to operate more quickly. The scenarios were run with two to five straddle carriers per crane using 80% or 90% crane service times per lift. (The 80% or 90% crane service times are 80% or 90% of the realized random numbers, according to the service time distributions.) No further reduction in crane service time was tested, because according to WorldCargo News, a skil lful crane operator can only achieve approximately 40 lifts per hour at maximum, which corresponds to the 80% of the base case. The results are listed in Table 6, 7 and 8. 22 Table 6: Crane productivities (lifts/hour) from the Scenario Analysis using the SC Model with 90% Crane Service Time Vessel name Crane 5 T/T 4 SCs Difference 3 SCs Difference 2 SCs Difference A 1 29.11 32.7 12.22% 32.5 * s 11.60% 3114 . 7.83% 2 26.73 30.3.- 13.47% 30.3 . \ 13.47% 30.r 12.64% 27.91 31.5 12.85% 31.4 12.53% 30.8 10.20% -B 1 26.04 29.3 12.46% 29.1 11.88% 27.2 4.60% 2 28.24 31.0 9.85% 31.1 9.99% 27.7 -1.85% 27.31 30.3- 10.94% 30.3 10.78% 27.5' 0.77% C 1 24.49 27.4 11.79% 27.2 11.06% 25.3 3.12% 2 25.53 28.6 12.03% 28.4 11.36% 27.5 . 7.81% 3 26.75 29.4 • 9.74% 29.2 9.12% 27.4 • 2.32% 25.57 28.4 11.12% 28.3 10.45% 26.6 . 4.07% D 1 27.83 31.5 13.28% 31.6 . 13.45% 30.2 8.58% 2 26.89 29.8 ; 10.74% 29.8 10.74% 29.5 9.75% 27.36 30.7. ' 12.02% 30.7 12.11% 29.9 9.15% *: Difference columns represent the productivity differences between the results from the straddles model (90% crane service time) and the tractor/trailer model with 5 tractor/trailers (100% crane service time). Table 7: Crane productivities (lifts/hour) from the Scenario Analysis using the SC Model with 80% Crane Service Time Vessel name Crane 5 T/T 4 SCs Difference 3 SCs Difference 2 SCs Difference A . 1 29.11 35.9 23.17% 35.6 22.18% 31.5 15.21% 2 26.73 33.1 23.74% 33.1 23.74% 32.5 21.54% 27.91 34.5-. 23.46% 34.3 22.96% 33-' 18.31% B 1 26.04 32.1 , 23.41% 31.7 • 21.81% 27.7 6.29% 2 28.24 34 ' • 20.40% . 33.6 - 19.13% 28.5. < 0.78% 27.31 33.2 ' " 21.65% 32 8 20.25% 28.1 ~ 3.03% C 1 24.49 29.2 • 19.35% 28.8 17.43% 26.1 6.44% 2 25.53 30.7: ' 20.16% 30.3 18.63% 29.5- 15.68% 3 26.75 31.5. 17.60% 31' 15.91% 28 6 6.95% 25.57 30:4: 18.94% 30 17.21% 27.9 9.00% • , D 1 27.83 34.9 25.45% 34.5 24.02% 32.3 16.06% 2 26.89 32.5 20.99% 32.5 • 20.79% 31.7 18.06% 27.36 33.7* • 23.22% 33.5 22.41% 32 17.03% *: Difference columns represent the productivity differences between the results from the straddles model (80% crane service time) and the tractor/trailer model with five tractor/trailers (100% crane service time). 23 Table 8: Comparison of Productivities Among Different Scenarios Vessel name 5 T/T 3 SCs(100%) Difference 3 SCs(90%) Difference 3 SCs(80%) Difference A 27.91 . ' 29.08 4.19% 1 31.41 12.54% 34.32 22.97% B 27.31 27.83 1.90% 30 26 10.80% 32 84 20.25% C 25.57 26.37 3.13% 28 25 10.48% 29 97 17.21% , D 27.36 ,27.93 2.08% 30.68 12.13% 33 50 22.44% *: Difference columns represent the productivity differences between the results from the straddles model and the tractor/trailer model with five tractor/trailers (100% crane service time). Productivity Comparison • — A -+—B * - C — D 5 T/T 100% 90% 80% Scenarios Figure 13: Comparison of Productivities Among Different Scenarios The results show that assigning 2 straddle carriers per crane achieves almost the same productivity as 5 tractor/trailers per crane. Using 3 straddles per crane can increase the productivity significantly i f crane service time can be reduced. Another observation is that i f crane service time can be reduced to 90%, straddle carriers can increase crane productivity by more than 10%. However, i f crane service time can be reduced to 80%, straddle carriers can increase crane productivity by less than 20%. This is mainly because of the increasing impact of the hang time caused by export containers. (Crane productivity = Number of Containers Loaded and Unloaded for a Vessel / Total Time Spent on that Vessel) As mentioned before, hang time can only be reduced to a 24 certain level. If cranes work faster, then the production time is shortened and thus for a relatively fixed hang time, the proportion of hang time in the total time spent on a vessel is increased, so the reduction of total time spent on a vessel in percentage is always less than the reduction of crane service time in percentage i f the hang time can not be further significantly reduced. The smaller the reduction of total time spent on a vessel, the smaller the increase of crane productivity. In conclusion, i f cranes can work faster, crane starving wi l l become a bigger issue. 5.2 Results from Sensitivity Analysis The objective of our sensitivity analysis is to establish whether the results from scenario analysis still hold i f the crane service time is different. First, the T/T model was tested with 80% crane service time to check i f 5 tractor/trailers per crane is still the practical optimal choice for the current operations when cranes can work faster. The results are listed in Table 9. According to Table 9, the results show that five T/Ts per crane is still optimal in practice and that increasing the number of tractor/trailers per crane from five to six increases the productivity by less than 2%. Second, the results from the T/T model with 80% crane service time are compared to the results from the SC model with 80% crane service time to check i f 3 straddle carriers per crane is still better than 5 T/Ts. The results are listed in Table 10. 25 Table 9: Crane productivities (lifts/hour) from the Sensitivity Analysis using the T/T Model with 80% Crane Service Time Vessel name Crane 6 T/Ts Difference 5 T/Ts Ideal Productivity 4 T/Ts Difference A T . 32.13 1.46% 31:67 41.12 29.50 -6.86% 2 29.73 0.90% 29.46 36.05 ',27.31 -7.31% 30.93 1.18% 30.57 38.51 • 28.40 -7-08% 1 30.16 1.58% "29.69 35.90 26.94 -9.26% 2 32.61 0.26% '32:53 38.87 29.08 -10.60% 31.58 0.81% ',31.32 37.62 .28.18 -10.04% >- -. c c 1 27.06 0.76% ' 26.85 38.06 - 25.f99 -3.21% 2 28.14 0.59% 127'.97 36.30 26.42 -5.56% 3 29.52 0.91% >29.26 38.74 ,•-28.11 -3.90% 28.22 0.77% 28.01 37.81 , 26.86 -4.10% * ' IP, D, 1 30.74 1.16% 30.39 37.31 26.53 -12.69% 2 29.95 0.00% 29.95 36.18 26.10 -12.86% 30.36 0.60% 30.18 36.76 26.32 -12.77% *: The Difference columns show the differences between the results of tractor/trailer model with 80% crane service time using different number of tractor/trailers per crane and the results of the tractor/trailer model with 80% crane service time using five tractor/trailers. Table 10: Comparison of the Crane productivities (lifts/hour) from the Scenario Analysis using the SC Model with 80% Crane Service Time and the Results from the Sensitivity Analysis using the T/T Model with 80% Crane Service Time Vessel name Crane 80% T/T 4 SCs Difference 3 SCs Difference 2 SCs Difference A 1 31.67 35.85 13.21% 35.56 12.30% ' 33.54 5.89% 2 29.46 33.08 12.27% 33.08 12.27% 32.49 10.28% 30.57 34.46 12.74% 34.32 12.29% ' 33.02 8.04% D 1 29.69 32.13 8.24% 31.72 6.84% 27.68 -6.77% 2 32.53 34^ 00 4.53% , 33.64 3.43% ' 28.46 -12.50% 31.32 33.22 6.07% ~32.84 4.85% 28.14 -10.16% c 1 26.85 29.23 8.86% 28.-76 7.11% 26.07 -2.91% 2 27.97 30.68 9.68% ""'30.29 8.28% «,29.53 5.59% 3 29.26 31.46 7.52% 31.00 5.98% , -28.61 -2.21% 28.01 30.42 8.60% 29:97 7,02% 27.87 -0.48% D 1 30.39 34.91 14.88% 34.51 13.56% 32.29 6.27% 2 29.95 32.53 8.60% 32.48 8.42% 31.74 5.97% 30.18 33.72 11.74% 33.50 11.00% 32.03 6.12% 26 According to Table 10, the results also show that using three straddle carriers per crane brings higher productivity than five tractor/trailers per crane. In addition, the results showed that assigning only two straddles carriers per crane may reduce the productivity severely and assigning four straddles does not increase the productivity significantly. 5.3 Conclusion According to the results of the scenario analysis and sensitivity analysis, in Vanterm, replacing tractor/trailers with straddle carriers w i l l increase crane productivity. In addition, simulation reveals the performance trends when changing the number of tractor/trailers or straddle carriers. For current operations with tractor/trailers, 5 tractor/trailers per crane is the best choice. For operations with straddle carriers, in most cases, 3 straddle carriers per crane can achieve at least the same productivity as 5 tractor/trailers per crane. Even though each straddle carrier costs about 500,000 dollars while each tractor/trailer only costs around 70,000 dollars, replacing tractor/trailers with straddle carriers can save wage costs and reduce the risk of not having enough labour. Moreover, i f using straddle carriers can reduce crane service times and increase the crane productivities, TSI may attract more business from shipping companies, to whom faster turnaround means increase in their vessel utilization. 27 6. F U R T H E R STUDY 6.1 More Simulation Several simplified simulation models are developed to understand the impact of different configurations. The reason not to use the models developed for TSI is because for each test, running those models requires preparing lots of input files, which is time consuming. 6.1.1 Tractor/trailer Operation • Models Several models were developed, three for the unloading process, another two for the loading process. Those models are developed to test different operating policies. In the complete model of unloading (Model A) , there is a buffer under one crane, so the crane can drop off containers on the ground when there is no tractor/trailer available for a pickup. A top lifter is assigned to clean the buffer. This buffer has no use for crane in the loading process because tractor/trailers cannot drop off containers by themselves, so there is no need to build a simulation model of loading process with a buffer. In the simpler model of unloading (Model Bu), the buffer is removed. Model A , Model B u and Model BI are all based on operating policy A, which means that the crane and the R T G can work without tractor/trailers' presence. In Model Cu (unloading) and Model CI (loading), the crane and the R T G can only work with at least one tractor/trailer's presence, so the tractor/trailers are not released until the end of a crane or R T G service, which is operating policy B. Nonetheless, since the present models for further studies are different from the models developed for TSI in several aspects, it is considered that those differences may affect the results. In that case, the productivities from the models here may not be realistic. The major two differences are listed below: 1. in the present models, the working sequence of the cranes is now simplified to only loading or unloading, and these two different processes are never mixed together; 28 2. in order to get more accurate long term crane productivities, the number of containers to be handled in the simplified models is 5000, which is significantly larger than the numbers in the real operations. The impact of the first difference is not very large. Since the T/Ts w i l l be called to move to a crane i f it is unloading or to an R T G i f the crane is loading, when the process switch from one to the other (e.g. from loading to unloading), there wi l l be an approximate 2-minute delay in the real operation, which is the travelling time of a T/T to move between R T G and Crane. When the number of containers to be loaded or unloaded in one batch is large enough, say 20 containers, this delay wi l l not make a large difference in the crane productivities between the present models and the real operations. More scenarios are run to test the impact of the second difference. The number of containers to be handled is reduced from 5000 to 20, which is close to the mean number of containers per batch in the real operations. • Results Table 11: Comparison of Simulated Crane Productivities (Lifts/Hour) from Different Models of unloading process Number of T/T 1 2 3 4 5 6 7 8 Model A (no buffer size limit) 35.73 35.73 35.73 35.73 35.73 35.73 35.73 35.73 Model A (limited 22^ 65 buffer space) 14.50 30.53';'' 3 5.;76 V 35 69 35.66 3,5.75 35.79 '* Increase 56.22% 34.83% 17.13% -0.21% -0.07% 0.23% 0.12% Model'Bu . *• 9.49 14.78 ^ 23.09 , 28.60 31.29 3 1.93 32:00 32.07 Increase 55.70% 56.20% 23.89% 9.41% 2.03% 0.22% 0.23% Model Cu ~ ' 7148 11.63 , 18.'72?: 23.94 29.03 . 