Simulation Modeling as a Decision Analysis Support Tool at the Vancouver Container Terminal

Transcription

1 Simulation Modeling as a Decision Analysis Support Tool at the Vancouver Container Terminal by AIMEE(ZHIWEI) ZHOU B.Econ(World Economics), Fudan University 2000 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN BUSINESS ADMINISTRATION in THE FACULTY OF GRADUATE STUDIES FACULTY OF COMMERCE AND BUSINESS ADMINISTRATION We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA March 2003 Aimee(Zhiwei) Zhou, 2003

2 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia Vancouver, Canada

3 ABSTRACT The objective of this research is to find whether replacing tractor/trailers in Vanterm (Vancouver Container Terminal) with straddle carriers will 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 of the straddle carriers in terms of productivity increases. The results of this project will 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. ii

4 TABLE OF CONTENT ABSTRACT ii LIST OF TABLES iv LIST OF FIGURES v ACKNOWLEDGEMENT. vi 1. INTRODUCTION 2 2. BACKGROUND Equipment Used in Vessel Operation Current Strategy Double Buffering Strategy 5 3. LITERATURE REVIEW 6 4. METHODOLOGY Process Mapping Data Collection Model Development Scenario Analysis Sensitivity Analysis RESULTS ResultsfromScenario Analysis ResultsfromSensitivity Analysis : Conclusion FURTHER STUDY More Simulation Jackson Closed Network 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

5 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 Resultsfromthe Sensitivity Analysis using the T/T Model with 80% Crane Service Time 26 Table 11: Comparison of Simulated Crane Productivities (Lifts/Hour)fromDifferent Models of unloading process 29 Table 12: Comparison of Crane ProductivitiesfromDifferent Models of loading process (Unit: Lifts/Hour).' 30 Table 13: Comparison of Crane ProductivitiesfromDifferent Models of unloading process with 20 containers (Unit: Lifts/Hour) 31 Table 14: Comparison of Crane ProductivitiesfromDifferent Models of loading process with 20 containers (Unit: Lifts/Hour).32 Table 15: Comparison of Crane ProductivitiesfromModel of Unloading Process with Different Buffer Size (Unit: Lifts/Hour) 35 Table 16: Comparison of Crane ProductivitiesfromModel of Loading Process with Different Buffer Size (Unit: Lifts/Hour) '. 36 Table 17: Long Term Crane Productivities (Unit: Lifts/Hour) Calculatedfromthe 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

6 LIST OF 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

7 ACKNOWLEDGEMENT 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 COE 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 COE 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.

8 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 RTG 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

9 2. BACKGROUND 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. Figure 3: Tractor/Trailer P 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

10 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. RTG 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

11 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 will 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

12 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. An RTG and Tractor/Trailer system can be considered as a closed network if the buffer under the crane is ignored, because the number of tractor/trailers dictates the WIP level. In an RTG 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, RTG 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

13 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 RTG 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 will 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 RTG and Crane service times are relatively small, the operations could be modeled as tandem queues with deterministic input if the straddle carriers are viewed as input to the systems and the fleet size is large enough to keep Crane and RTG 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

14 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 Kwai 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-Vaziri 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

15 4. METHODOLOGY 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 ARENA 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

16 Table 1: Service Time Distributions Equipment Distribution Unit Mean (seconds) SD 1 SCV 2 NB 3 SE 4 Crane (vessel to TT) WEIBULL(30, 1.14) Second Crane (TT to vessel) ERLANG(7.39, 4) Second *BETA(0.719, RTG (pickup) 0.961) Second RTG (stacking) WEIBULL(32.1, 1.25) Second Top Lifter, Side Loader & SC (pickup) ERLANG(3.14, 3) Second Top Lifter, Side Loader LOGNORMAL(10.5, & SC (dropoff) ) Second Stacker WEIBULL(15.8, 1.71) Second Distance Meter Top Lifter speed 9 Km/hour Tractor/Trailer & SC speed 8 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 infittingthe 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 RTG 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 of the service times by comparing the simulation results of the tractor/trailer model with those service time distributions and the recorded operation results, which will be discussed in the model validation. The results of the 10

17 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 will spend between locations. The travelling time will affect the crane productivity efficiency, as will 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 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 RTG and Tractor/Trailer model animation is in Appendix C, the Simulation Manual 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 SC direct operations Containers Three Cranes, Six RTGs and One Side Loader Tractor/Trailers and One Top Lifter Straddle Carriers 11

18 4.3.3 Assumptions Before building our simulation models, some assumptions are made to simplify the work: All the entities are identical. All 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 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 Model Validation The RTG 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 RTG 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

19 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 if 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

20 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 Actual time spent on each bay Figure 6: Detailed Validation Analysis on Vessel A (In Total) 14

21 Validation (Vessel A Discharging) Validation (Vessel A Loading) Actual time spent on each bay Actual time spent on each bay Figure 7: Detailed Validation Analysis on Vessel A (Discharging) 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 Variance Observations P(T<=t) two-tail- ' 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 well 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 will also increase if 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

22 We decided that if 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

23 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

24 5. RESULTS 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. Hang Time Number of T/Ts Figure 9: Simulated "Hang Time" Using Different Numbers of Tractor/Trailers 18

25 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 ' 0.00% % % v -1.91% % 27.91, ;-2.16% ^ t if i t { B % ; -5.04% 2' % % 27.5 ' 0.71% 27.31'- / V > -5.56% ( T 0.20% :71, -3.21% il 2 25^53 > 0.00% 25:53 * ; % % % % % V,! r < D % 27.83"' / \ % % , ' -7.58% * 0.27% 27.36~ i " * -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. Net Productivity 5-0 "I 1 1 1! i Number of T/Ts Figure 10: Simulated Net Crane Productivities Using Different Numbers of Tractor/Trailers 19

26 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 will 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

27 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,,,,,,, Number of SCs Figure 11: Simulated Hang Time Using Different Numbers of Straddle Carriers Net Productivity (Lifts/Hour) , 28.5 J Number of SCs Figure 12: Simulated Net Crane Productivities Using Different Numbers of Straddle Carriers 21

28 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 :15 * 3.59% 30.15, ' 3.59% 29' % % ' 4.77% :* 4.41% % % % '» 5 V! ' * 5 B % % % % i 0.78% % v ' % % 26.46; s -3.10% % 25.49, 4.07% % 2, % * 3.76% 25.77, ' 0.95% , 1.25% % % % 26.3If' 3.13% > -0.83% '< D \«3.55% % 28.12' % % % % ' 2.62% % 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 usingfivetractor/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 if 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 skillful 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

29 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 % 32.5 * s 11.60% % % \ 13.47% 30.r 12.64% % % % B % % % % % % % % 27.5' 0.77% - C % % % % % % % % % % % % D % % % ; 10.74% % % ' 12.02% % % *: 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 % % % % % % % % 33-' 18.31% B , 23.41% % % ' 20.40% % < 0.78% ' " 21.65% % 28.1 ~ 3.03% C % % % : ' 20.16% % % % 31' 15.91% % :4: 18.94% % % D % % % % % % * 23.22% % % *: Difference columns represent the productivity differences between the results from the straddles model (80% crane service time) and the tractor/trailer model withfivetractor/trailers (100% crane service time)., 23

30 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 ' % % % 1 B % % % C % % %, D 27.36, % % % *: Difference columns represent the productivity differences between the resultsfromthe straddles model and the tractor/trailer model withfivetractor/trailers (100% crane service time). Productivity Comparison 5 T/T 100% 90% 80% Scenarios A -+ B *-C D 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 if crane