31 35 3r!99 . 32.05 Increase 55.54% 60.99% 27.91% 21.25% 8.00% 2.03% 0.21% Difference (Bu&A)~ 73:43% 58.63%-' 35:39% 19.95% ' 12.42% 10'.64% 10.44% 10.24% Difference (Cu&Bu) 21.25% 21.33% 18.92% 16.29% 7.23% 1.81% 0.03% 0.05% Difference (Cu&A) 79.08% 67.46% 47.61% 32.99% 18.75% 12.26% 10.47% 10 28% T: All the results above are obtained after 10 replications. All the standard errors from each scenario are under 0.2. **: The differences are the differences between the results from two models while the number of T/Ts per crane is the same. ***: The crane and RTG service times used in Model Cu is the summation of two parts of the service time used in Model Bu. ****. j n e buffer size is defined as 16, which is an estimate of the size of the buffer in Vanterm. *****. j n e distance u s e c j m t n e models is 600. 29 C r a n e P r o d u c t i v i t i e s f r o m t h e T / T U n l o a d i n g M o d e l s 40 0 1 , ^ — n , , , r — 1 2 3 4 5 6 7 8 Number of T/Ts Figure 14: Comparison of Crane Productivities (Unit: lifts/hour) in the Unloading Process From Different Tractor/Trailer Models Table 12: Comparison of Crane Productivities from Different Models of loading process (Unit: Lifts/Hour) Number of T/T 1 2 3 4 5 6 7 8 Model BI 9.70 15.93 23.94 30.40 31.76 32.01 32.07 32.08 Increase " , 64.26% , 50.32% • 27.00%', 4.47% 0.77% 0.19%* 0'.03%^ Model CI 7.48 11.69 19.26 24.75 30.23 31.72 32.01 32.05 Increase,1. ; ' , 56.36% 64.72% 28.54% 22.12% 4.93%, 0.92% 0.14% Difference 29.68% 36.23% 24.32% 22.82% 5.07% 0.91% 0.19% 0.08% *: All the results above are obtained after 10 replications. All the standard errors from each scenario are under 0.2. **: The difference is the difference between the results from two models while the number of T/Ts per crane is the same. ***: The crane and RTG service times used in Model CI is the summation of two parts of the service time used in Model BI. ****: The distance used in the models is 600. 30 C r a n e P r o d u c t i v i t i e s f r o m t h e T / T L o a d i n g M o d e l s +— Model BI •A—Model CI 1 2 3 4 5 6 7 8 Number of T/Ts Figure 15: Compar i son of C rane Product iv i t ies (Unit: L i f ts/Hour) in the Load ing Process f rom Dif ferent Tractor/Tra i le r Models Table 13: Comparison of Crane Productivities from Different Models of unloading process with 20 containers (Unit: Lifts/Hour) Number of T/T 1 2 3 4 5 6 7 8 Model Bu 9.87 •15.19 , ,23.92 29.37 32.85 34.56 35.48 . 35.76 Increase 53.93% 57.50% 22.75% 11.86% 5.22% 2.67% 0.77% Model Cu 7.79 12.36 19.72 25.08 30.42 , 33.35 34.78 35.50 Increase 58.56% 59.59% 27.20% 21.26% 9.63% 4.29% 2.08% Difference(Cu&Bu) 21.03% 18.65% 17.57% 14.58% 7.40% 3.52% 2.00% - 0.72% Crane Productivities from the T/T Unloading Models 4 0 0 0 - r IS 3 5 0 0 5 3 0 0 0 -1 2 5 0 0 -? 2 0 0 0 0. 1 5 0 0 1 0 0 0 -o 5 0 0 -0 0 0 -3 4 5 6 Number of T/Ts 8 •20 containers (Bu) 20 containers (Cu) • 5000 containers | (Bu) 5000 containers | (Cu) Figure 16: Compar i son of Crane Product iv i t ies (Unit: L i f ts/Hour) in the Un load ing Process f rom Different Tractor/Tra i ler Models wi th Different Numbe r of Conta iners 31 Table 14: Comparison of Crane Productivities from Different Models of loading process with 20 containers (Unit: Lifts/Hour) Number of T/T 1 2 3 4 5 6 7 8 Model Bu , , . 10.32 16.91 ^25544 ".31.85 32.88 33.14 33.15 * ,33.15 Increase 63.86% 50.44% 25.20% 3.22% 0.79% 0.03% 0.00% Model Cu- 7.99 12.95 20.54 <26.09 31.72 32.99 "33.24 33.24 Increase 62.15% 58.65% 27.00% 21.57% 4.00% 0.77% 0.00% Difference(Cu&Bu) 22.62% 23.43% 19.25% 18.08% 3.52% 0.45% -0.29% -0.29% (0 o 3 T3 2 o_ c 15 o C r a n e P r o d u c t i v i t i e s f r o m t h e T / T L o a d i n g M o d e l s 35 00 i 30 00 -25 00 -20 00 -15 00 -10 00 -5 00 -0 00 3 4 5 6 Number of T/Ts — • — — 20 Containers (Bu) A— — 20 Containers (Cu) - - - B - - - 5000 Containers (Bu) • - -x- - - 5000 Containers (Cu) Figure 17: C o m p a r i s o n of Crane Product ivi t ies (Uni t : Li f t s /Hour) in the Load ing Process from Different Trac to r /Tra i l e r Models wi th Different N u m b e r of Con ta ine r s • Analyses and Conclusions First, the study was focused on the effect of the buffer. According to Table 11 and Figure 14, for unloading operations, the crane productivity from Model A is the highest. The existence of a buffer reduces the chance of crane blocking when waiting for tractor/trailers. The size of the buffer can affect the crane productivity. If the size of the buffer is unlimited, then in the unloading process, the crane productivity from Model A is the same as the one from the straddle carrier model with no buffer size limit, because in both cases, the crane is not blocked. If the buffer size is limited, which happens in reality since there is only one top lifter assigned to "clean" the buffer, it can be predicted that when there are not enough tractor/trailers, the buffer wi l l f i l l up and then the crane may be blocked. In Figure 16, when the number of containers to 32 be handled is small, the crane productivity is higher. The reason is because the buffer can not be fil led up when there are only a few containers to be handled, compared to the buffer size. Based on the findings, it can be concluded that the existence of a buffer can improve crane productivity and a larger buffer is always preferred. Second, the effect of releasing tractor/trailers during a crane or R T G service is studied. In Figure 14, the crane productivity of Model Cu is the lowest in those of the three models of unloading process. It is lower than that of Model Bu, where tractor/trailers are released during a crane or R T G service. When the number of tractor/trailers is increased to a certain level, the productivity from Model Cu is very close to the one from Model Bu. The reason is that when the number of tractor/trailers is large enough, they are more likely to wait in queue for service, so even though in the original model a tractor/trailer can leave during the service, it still has to wait for the crane or R T G becoming idle after serving the previous tractor/trailer. As a result, there is little time gain from leaving during the service and the time a tractor/trailer spent on waiting is very close in both models. In Figure 15, the crane productivity of Model CI is lower than that of Model BI. As for the unloading process, when the number of tractor/trailers is increased to a certain level, the productivity from Model CI is very close to the one from Model BI. The reason is the same as for the unloading process: when the number of tractor/trailers is large enough, they are more likely to wait in queue for service, so even though in Model BI, a tractor/trailer can leave during the service, it still has to wait for the crane or R T G becoming idle after serving the previous tractor/trailer and then the time a tractor/trailer spent on waiting wi l l be equal in both models. It can be concluded that when the number of tractor/trailers is large enough, the effect of releasing tractor/trailers during a crane or R T G service is negligible. 6.1.2 Straddle Carrier Operation • Models 33 Two simplified simulation models were developed, one for the unloading process, another for the loading process. Two buffers are created to reduce the probability of crane blocking, Buffer A under each crane, Buffer B under an RTG . Containers are first dumped into buffers and then handled by straddle carriers. Straddle carriers are responsible to transport the containers to the other buffer. Depending on whether they are import or export containers, containers are finally picked up by the crane or the RTG , and then stacked. If the size of Buffer A is unlimited, there is no possibility of crane blocking, so the crane can achieve highest productivity without any intervention from the Buffer B. Otherwise, the buffer size can affect the crane productivity in the unloading process greatly when the number of straddle carriers is low. The sizes of two buffers affect crane productivity differently. Different buffer sizes have been tested. The number of containers to be loaded and unloading in one batch may affect the crane productivity. However, it can be expected that the impact wi l l be similar to that on the crane productivity of the R T G and Tractor/Trailer operations. • Results Crane Productivities from the S C Unloading Models - • — Tw o Unlimited Buffer (A) -A— Limited Buffer A Unlimited Buffer B(B) -x— Limited Buffer A & Buffer B (C) 1 2 3 4 5 6 7 8 Number of SCs Figure 18: Comparison of Crane Productivities (Unit: Lifts/Hour) in the Unloading Process From Different Straddle Carrier Models 34 Table 15: Comparison of Crane Productivities from Model of Unloading Process with Different Buffer Size (Unit: Lifts/Hour) Number of SCs 1 2 3 4 5 6 7 8 Two Unlimited Buffer (A) 35.74 35.74 35.74 35.74 35.74 35.74 35.74 35.74 Limited Buffer A Unlimited Buffer B (B) 8.63 14.74 2Ar3 31.32 35175' 35V75 '«, 35.75 35.75 Increase 70.86% 65.46% 28.41% 14.13% 0.00% 0.00% 0.00% Limited Buffer A & Buffer B (C) 8.63 14.74'- * 24.39 ' 30;74 32.36 32.44 32.40 32.3,7 Increase 70.86% 65.46% 26.04% 5.24% 0.26% -0.13% -0.09% Difference (B&A) 75.86% 58.75%' 31.75% 1-2.36% -0:02%, -0.02% : -0:02%; -0:02%,; Difference (B&C) 0.00% 0.00% 0.00% -1.85% -9.49% -9.26% -9.38% -9.46% Difference (C&A) . j 75.86% 58.75% 31.75% 13.98% 9.47% v 9,24%= . 9.36% . 9.44% *: All the results above are obtained after 10 replications except the case when there are 4 straddle carriers with unlimited Buffer B. The result of that scenario is obtained from 100 replications. All the standard errors from each scenario are under 0.2. **: The difference is the difference between the results from two models while the number of straddle carriers per crane is the same. ***: The size of Buffer A is 16. The size of Buffer B is 30. They are both arbitrary numbers. ****: The distance used in the models is 600, which is also an arbitrary number. 35 30 25 20 a. 1 5 <u 10 c SS 5 ° 0 '> '-#-» u O Crane Productivities from the SC Loading Models 3 4 5 6 Number of SCs -*— Unlimited Buffer A & Buffer B(A)| - Limited Buffer A Unlimited Buffer B(B) - Limited Buffer B Unlimited Buffer A ( Q - Limited Buffer A & Buffer B (D) Figure 19: Comparison of Crane Productivities (Unit: Lifts/Hour) in the Loading Process From Different Straddle Carrier Models 35 Table 16: Comparison of Crane Productivities from Model of Loading Process with Different Buffer Size (Unit: Lifts/Hour) Number of SCs 1 2 3 4 5 6 7 8 Unlimited Buffer A & Buffer B (A) 8.6 14.7 24.3 31.97 32.1 32.1 32.1 32.1 Increase 70.86% 65.32% 31.54% 0.42% 0.00% 0.00% 0.00% Limited Buffer A Unlimited Buffer B (B) 8.6 14.7 24.31 32.03 32.1 32.1 32.1 32.1 Increase 70.86%.- 31.77% , 0.22% 0.00% ' 0.00% 0.00% Limited Buffer B Unlimited Buffer A (C) 8.6 14.7 24.31 31.97 32.1 32.1 32.1 32.1 Increase 70 86% 65 37% 31 50% 0 42% 0 00% 0 00% 0 00% Limited Buffer A & Buffer B (D) 8.6 14.7 24.31 31.97 32.1 32.1 32.1 32.1 Increase 70.86% 65.37%' 31.50% 0.42% 0.00% 0.00% 0.00% Difference (A&B) 0.00% 0.00% -0.02% -0.21% 0.00% 0.00% 0.00% 0.00% Difference (A&C) ' 0.00% 0.00% -0.02% 0.00% - 0.00%' 0.00% 0.00% 0.00% Difference (A&D) 0.00% 0.00% -0.02% 0.00% 0.00% 0.00% 0.00% 0.00% Difference (B&C) . 0.00% 0.00% 0.00% 0.21% 0.00% 0.00% 0.00%. 0.00% Difference (B&D) 0.00% 0.00% 0.00% 0.21% 0.00% 0.00% 0.00% 0.00% Difference (C&D) 0.00% 0.00% 0.00% 0.00% 0.00% ' 0.00% 0.00% 0.00% *: All the results above are obtained after 10 replications except the case when there are 4 straddle carriers with unlimited Buffer B. The result of that scenario is obtained from 100 replications. All the standard errors from each scenario are under 0.2. **: The difference is the difference between the results from two models while the number of straddle carriers per crane is the same. ***: The size of Buffer A is 16. The size of Buffer B is 30. They are both arbitrary numbers. ****: The distance used in the models is 600, which is also an arbitrary number. • Conclusions In both loading and unloading processes, according to the results, the size of Buffer B is not as important as the size of Buffer A . According to Table 15 and Figure 18, in the unloading process, Buffer A is extremely useful. Buffer B becomes useful in the unloading process when the number of straddle carriers is large, because in that case, the arrival rate of containers for R T G service exceeds the R T G service rate. 36 According to Table 16 and Figure 19, in the loading process, both Buffer A and Buffer B do not help much. The reason is that since an R T G works slower than a crane, it is more likely to have a starving crane than a full buffer. 6.2 Jackson Closed Network The queue length of the export containers waiting to be served by RTGs and the queue length of the import containers waiting to be served by cranes can be infinite i f the container terminal keeps serving vessels and receives containers continuously. Since we are not interested in those queues, they are excluded in the systems. One observation of the current operations, is that the system is stable regardless of the service rate of cranes, RTGs and travelling time of tractor-trailers. The reason is that WIP, the number of containers being served by the cranes, RTGs or tractor-trailers, is finite. It cannot exceed the number of cranes, RTGs and tractor-trailers. However, for Straddle Carrier Operation, the system can be unstable i f there is no limitation on buffer size. If the cranes are faster than the RTGs, for unloading, WIP may keep increasing, as would cycle time. That wi l l also happen in the loading process i f the RTGs are faster. But in reality, since the space of a terminal is precious, the buffer size is always finite, so WIP is constrained. Since with limited buffers both systems are stable, queuing theory can be applied in this study. In order to observe the long term performance, we assume the number of containers to be handled is infinite, which means that there are always containers waiting to be loaded or unloaded. For the current operations, in order to keep the model simple, buffers are not included in this study. As we know, when the buffer size is limited, the buffer wi l l be filled up eventually i f the number of tractor/trailers is not comparable to the number of containers to be handled. Since there is now an infinite number of containers to be handled and only one top lifter cleaning the buffer, which moves slowly compared to tractor/trailers in 37 transporting a container, it is ignored in the study. Since the buffers won't be cleaned, then they are not of much use after they are fi l led up, which means that they can also be ignored. If there is no buffer, then a Jackson Closed Network can be well applied to the current operations, since the WIP level is now dictated only by the number of tractor/trailers. First, the operating policy is assumed to be policy B, the R T G and the Crane can not work without a T/T's presence. Second, the service time and the travelling time distributions are all assumed to be exponential to ease the calculations. Third, T/Ts are treated as jobs. Fourth, the discipline of R T G and crane's service is assumed FIFO. We obtain a Jackson Closed Network problem with exponential service time at each station. Station 1: an RTG, Rubber Tire Gantry Station 2: Tractor/Trailers traveling from the R T G to a crane Station 3: a crane Station 4: Tractor/Trailers traveling from the crane to the R T G T/Ts Figure 20: Jackson Closed Network If there are n T/Ts working in the system, the states are defined as follows: S = ( S i , s 2, s 3, s 4) Si is the number of T/Ts being served by station i and those waiting to be served. Since it is a closed network and there are only n T/Ts, S i + s 2 + S3 + S4 = n. The stationary probability of each state can be calculated by using formulas listed in Appendix G. By summing up all the probabilities of the states at which the crane is busy, 38 we are able to get the proportion of time when the crane is working in the long term. Since we already have the crane service rate, the long term crane productivity can thus be obtained by using the formula: Crane Productivity = Crane Service Rate * Util ization of the crane = Crane Service Rate * Probability (the crane is busy) Since it is a closed network, in long term, the total number of jobs served by the R T G must be equal to the total number of jobs served by the crane, so the crane productivity must be equal to the R T G productivity. Then the long term crane productivity can also be obtained by using the formula: Crane Productivity = R T G Productivity = R T G Service Rate * Util ization of the R T G = R T G Service Rate * Probability (the R T G is busy) One important observation is that when the number of tractor/trailers per crane increases, the number of states increases at the same time, so it becomes harder to calculate the stationary probability of each state and then obtain the long term crane productivity. The detail of calculations is also in Appendix G. The calculated long term crane productivity is listed in table 17. Table 17: Long Term Crane Productivities (Unit: Lifts/Hour) Calculated from the Jackson Closed Network Model with Exponential Service Times Number of T/Ts 1 2 3 4 5 6 7 Productivity 9.49 16.42 21.17 24.30 26.34 27.70 28.65 Increase ' , 0. 73.07% 28.91% 14.75% 8.40% 5.19% 3.40% *: Increase is the increase in crane productivity after assigning one more tractor/trailer to the crane 39 C o m p a r i s o n o f C r a n e P r o d u c t i v i t i e s — Jackson Closed Network *—Simulation 1 2 3 4 5 6 7 Number of T/Ts Figure 21: Comparison of Crane Productivities (Unit: Lifts/Hour) from Jackson Closed Network Model and Tractor/Trailer Simulation Model According to Figure 21, the results are not very close to the results from the simulation model Cu, the simulation model based on operating policy B. The differences between the results from two models with same number of tractor/trailers per crane are in 1% -30% range. These differences may be explained as follows: A crane is starved i f there is no tractor/trailer under it. The tractor/trailers are served by the crane in cycles. After the crane serves all the tractor/trailers in a cycle, i f the tractor/trailer the crane serves first in that cycle has not come back, then the crane wi l l be starved. In order to present the crane to be starved, the time for the crane to serve all the tractor/trailers in a cycle must be greater than or equal to the time for the first tractor/trailer in that cycle to come back to the crane after being served. The standard deviation of the exponential service time distribution is much larger compared with the deviation of the real service times when the means are the same. Since the service times in the model are assumed exponentially distributed, the time for the crane to serve all the tractor/trailers in a cycle and the time for a tractor/trailer to come back to the crane after being served by the crane have larger variation than using the real distribution. 40 When the number of T/Ts is small, in the real operation, the time for the crane to serve all the tractor/trailers in a cycle is usually shorter than the time for the first tractor/trailer in that cycle to come back to the crane after being served, so it is very likely for the crane to be starved. However, when service time variations are large, it becomes more likely that the time for the crane to serve all the tractor/trailers in a cycle is greater than or equal to the time for the first tractor/trailer in that cycle to come back to the crane after being served, so the crane is starved less than in the real operation. That explains why the productivities from the simulation are lower than the results from the Jackson Closed Network model when there are only 1 to 3 tractor/trailers in use. When the number of T/Ts is greater than 4, larger service time variations become harmful. In the real operation, the time for the crane to serve all the tractor/trailers in a cycle is usually longer than the time for the first tractor/trailer in that cycle to come back to the crane after being served, so it is less l ikely for the crane to be starved. However, when service time variations are large, compared to the real operation, it is more possible that the time for the crane to serve all the tractor/trailers in a cycle is less than the time for the first tractor/trailer in that cycle to come back to the crane after being served, so the crane is be starved more than in the real operation. That explains why the results from the simulation are higher than the results from the Jackson Closed Network model when there are more than 4 tractor/trailers in use. In order to avoid the problem caused by larger standard deviations, the real service time distributions may be approximated as the sum of several exponential distributions. In order to make it easier to understand, the service of each station is now looked as a sequence of activities, of which the service time distribution are exponential. According to the data collected from the real operation, it can be observed that the squared coefficient of variation (SCV) of each service time distribution is very small. Because of that, the minimum number of exponential distributions required to approximate each of the real service time distribution is large. The detail of the estimation is in Appendix H. The estimates of the minimum number of exponential distributions required to approximate each service time distribution are listed in table 18. 41 Table 18: Estimate of the Minimum Number of Exponential Distributions Required to Approximate Each Service Time Distribution Equipment Distribution Unit (seconds) (seconds) SCV n* Crane (vessel to TT) 30 + WEIB(30, 1.14) Second 58.7 26 0.12 9 Crane (TT to vessel) 12.5+ ERLA(7.39, 4) Second 42.1 15.2 0.13 8 31.5 + 47 * RTG (pickup) BETA(0.719, 0.961) Second 50.2 14.5 0.08 13 RTG (stacking) 30.5 + WEIB(32.1, 1.25) Second 60.4 24.2 0.16 6 Stacker 14.5 + WEIB(15.8, 1.71) Second 28.6 8.47 0.09 12 *: n is the minimum number of exponential distributions required to approximate each service time distribution. The definition of the states is changed to accommodate the approximation. S = (Si, S 2 , S 3 , S 4) Sl=(V.../1/71) 5 2 = ( 5 2 1 > . . . / 2 A ) 53 = ( ^ , . . . / 3 * ) 5 4 = ( 5 4 1 , . . . / ^ 4 ) Pi: The number of steps in the service at station 1, 2, 3 and 4. S i i : The number of T/Ts being served by station i at step 1 and those waiting to be served. Sy (j * 1): The number of T/Ts being served by station i at step j . |SJ|: The number of T/Ts being served by station i and those waiting to be served. |SJ| = Pi I*, Since it is a closed network and there are only n T/Ts, |si| + |s2| + |s3| + |S4J = n. 42 Because the number of steps of each station is large, when the number of tractor/trailers, n, increases, the number of states wi l l increase dramatically. The number of states when there are n tractor/trailers in the system is estimated before any attempt to solve the problem, since it affects the size of the problem. The detail of the estimation is in Appendix I. It can be observed that the number of states increases very quickly with the number of steps in each station. When there are 8 tractor/trailers in the system, the number of states would be over 16 mil l ion. Since the number of states is large, it increases the difficulty to obtain the stationary probability by solving a system of equations, of size related to the number of states. Due to the computational complexity, applying Jackson Closed Networks does not seem to be an efficient method for estimating the crane productivities. 6.3 Deterministic Models When we were trying to find a way to solve the Jackson Closed Network model, we found that some random variables were dependent, which made it very difficult to obtain their distributions. However, in deterministic models, there is no dependency between any two variables. Two deterministic models were thus developed in order to provide us some insights. In order to simplify the models, the crane and the R T G start working after the arrival of tractor/trailers and become idle after releasing the tractor/trailer, so the tractor/trailers won't be released during a crane or R T G service, which is exactly the same as operating policy B. Another assumption is that the discipline of RTG ' s service is FIFO. In the deterministic models, the sum of waiting times for any cycle is a fixed amount in steady state. (A cycle in R T G and Tractor/Trailer Operation is defined from the time an R T G begins working on a tractor/trailer to the next time the R T G begins working on the same tractor/trailer. A cycle in Straddle Carrier Operation is defined from the time a straddle carrier picks up or drops off a container at the R T G side to the next time the same straddle carrier comes back to the R T G for another pickup or dropoff.) 43 The above statement is approved as follows: In the current operations, suppose there are n tractor/trailers in the system (in the figure below, n = 2). The R T G and Crane service times and travelling times for each tractor/trailer are the same. In Figure 22, a cycle is observed from both the R T G side and the tractor/trailer side. Case 1: l< A Cycle >l RTG: R RW 2 ' R ! RW RW 2 i R RW -> T/T.U T/T2: TRP C W t C LCB_ T. RC C T, CR C . T« CB_ -> Case 2: Case 3: Figure 22: A cycle of RTG and Tractor/Trailer Operation in 3 cases 44 R: R T G service time C : Crane service time RWJ: R T G waiting time for Tractor/Trailer i in steady state RWj ' : R T G waiting time for Tractor/Trailer i in initial state TRC: Tractor/Trailer travelling time from R T G to Crane TCR: Tractor/Trailer travelling time from Crane to R T G CWJ: Tractor/Trailer i waiting time for Crane service in steady state DJ: the difference between RWj ' and RW, First, it can be easily observed that in steady state, CWj , the time tractor/trailer 1 spent on waiting for crane service is 0, i f the crane works faster than the RTG . The reason is that the inter-departure time of tractor/trailers from the RTG , which is also the inter-arrival time of tractor/trailers at the crane, wi l l be longer than the service time of the crane, and thus after one cycle, there wi l l be no tractor/trailer waiting for crane service. Second, in steady state, RWj can not be longer than TRC + TCR + C. If there is any RWj greater than or equal to TRC + TCR + C like RW2 in case 2 in Figure 22, which means that this T/T is not used in the current and previous cycles and those cycles have one fewer T/Ts. When this T/T is put into use, we can simply make it T/T l and mark the other T/Ts from 2 by their arrival sequence. Then from this cycle, RWj is less than TRC + TCR + C. Third, i f T R C + T C R + C ^ '=2 + (n -1 )R like case 3, then one tractor/trailer has to wait for the R T G service, which wi l l reduce the R T G waiting time for the next tractor/trailer and thus decrease the total R T G waiting time in the next cycle. RWj wi l l be adjusted like case 3 and then becomes fixed in steady state. It can be concluded that in steady state, the cycle looks exactly like case 1. Fourth, R W i = r 0 i f T R C + T C R + C ^ '-2 + (n -1 )R . TRC + TCR + C - / = 2 - (n -1 )R otherwise 45 i f TRC + TCR + C — (n- l)R otherwise Now it is proved that in the deterministic tractor/trailer operation model, the sum of waiting times for any cycle is a fixed amount in steady state. Reducing the total R T G waiting time can decrease the inter-arrival time at the crane and thus increase the crane productivity, so i f the main target is to increase the crane productivity, increasing the number of tractor/trailers can serve the goal. As long as TRC + TCR + C ^ (n-l)R, there wi l l be no R T G waiting time, so in practice, an optimal n is the minimum number satisfying that inequality. Given the number of tractor/trailers in the system and all the service and travelling times, the sum of waiting times for any cycle in steady state can be calculated. Since the sum of waiting times in any cycle is a fixed amount and the service and travelling times are deterministic, the time to complete a cycle is also a fixed amount. Since it is a closed network, the crane productivity must be equal to the R T G productivity. Thus the crane productivities can be calculated as: (\-^~ ) Crane Productivity = R T G Service Rate * '=< When the number of tractor/trailers per crane and the R T G service time are fixed, reducing the sum of R T G waiting time in each cycle can increase the crane productivities. There are two ways of reducing the sum of R T G waiting time in each cycle: first, reducing the tractor/trailer travelling time, which is TRC + TCR; second, reducing the crane service time. In steady state, we wi l l have ;=1 0 T R c + T C R + C - ( n - l ) R 46 The crane productivities with n = 1 to 8 tractor/trailer in the system are calculated and listed in Table 19. Table 19: Steady State Crane Productivities (Lift/Hour) of the Tractor/Trailer Deterministic Model Number of T/Ts 1 2 3 4 5 6 7 8 Productivity 7.50 15.00 22.50 30.00 32.55 32.55 32.55 32.55 Increase ' 0 100.00% 50 00% 33.33%' '2.03%, 0.00% 0 00% 0.00% *: Increase is the increase in crane productivity after assigning one more tractor/trailer to the crane In Straddle Carrier Direct Operation, suppose there are n straddle carriers in the system (in the figure below, n = 2). The R T G and Crane service times and travelling times for each straddle carrier are the same. In Figure 23, a cycle is observed from both the R T G side and the Straddle Carrier side. R: R T G service time C: Crane service time RWJ: R T G waiting time for Straddle Carrier i in steady state RWj ' : R T G waiting time for Straddle Carrier i in initial state TRC: Straddle Carrier travelling time from R T G to Crane, including the pickup or drop-off time TCR: Straddle Carrier travelling time from Crane to RTG , including the pickup or drop-off time CWJ: Straddle Carrier i waiting time for Crane service. Di: the difference between RWj ' and RWj The R T G waiting times in the loading process in the straddle carrier operation model is different from the ones in the tractor/trailer operation model. They are the R T G waiting time for a straddle carrier to pick up a container in the full buffer. In deterministic model, i f the buffer size is limited and the number of straddle carriers is not big enough, the buffer wi l l be filled up eventually and then the R T G has to wait for an empty spot to 47 ground a container. When the number of straddle carriers is big enough, the buffer wi l l not be fi l led up and then there is no such an R T G waiting time at all. Case 1: RTG: R RWi < A Cycle > R RW 2 , R RWi t a i n R RW2< , a a N SCI : i i TRC Q W I T C R t ? 1 1 1 1 1 1 N SC2: I t 1 i TRC C * #_ i ' . 1 > 1 : t W 2 T C R ; • • > I 1 ;< A Cycle >; x Case 2: RTG: . R . RWi t Case 3: RTG: Initial Cycle RW 2 ' -> A Cycle A Cycle Figure 23: A cycle of Straddle Carrier Operation in 3 cases 48 First, it can be easily observed that for the same reason as for the tractor/trailer deterministic model, C W i , the time straddle carrier 1 spent on waiting for crane service is 0, i f Crane works faster than RTG . Second, in steady state, RWj can not be longer than TRC + TCR - R. If there is any RWj greater than or equal to TRC + TCR - R like R W 2 in case 2 in Figure 22, which means that this straddle carrier is not used in the current and previous cycles and those cycles have one fewer straddle carriers. When this straddle carrier is put into use, we can simply make it SCI and mark the other straddle carriers from 2 by their arrival sequence. Then from this cycle, RWj is less than T R c + TCR - R. fjRWi Third, i f TRC + TCR - , = 2 + nR, then one straddle carrier has to wait for the R T G service, which wi l l reduce the R T G waiting time for the next straddle carrier and thus decrease the total R T G waiting time in the next cycle. RWj wi l l be adjusted like case 3 and then becomes fixed in steady state. It can be concluded that in steady state, the cycle looks exactly like case 1. Fourth, R W i 0 TRC + T C R - '=2 - nR i f TRC + TCR ^ <=2 + nR otherwise In steady state, we wi l l have ^RW, = (0 i f TRC + TCR — nR otherwise Now it is proved that in the deterministic straddle carrier operation model, the sum of waiting times for any cycle is a fixed amount in steady state. 49 Similar to the current operations, reducing the total R T G waiting time can decrease the inter-arrival time of Crane and thus increase the crane productivity, so i f the main target is to increase the crane productivity, increasing the number of straddle carriers can serve the goal. As long as TRC + TCR - nR, there wi l l be no R T G waiting time, so in practice, optimal n is the minimum number satisfying that inequality. T +T 1 RC T 1CR In the straddle carrier deterministic model, , = 1 = 0 when n ^ R . However, im in the tractor/trailer deterministic model, / = 1 = 0 when TRC + TCR + C TRC + TCR + C TRC + TCR n ^ R +1 . R + 1 > R ,so less straddle carriers are needed to reduce the sum of waiting times to zero. Even i f the sum of waiting times can im not be reduced to zero, with n tractor/trailers, , = 1 = TRC + TCR + C - (n-l)R, while im , = L = TRC + TCR - nR for n straddle carriers. TRC + TCR - nR < TRC + TCR + C - (n-1)R, which means that operations with straddle carrier have less waiting time in a cycle than the operations with same number of tractor/trailers. So less straddle carriers are required to achieve the same crane productivities than tractor/trailers. Similar to the tractor/trailer deterministic model, the crane productivities of the straddle carrier deterministic model can be calculated as: im ) Ym+nR Crane Productivity = R T G Service Rate * '=' When the number of straddle carriers per crane and the R T G service time are fixed, reducing the sum of R T G waiting time in each cycle can increase the crane productivities. Unl ike the current operation, there is only one way of reducing the sum of R T G waiting time in each cycle in the straddle carrier direct operation, which is to reduce the straddle carrier travelling time, which is TRC + TCR. 50 The crane productivities with n = 1 to 8 straddle carriers in the system are calculated and listed in Table 20. Table 20: Steady State Crane Productivities (Lift/Hour) of the Straddle Carrier Deterministic Model Number of SCs 1 2 3 4 5 6 7 8 Productivity 13.40 26.81 32.55 32.55 32.55 32.55 32.55 32.55 Increase-1 '*> 0 100.00% 8.50".. 0.00% 0.00% ,0.00% - 0.00% 0.00% *: Increase is the increase in crane productivity after assigning one more tractor/trailer to the crane. 35 30 h 2 5 | 20 1 15 ^ 10 5 0 Crane Prodcutivities —Crane Prodcutivities from T/T model -•—Crane Productivities from S C model 2 3 4 5 6 7 Number of Tranporters Figure 24: Crane Productivities from the Deterministic Models According to Figure 24, the optimal numbers of T/Ts and Straddle Carriers are 3 and 5, the same as the practical optimal numbers concluded from the simulation models developed for Vancouver Container Terminal. In addition, i f we can reduce the tractor/trailer or straddle carrier travelling time, with fixed R T G service time, fewer tractor/trailers or straddle carriers per crane can help achieve the same crane productivities. So stacking the containers as close to the vessel as possible wi l l help increase the crane productivities. However, it may reduce the accessibility of the containers, which means that it wi l l increase the average difficulty to retrieve the containers, and thus disturb the other operations. If the travelling times can not be reduced, assigning two or more RTGs to assist the crane may help increase crane 51 productivities, since the R T G is the real bottleneck of the operation. However, these topics are out of the scope of this study, so they are not studied in details. 52 R E F E R E N C E Ardavan Asef-Vazir i , Behrokh Khoshnevis(2002) Potentials for ASRS andAGVS in Maritime Container Terminals W. B6hm(2000) Non Coincidence Probabilities and the Time-Dependent Behavior of Tandem Queues with Deterministic Input Stochastic Processes and Their Applications, 89, 2,305-314 Constantinos Boulis, Laura Ing(2000) Simulation and Analysis of the Tandem Queues with Blocking Hong Chen, David D. Yao(2001) Fundamentals of Queueing Networks: performance, asymptotics, and optimization Springer-Verlag, New York W . M . Nawijn(2000) Note on a tandem queue with delayed server release Rai f O. Onvural(1990) Survey of Closed Queuing Networks with Blocking A C M Computing Surveys, Vol.22, No.2, June 1990 A .A . Shabayek, W.W. Yeung(2002) A Simulation model for the Kwai Chung container terminals in Hong Kong European Journal of Operation Research 140(2002) 1-11 Itsuro Watanabe (2001) Container Terminal Planning-A Theoretical Approach Chapter 6P95-152 53 -3-A P P E N D I X B - Service T ime Distr ibutions Crane Service Times: Data Summary Time to Pick up a container from a vessel and drop it on a T/T Unit Seconds Distribution 30 + WEIB(30, 1.14) Number of Observations 112 Min Data Value 30 Max Data Value 173 Sample Mean 58.7 Sample Standard Deviation 26 Crane service times were adjusted to fit models to the reality. Data Summary Time to Move back from a T/T and drop a container onto a vessel Unit Seconds Distribution 12.5 + ERLA(7.39,4) Number of Observations 112 Min Data Value 13 Max Data Value 96 Sample Mean 42.1 Sample Standard Deviation 15.2 60 RTG Service Times: ' ' V * *JL r v3 » Data Summary Time to pick up a container from a T/T Unit Seconds Disitribution 31.5 + 47 * BETA(0.719, 0.961) Number of Observations 17 Min Data Value 32 Max Data Value 78 Sample Mean 50.2 Sample Standard Deviation 14.5 Data Summary Time to Stack a container Unit Seconds Distribution 30.5 +WEIB(32.1, 1.25) Number of Observations 37 Min Data Value 31 Max Data Value 122 Sample Mean 60.4 Sample Standard Deviation 24.2 61 Service time to remove stackers from a container or to put stackers on a container: Data Summary Time to place/remove stackers on/from a container Unit Seconds Distribution 14.5 + WED3(15.8, 1.71) Number of Observations 36 Min Data Value 15 Max Data Value 53 Sample Mean 28.6 Sample Standard Deviation 8.47 62 Top Lifter/Straddle Carrier Service Times (Detail): Data Summary Time to Drop off a container Unit Seconds Distribution 7.5 + LOGN(10.5, 15.5) Number of Observations 20 Min Data Value 8 Max Data Value 37 Sample Mean 17.1 Sample Standard Deviation 9.1 Data Summary Time to Pick up a container Unit Seconds Distribution 2.5 + ERLA(3.14, 3) Number of Observations 40 Min Data Value 3 Max Data Value 30 Sample Mean 11.9 Sample Standard Deviation 5.41 63 APPEND IX C - Container Operations Simulation Model - User Guide Introduction The Vanterm Container Operations Modeling Tool, developed by the Centre for Operations Excellence of the University of British Columbia, is a visual replication and analysis tool for container operations at Vanterm, Vancouver's largest container terminal. The simulation was developed using Arena 6.0 simulation software. To model the container traffic at Vanterm, the tool simulates the loading and unloading operations for vessels of various sizes and with any number of containers. Random stream parameters provide variation when running multiple replications of the model, and the animation provided allows the user to visualize the traffic at the container yard. In addition to providing a visualization of the yard traffic, the simulation provides statistics output in real time over the duration of a simulation run. Final statistics are also collected in output files at the end of each simulation run. Output statistics displayed during a run include: crane moves per hour, accumulated hang time, Tractor Trailer/Straddle Carrier utilization, etc. The modeling tool requires five input files in order to operate. A complete set of input files provides the modeling tool with sufficient information to simulate a vessel. Included in the package are ten sets of input files corresponding to ten different vessels. If it is desirable to create a new set, the Inputs section, which gives a discussion on the stmctures of all input files, can be used as a guide. Included in this package are two model versions. Each is driven by its own logic, but the animation shows only slight differences. The following table gives a brief discussion of each model. 64 MODEL VERSION DESCRIPTION Tractor Trailer Model Based on current Vanterm operations Uses Tractor Trailers and Top Lifter to transport containers Straddle Carrier Model Proposed method for conducting operations at Vanterm Uses Straddle Carriers to transport containers Table 1: Model Version and Description Logic Overview The logical framework of the Vanterm Container Operations Modeling Tool is the simulation engine driving the interactive animation screens and generating real time statistics for productivity analysis. It is this logic that defines how containers are handled throughout the operation. The logical framework includes two major logic sections representing the container discharging and loading operations and three logical sub-models representing the three dockside gantry cranes. The three logical sub-models coordinate the unloading and loading processes according to the sequence specified in the input files. The modeling tool simulates container movements from the bay of a vessel to a yard location (discharging) and from the container yard to a vessel bay (loading). All containers involved in the unloading and loading operations are created at the beginning of the simulation. Each of these two types of containers is assigned different attributes based on the input files linked to the model. These attributes, which include information such as the original location and final destination of the containers, affect how the containers are handled further along the process. After containers have been assigned attributes, they are temporarily held at their respective storage locations. When the containers are to be handled in the current sequence of operation, the crane's logical sub-model will trigger their releases and drive them through the rest of the simulation logic. The container handling procedures in the Tractor Trailer Model and Straddle Cairiers Model are very similar, but differences exist between the operations of T/Ts and Straddles. The differences in logic are outlined in the next two sub-sections. Tractor Trailer Model 65 Unloading process After the crane becomes available to a container, several conditions are checked to decide how the container wil l be transported to its yard location. If a Tractor Trailer is available under the gantry, the container wil l be discharged onto the Tractor Trailer directly. If a Tractor Trailer is returning to the gantry, the container is hanged until the T/T arrives. If both above conditions are not met, the availability of dockside buffer space is examined. If buffer space is available, the container is dropped to the buffer space, where it is held temporarily. If no buffer space is available, the container is again hanged until a T/T arrives. Once a container is placed onto a T/T, the T/T transports the container to its destination. There are five unload locations specified in the model, each with its own working RTG (Side Loader in the empty container yard). Once at the yard location, the loaded T/T's line up for RTG service. Once the RTG is available, it lifts the container off the T/T and places it in the stack. The containers being temporarily stored in the buffer are transported to their respective yard locations using a Top Lifter. Unlike the containers transported via the T/T, the containers are stacked directly by the Top Lifter instead of by the RTG. Once a container has been stacked, the Top Lifter goes back to the dock to pick up another container. Loading process Once the RTG is available to remove a container from its yard location, a T/T is requested to the yard location. The T/T then transports the container to the dockside, where the container waits for the gantry to load it on the vessel. The process is complete when the gantry lifts the container off the T/T and loads it onto the vessel. The service times associated with the dockside gantry, RTG, Side Loader, and Top Lifter are distributed according to collected data. The distances for transporters moving between 66 the various yard locations were derived from a scaled map of the Vanterm container yard. A screenshot of the Tractor Trailer Model logic framework is shown in Figure 1. Unloading Optratian Figure 1 Straddle Carriers Model Unloading process Since the crane cannot directly place a container onto a straddle carrier, all containers in the Straddle Carriers Model are required to go through the dockside buffer during the unloading process. As a result, the crane does not need to wait for the arrival of a straddle carrier, and can continuously drop containers into the buffer until all spaces are filled. Similarly, when the straddle carrier arrives at its yard location, it does not have to wait until the RTG is available. It drops the container directly into the RTG buffer zone, and is released for the next container. NOTE : The size of the RTG buffer zone is not restricted in this model. 67 Loading process Straddle carriers in the loading process are used similarly to the unloading process. When the RTG picks up a container off the storage stack, it drops the container directly into the buffer zone without having to wait for the arrival of the straddle. Similarly, a straddle carrier arriving at the dock does not need to wait until the crane is available before it drops the container into the dockside buffer. This process is only delayed if no buffer space is available. Once a container has been dropped in the buffer, the crane picks it up from the dockside and loads it onto the vessel. It is important to note our assumption that loading containers have higher priority when requesting a straddle carrier over unloading containers. This helps minimize the crane's inactive time due to full dockside buffers. A screenshot for Straddle Carriers Model is shown in Figure 2. urioMng Opinion L o a d i n g Opcrart ion * £ = i i — I T H _ , jtn. 1 "fats*!* «-=••. Figure 2 68 Animation Screen The graphical animation screen that accompanies the simulation allows users to assess the current state of the model and determine how well the system is operating. All containers and yard equipment, along with associated queues, have been animated and layered over a map of the Vanterm container yard. A screen shot of the animation can be seen in Figure 3. a r t « " c o w J l c e : W H O * - o w f « p * o p « f * l a i : * r t o i « w € f * K p :wM<* * Figure 3 The actions of the three Dockside Gantry Cranes are illustrated at the top of the animation screen. For each gantry, information regarding the current active bay and current action (unload or load) is displayed. In addition, a cross-sectional view of the current bay is also animated. It provides users with a view of the containers to be unloaded from the bay and containers that have been loaded onto the bay. When the 69 gantry is working on a particular bay, the corresponding strip on the vessel wil l turn red, indicating that the bay is busy. Note: the shape of the bay's cross section and the container stacking sequence do not necessarily reflect reality. The status of equipment and resources on the container yard are animated using different graphic icons positioned on the Vanterm map. Table 2 provides a comprehensive list of icons used in the animation. Equipments Idle Busy Description RTG RTG is busy when hanging a container, or adjusting its position Side Loader Side Loader is busy when stacking a container Top Lifter (T/T model) tfsH Top Lifter is busy when it has received a request or it is carrying a container Tractor Trailer (T/T model) m T/T is busy when it has received a request or it is carrying a container Straddle Carriers (SC: model) # Straddle is busy when it has received a request or it is carrying a container Dockside Gantry 4 Gantry is busy when hanging a container/hatch lid, or adjusting its position. Table 2: Graphic Animation Icons Due to software limitations, the movements of some equipment, such as the RTG and the Dockside Gantry, are not animated. In addition, the containers temporarily stored at the dockside buffer are not visible to the users. The animation has been replaced with a display screen indicating the number of containers currently being stored at each buffer space. When lids are placed in the buffer, they occupy the entire space and a red box is activated to indicate that the buffer is unavailable. This screen is accessible by pressing the shortcut key "b". A screen shot of the buffer usage screen (T/T Model) is shown in Figure 4. 70 Buffer Usage and Availability Mid Legs Rear Legs 1 2 3 4 5 6 7 8 9 1011121314151617181920212223 0 0 0 0 0 0 °l ° l 0 0 0 | | 0 0 0 0 (i o 0 0 0 0 0 0 0 0 0 2 0 o| ol 0 0 olol 0 0 0 2 ofo 0 0 0 0 0 Figure 4 Shortcut Keys There are many screens in the simulation models that are accessible with shortcut keys. The user can simply press a key on the keyboard to gain the best view of certain simulation screens, such as the main animation screen and the statistics screen. Commonly used shortcut keys are listed in Table 3. Shortcut Key Description a Main animation screen s Dynamic statistics screen b Dockside buffer usage and availability t Container transporters used in the model 1 A view that includes all logic blocks Talble 3: Shortcut Keys The contents of the dynamic statistics screen wil l be further discussed in the Output section. Inputs The Container Operations Modeling Tool requires 5 different input files to operate correctly: unload containers list, load containers list, crane 1 working sequence, crane 2 working sequence and crane 3 working sequence. Each of these files wil l be discussed in the following sections. 71 Unload containers list The purpose of this input file is to provide the model with information about each container that will be unloaded from a vessel. This information is needed to determine in which bay the containers are located, the crane used to discharge the containers, and where to route the container. The unload container list input file is a 3-column text file containing the bay number, the crane used, and the yard destination. Each row of data within the file corresponds to one container. The valid range of the bay numbers, specified in column one, is from 1 to 70. This number can be obtained from the unloading sequence paper file. The second column contains the number of the crane that will be unloading the container; this number can be 1, 2 or 3. Finally, the third column contains a number corresponding to one of the five different destinations at the container yard. Table 4 provides a list of the valid inputs for column three and the locations they represent. Column 3 Input Yard Destination Locations 1 Unload yard location 1 (D683 to D57) 2 Unload yard location 2 (D633 to D681) 3 Refrigerated containers yard 4 Empty containers yard 5 Intermodal/rail yard Table 4: Column 3 Input of Unload Containers List Load containers list The load containers list provides the model with information for each container to be loaded onto a vessel. Its structure is very similar to the unload containers list input file. The first column contains the number of the bay the container will be loaded onto. The second column specifies which crane will be used to load the container (crane number assignment should be consistent in all input files). The third column contains a number corresponding to the yard location where container was originally stored. Table 5 72 describes the input values and their corresponding locations for column three of the input file. Column 3 Input Yard Destination Locations 1 Yard location 1 (A083 to A159, B2813 to B359, F083 to F143) 2 Yard location 2 (A033 to A081, B233 to B281, E839 to E881) 3 Refrigerated containers yard 4 Empty containers yard Table 5: Column 3 Input of Load Containers List Crane-working sequence The crane-working sequence files for crane 1, crane 2, and crane 3 all have the same format. Each input file is a 5-column text file specifying five different types of crane action: unload bay, load bay, remove hatch lids, replace hatch lids, and end of operation. Each row in the crane-working sequence file corresponds to one of the above crane actions. To properly model the crane's activities, these files must be ordered according to the actual operational sequence. Tables 6 and 7 provide detailed input requirements for columns 1, 2, and 3 of the input file for each type of crane action. Crane Actions Column 1 Unload a bay The bay number from which the containers are unloaded Load a bay The bay number onto which the containers are loaded Remove/replace hatch lids The bay number from which lids are removed or to which lids are replaced End of operation 0 Table 6: Column 1 Input for Crane Working Sequence 73 Crane Actions Column 2 Column 3 Unload a bay 1 Number of containers to be unloaded Load a bay 0 Number of containers to be loaded Remove/replace hatch lids 1 for removing lid 0 0 for replacing lid End of operation 0 0 Table 7: Column 2 and 3 Input for Crane Working Sequence Column 4 indicates whether or not the crane must move to the current bay location before starting its action. Table 8 provides the list of valid inputs for Column 4. Column 4 Input Input Description 0 No move is required 1 A short move 2 A medium move 3 A long move (bloom will be lifted) Table 8: Column 4 Input for Crane Working Sequence Column 5 indicates whether or not the crane is required to move any lids. Table 9 provides the list of valid inputs for Column 5. Column 5 Input Input Description 0 No lid is moved 1 1 lid is removed from vessel 2 2 lids are removed from vessel 3 3 lids are removed from vessel 4 1 lid are loaded to vessel 5 2 lids are loaded to vessel 6 3 lids are loaded to vessel Table 9: Column 5 Input for Crane Working Sequence 74 The operation is completed by placing a row of zeroes at the end of the crane- working sequence file. A sample crane working sequence file is shown in Figure 5. The first row indicates that there are 20 containers to be unloaded from bay 1. After the twenty containers have been unloaded, 3 lids are removed from bay 1, as shown in row 2. Row 3 shows that following the lid removal another 20 containers are unloaded from bay 1. igUntitled -Notepad File Edit Format Help t 4 x V ' % - - * 1 1 2 0 0 0 1 1 0 0 3 1 1 2 0 0 0 A 0 1 0 1 0 0 0 0 0 0| - L L „ 31 21/A Figure 5 After working in bay 1, the crane moves to bay 4 and loads 10 containers. This short move is indicated by the input value 1 in column 4 of row 4. Finally, a row of zeroes indicates that the crane has finished the whole operation. A l l input files mentioned above must be saved in text format (.txt file extension). An easy way to generate text files is to build the input file using Microsoft Excel, then save the file as text. IMPORTANT : Column headings must not be included in the text file: this wil l cause an error in the Arena model. A l l input and output files are linked to the model via the "File" module in the advanced process panel, found on the left side in the Arena interface. After clicking on the file module, a spreadsheet allowing users to edit file directories appears on the screen. A portion of the spreadsheet for this model is shown in Figure 6. Op'era'tintfSystem Filename N a m e mm -JlSgfei -Structure End of Fi le A c t i o n I C o m m e n t Character 1 0 V .11 :•*.-•; load craneSeq2 craneSeqt C1 patches C2_t>6rtches ci_stats C2_stats craneSeq3 C3_batcries C3"stats J un load .txt bad.txt i c r a n e 2 . i x i ; c r e n e l .txt : c i_ b e t c h 9 s . t x t i3j3chBsi3 :C2_s tu ts_ '0 . t3 r t [crane3.txt 'cn_BHtches.tM C 3 _ 3 t a t s _ 7 C t x t [Free Format iFree Format jFree Format [Free Format I Free Format iFree Format |Free Formal [Free Format iFree Format iFree Format iFree Format i R e w i n d i R e w i n d i R e w i n d [ R e w i n d I D i s p o s e {D ispose [D ispose I D i s p o s e I R e w i n d [D i spose [D i spose |No ;N:> i.Ncj ;NO j N o Wo" "|NO"" [No •No "[NO" [No Figure 6 75 The file names unload, load, craneSeql, craneSeq2 and craneSeq3 refer to the unload containers list, the load containers list, and the working sequences for the three dockside cranes. The files not mentioned above are the model's output files. The significance of these output files will be separately discussed in a latter section. IMPORTANT : the "Operating System File Name" field should contain only the input file name and three-letter extension (.txt). All input files must be located in the same directory folder as the Arena model file (.doe file) When linking new input files to the model, two "create" modules may require adjustment. One of these is the "Create containers to be unloaded'' module located at the beginning of the unloading logic. The "entities per arrival" field in this block must be set to the total number of containers to be unloaded, which is equal to the number of rows in the unload containers list file. The second module requiring adjustment is the "Create containers to be loaded' module located at the beginning of the loading logic. The "entities per arrivaF field in this block must be set to the total number of containers to be loaded. This number is equivalent to the total number of rows in the load containers list file. The positions of the two create modules discussed above can be seen in Figure 7. •DIE Lite unta id a Create Containers to be unloaded Module " 4 - -. . . JT Create Containers to be loaded Module U I I I H C * i t » j * Figure 7 76 An example of the dialog box for a "create''' module is shown in Figure 8. The "Entities per Arrival" field must be set equal to the number of rows in the corresponding input file. Create Mane EtYrty Type WUJUJJJ.M.FJllMAHimMiL5i T] JEnlity 1 it-Time Between Atns - -•i Type Value Units j Constant j j] [i i les ppr Ainvcil Man A r vak |H0UIS First Creation • J?J*1 1] 3 Figure 8 I M P O R T A N T : When linking new input files to the model, the "entities per arrival" field in the two create modules must be set equal to the number of records in the input files. 77 The default version of the model is set up under the assumption that the vessel is stationed at berth 5. If the vessel to be modeled is stationed at berth 6 during an operation, one should manually change the distance sets associated with the transporters used in the model. This can be done by clicking on the "Transporter" module at the Advanced Transfer Panel. A spreadsheet will appear at the bottom of the screen. Under the "Distance Set" column of the spreadsheet, one can select between the berth 5 and berth 6 distance sets in a drop down manual. A screenshot of the spreadsheet (Straddle Carrier Model) is shown in Figure 9. - I n l xl fcftwriced T rans fe i lis I P'P* 3! * | •»• v 1 / i j a: *• M >• H H • | ip ©osic Process Transport m Segment m Transporter m Activity Area M S n n c e d P r a c e s a Q Reports "6 Navigate | c a p i straddle! straddles 3 straddls2 3 Oouble .clmk ner*: V e t a c l t y j U n i t s [inttW P M r r k i n a taport S M M I e t | 30CL* Per Minute 1 rows p 3 0 ™ Per Minute 1 rows P P 300 Per Mhute 1 rows "3 Buffer Availablity Buffer 1 Buffer 13 l Buffer 2 Buffer 14 1 Buffer 3 Buffer 15 1 Buffer 1 Buffer 16 1 Buffers Buffer 17 I Buffer 6 Buffer 18 1 Buffer 7 Buffer 19 1 Buffer 8 Buffer 20 1 Buffer 9 Buffer 21 1 Buffer ID Buffer 22 1 Buffer 11 Buffer 23 1 Buffer 12 J Stradde carriers Select berth 5 or berth 6 distances from the Figure 9 78 Outputs The Vanterm Container Operations Modeling Tool collects a number of useful output statistics describing the system's performance given the specified vessel data and resource parameters. These statistics are both collected in output files and displayed via dynamic on-screen displays. Output Files There are two different post-run output files for each crane (six in total). The "C batches" output files record the start time and end time for each sequence of the crane's operation. The "Cjstats" output files record the crane's total working time, the accumulated hang time in the unloading process, and the crane's idle time in the loading process. These three numbers appear, in order, as the three columns of the file. Each row of the "Cjstats" input file represents one replication of the model. IMPORTANT: In order for Arena to write the output file, the full directory path name must be typed in the "Tally Output File''' or "Output File" field of the "File" module in the Advanced Process panel. Please refer to Figure 6 for a screenshot of the "Fi le" module. Dynamic On-screen Displays In addition to being shown on the post-run reports, some model outputs have been animated and update as the simulation run progresses. These outputs are shown when the shortcut key "s" is pressed. A screen shot of the information display is shown in Figure 10. 7 9 Dynamic Operating Statistics | Crane 1 Crane 2 Crane 3 Total Dockside Gantry Productivity -Number of Containers Unloaded -Number of Containers Loaded - ,o Hi® -Total Number of Containers Moved » o msi -Total Moves Per Hour \ 0 > fit-Accumulated Hang Time (minutes) '^Q Tractor Trailers Utilization ; o B I 0 End Time (minutes) Figure 10 The statistics included in this display are described in Table 10. Statistic Description Number of Containers Unloaded Number of containers that have been discharged from the vessel Number of Containers Loaded Number of containers that have been loaded onto the vessel Total Number of Containers Moved Total number of containers unloaded and loaded Total Moves per Hour Dockside crane productivity - number of container moves per hour Accumulated Hang Time Number of minutes the crane spent hanging the containers during the unloading process Tractor Trailers Utilization Number of Tractor Trailers currently in use End Time Number of minutes for the crane to finish all of its tasks Table 10: Dynamic Statistics Outputs 80 APPEND IX D - Validation Details Vessel A" ' ," ' B 4 „ c D E , j *• Simulated Productivity 27.91 27.31 25 57' , 27.36 30 30 ' ' Actual Productivity 28.12 26.43 I, * 25 21 26.98 28 32 Difference 0.74% -3.33% -1 46% -1.41% -6 9X"„ Vessel F G H I J Simulated Productivity 26 ll\ 28.30 29 86 27.48 28 38 Actual Productivity 24 10'- 26.41 27*12 23.18 26:32 • • Difference -11.08% ; -7.17% -10 11% ' -18.53% -7.81%" 1 *: Unit of productivities is Lift/Hour. **: For each vessel, we ran 20 replications of the simulation. The simulated productivities are the average simulated productivities from 20 runs. ***: The differences are the differences between the simulated productivities and the actual productivities for those vessels. 81 o o u <u '« u H o u es u H OI JS CD B Vi n c < « c u (Z3 o vi <U X Q Z W OH OH < s ° N? o s co "•5 o s 00 SO oN Os CN = oN r~ CO s ° 0X CN SO \ ° O S OO s ° O S CO co ':0> |CJS. \ = oS-CS <n \ = O S >o = O S CS Os OS hr co i 00 SO in • co in 1 1 co -?T O 1 :oo SO 00 >Sq; co r> so OS CN m 00 CN t SO v i CO CN CN CO <ri co r— N* CO <p *o^ ; OS © N? so N? 0 in CO N? CN O s = OS->n Os N? O S r-CO s ° O so O S ,cN •wp s ? O S s ° O S •^ r in s ? O S , •00 wo 00 i 1 i SO 1 CN • CO CN 1 SO 1 1 1 iSO CN 1 CN CN 1 CO CN 17 in SO r-i CI OO co CO SO 00 CN O cry Os OS co 00 Os co co CN co CN CN O CN CN 0 CN CN c s i CN i*CN 0 CS O CN O CN -7.20% O OO N? , o > o. o AO. O S 00 •*r Os 5^ o s •sf SO 1 = C=s •sf ip ** 1 s = oN CN r>: • s ? O S r-00 SO • o N t-; 1 :.s= O s 'co . ' i •s? o s OO 1 s O OS-CO s ° O S O * • o o in o CM O SO 0 0 0 O 0 00 0 0 O r-~ 0 0 in CN in CN .SO, CN co CN in CN CN c s i CN CO CN CN 'CO, CN co CS CO CN co CN s ? IN s-? ON * SO s - ? O S •sf 0 s ? OS-Os s ? O S SO "1 5^ 0 CN • s ? oS-CS SO s ? O S O CN ?o>; fcN' ico; s ° 0N V~t "O O S OO s ? o s 00 O • 1 CN i in 1 in • 1 CO 1 CO 1 co • :'cO 00 1 • 00 1 CN CN ;co CO r-SO in OS r>- SO OS 00 "CN1 ;,t>, IT) 00 in 00 CN SO CN >CN CN SO CN M, CN CO CN CN >/S CN CN CS CN in CS - co r- Os •<*• 0 CN OS 1- CO <f) in •X?. co 00 OS 00 SO CO ON CS NO CN CN SO CN 00 CN CN CN wi CN SO CN '"vri CN CN SO CN CN o s o N? Os Os s ? Os N? oN 00 co s? OS-CN CN s ? 0N s ? O S O CN •s? o s O O "s? O S O ,S0: ' O S . s ° O S CO v~t o N O O N? o > r~ CN o o O O O O O O 0 O 0 1 1 o o in o O •sr O co O IT) CO IT) OO To;' r-OS OS 00 •st os CN r--CN 00 CN SO CN 00 CN CN CN >o CN SO CN C/s CN CN sd CN t~ CN N? <=> o s ? o s CN 00 s O , © s S O O S CO CN s ° O S CN CN t 5 s ? O S SO 0 OS CN s § O S CO O S O s ? • O S .00. N? O S co IT) "s? O S s ? o o •O, — O O O 0 O 0 O O 0 F in Os co' 0 SO CO O CO OS SO ir> SO IT) 00 r-CN, so. OS O O Os •sr. os CN sa CN °o. CN SO CN 00 CN CN CN iri CN sd CN CN r>: CS CN r>: CN CN j>' CN • CN co CN < pq u Q CN 00 6 % c 1-. •5 cn oo 0> T3 O 1-"E u 05 1-tan s et B «< o ca c o> u C O V -3 o "3 I 3 z OH OH 2' L3L in m OS CN s ? OS v i o cn s ? OS v> cn ° cn cn 2' cn Si VI oo 0<| CN OS v> OS CN r-I O O . CN s y -:oo; 'oo1 I o Os CN o s SO © I fsl I oo CN os, cn' oo oo OS 0 0 CN SSI SO o. I <N I oo CN | r~-c^  CN t-s 'cn; V> OS' 0 0 : £ L _ Los ,W: \Kjt?i cn; <OSJ :'(NJ O S ' OS; '.cn so op, oo CN cn I f-so CN 'CNI 1<NI s ? O S SO o so IcN s ? 3 I vo| so CN 2? V> cn OS SO CN oo CN o CN| so V) 0 0 CN s ? O S v> cn Os so CN s ? o x Os so CN v ? O S r-CN s ? O S o SO SO CN v ? Os 0 0 cn 0 0 CN cn CN CN CN OS CN s ? : o S . CN O CN SO oo CN: s=> o N r--SO O cn • 0 0 CN s ? o s I (N I CN | 0 0 CN v ? O S cn oo CN I s ? o s cn • 0 0 i 0 0 ; CN v ? o s 0 0 r-o •<3-CN ©s v> Os O I f-| I tH v i CN S ? l o 3' v i CN s r OS Os v ; | v i CN v ? CN OS VI I CN 0 0 CN V l v i CN S ? l 0 0 CN ^ \ v> | v i CN v ? o s VI © CN V) O SO CN s ? O S V ) O JSL SO V) SO CN O O cn so CN I : O S ' CO 0 0 o SO. |-cn V ) CN: v ? cn, r-cn so CN VI ' © ' V) cn so •CN; 3 SO CN - S R O S OS : 0 0 SO ' O 1 CN SO CNL s ? O S cn CN CN SO CN O SO CN CN 0 0 CN CN OS • t CN v i so CN VI ,v> CN S ? l o oo |CN s ? r-CN 0 0 V) 0 0 I CN 0 0 CN CN cn oo CN V) V) cn oo ICN s ? O S OS Os CN SO SO 0 0 CN s ? o s f~ CN SO I VO CN so CN CN CN CN r-CN CN CN r-CN sK : o x (SO! CN ivsj! oo-CN' cn 0 0 CN LfNj Iml a o •3 in OJ t » .a 3 w O <u o C <D S a ° t l o Q -a • • a * a APPEND IX G: The Calculation of Stationery Probabilities In a closed Jackson network, i f there are J nodes(stations) and N jobs in the system, the service time of any node i is exponential and known as >^ and transition probability of any two nodes i j is known as py, then the stationery probability of any state can be calculated by applying the following theorem. Theorem(Fundamentals of Queueing Networks: performance, asymptotics, and optimization P20 Theorem 2.3): The closed Jackson network, with a total of N jobs, has ZJ the following equilibrium distribution: For all x 6 + such that |x| = N, we have |x| = N, 7t(x)=f\P[Yi=xiVF[\Y\=N] where P[Yi=n]=P[Yi=0] M » , Mi(n) = MWfi,(»)t n = l>2,..., with ^ MM) and x i ^ N. . J y v p.. vi is the solution to vi =•/'=' i = 1 i Remark: P[|Y|=N] = »=N <=' 84 APPEND IX H: The Estimation of the Min imum Number of Exponential Distributions Required in the Approximation In the approximation, the main target is to capture both the mean and the standard deviation of the service times. If the sum of n exponential distributions can capture both the mean (^) and the standard deviation (v) of a service time, let ' , " b e the means of those exponential distributions and then we wil l have: '•' = x (1) n ,., _v2 ( 2 ) When all A> > 0 i = 1, 2, ..., n, (<=' f ^ n <-i . It can be proved as following: ('=' f=^2+A,A2+... + AlXn + ... + AnA,+AnX2+... + A2 (3) Since 2ab ^ a 2 + b 2 Then according to (3), we have 5>. 1 1 +... 85 n I * = n '••» If there exist " satisfying both (1) and (2), we must have ^ ^ nv 2, which is i i 2 equal to n ^ v when v2 > 0. v The squared coefficient of variation (SCV) is equal to ^ , so n must be greater than the inverse of the SCV. 86 APPEND IX I: Estimation of the Number of States in the Jackson Closed Network model Since three are n T/Ts available and they can only be in the service of any station or waiting to be served, when there are only four stations, the number of states is the number of combinations of four non-negative numbers. The number of T/Ts must be greater than 0, so n>0. When all the T/Ts are served or waiting to be served at only one station, the number of c1 C 1 C° states is 4 , which is equal to 4 * " _ 1 . When n>l and all the T/Ts are served or waiting to be served at two stations, the number of states is 4 *(n-l), which is equal to 4 * "~ l . If n=l, then the T/T can only be at one station. When n>2 and all the T/Ts are served or waiting to be served at three stations, the number of states is 4 * '- 1 , which is equal to 4 * 2 (n-l)(n-2) and also c3 c2 4 * " 1 . If n = 1 or 2, then the T/Ts can not be at more than two stations. When n>3 and all the T/Ts are served or waiting to be served at three stations, the n-3 n-i-2 number of states is '~l j ~ x , which is equal to 6 (n-l)(n-2)(n-3) and also c4 c3 4 * n i . if n = 1, 2 or 3, then the T/Ts can not be at more than three stations. When, a station has t T/Ts being served or waiting to be served and there are i steps to fini sh the service, the number of states will be different. If the station has only one server, only 1 T/T can be served at that station and the rest T/Ts can only be waiting for the service, so the number of states is t. 87 If the station has as many servers as required, the T/Ts can be served at any step. The number of states is calculated as follows: . c1 When all the T/Ts are served at only one step, the number of states is 1 , which is equal C' C° to U ' * U < - ' . When t>l and all the T/Ts are served or waiting to be served at two stations, the number of states is ' *(t-l), which is equal to ' * . If t=l, then the T/T can only be at one station. When t>2 and all the T/Ts are served or waiting to be served at three stations, the number t-2 £ 3 c3 - c3 c2 of states is ' * p = l , which is equal to ' * 2 (t-l)(t-2) and also ' * M . If t = 1 or 2, then the T/Ts can not be at more than two stations. When t>3 and all the T/Ts are served or waiting to be served at three stations, the number 1-3 t-p-2 YY(t-p-g-\) I of states is p A 9 - 1 , which is equal to 6 (t-l)(t-2)(t-3) and also c4 r 3 2 or 3, then the T/Ts can not be at more than three stations. Based on the observations above, it is reasonable to guess that when there are total i steps in the service of the station, t T/Ts in the station and all of the T/Ts are in s steps (s ^  i and s ^  t), the number of states is ' * M . It can be proved by the following induction: First, from the above, when s = 1, 2, 3, 4, the result stands. Second, we assume that when s = m, the result stands and then we have the number of states is ' * / _ 1 , when there are total i steps in the service of the station, t T/Ts in the station and all of the T/Ts are in m steps (m ^ i and m ^ t). The number of permutations of m non-negative numbers with their sum equals to t is M . 88 Then when s = m + 1, i f we still have m+1 ^ i and m+1 ^ t, then the number of states wil l t-m Z rm-\ be * P=* m-\ p-i £<t-\-i C" Whenm = t-1, p = i = ^t-2 =\=^t-When m^t-2, we have: t-m / i t-n-\ s-tm-X s~im-\ s-~<m-\ s~tm-\ P=\ = + C / - 3 + + U m + U m - 1 When y C m - i / - t-n-\ s~im-\ f~\m-\ m = t-2 P = 1 =  M ~ L + "> (m + 1)! = 1 + m = m + 1 = w!l! = = t-m Ycm~] Z—i i-p-l s-<m-\ f~tm-\ s-~im-\ m = t -3 P = X = m~X + m + "'+' = 1 + m + 2 m(m+l) 1 (w + 2)! = 2 (m+l)(m+2) = »»!2! = ^ « + 2 = t-m m := t - 4 p = l = m - 1 + m + m+l + = 1 + m + 2 m (m+ l ) + 6 m(m+l)(m+2) 1 (w + 3)! = 6 (m+l)(m+2)(m+3) = mB. = u m + 3 = t-m y C m - i t-p-\ Q^m Based on the observations above, it is reasonable to guess that p = x = M It c:an be proved by the following induction: 89 First, from the above, when t - m = 1, 2, 3, 4, the result stands. Second, we assume that when t - m = n, the result stands and then we have t—m 77-1 Z- fim-\ X 1 /~im-\ l t-p-\ / J m-]+n /~im s~<m p=l = p=0 = U>-1 = ^m+n-\ t-m n n-1 W h e n t - m = n + l , = = P = 0 + m+n-l (m + n-\)\ (m + n-\)\ m\{n-\)\ + ( m - ! ) ! « ! (m + «)! (m-r-w-l)! So when m^t-2, we have: t-m Ycm~l Z_t ^ t-p-\ y^m The number of combinations of m steps in i steps is ' Then when s = m + 1, m+1 ^ i and m+1 ^ t, the number of states is ' * t-\ So after all, it is proved that when there are total i steps in the service of the station, t T/Ts in the station and all of the T/Ts are in s steps (s^i and s^t), the number of states is When there are pi number of steps in the service of station i and n T/Ts in the system, the number of states is calculated as follows: When all the T/Ts are served or waiting to be served at only one station, the number of states is 90 Pi P* p i + p3 + 5 = 1 + 5 = 1 When n>l and all T/Ts are served or waiting to be served at two stations, the number of states is pl*p3+(pl+p3)*( '=' *=> + '=> *=' )+ 1 = 1 s = i i = 1 . If n=l, then the T/T can only be at one station. When n>2 and all T/Ts are served or waiting to be served at three stations, the number of states is lie; *c- lie; *c;;,' gi(c; *c-'(£c;4CU)) plp3( '=' + *=> )+(pl+p3) '=> s = l ''=' If n = 1 or 2, then the T/Ts can not be at more than two stations. When n>3 and all the T/Ts are served or waiting to be served at three stations, the n-3 n—i-2 YY(n-i-j-D I number of states is 1 - 1 7 - 1 , which is equal to 6 (n-l)(n-2)(n-3) and also c4 c3 4 * " 1 . If n = 1, 2 or 3, then the T/Ts can not be at more than three stations. When the number of steps in each service is the number listed below: Number of Station Distributions RTG 19 T/T 12 Crane 17 T/T 2 The corresponding numbers of states when there are different numbers of T/Ts are: ber of T/Ts ber of States 1 2 3 4 5 6 7 8 50 968 10048 66266 339337 1435412 5230339 16910988 91 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0091122/manifest

Comment

Related Items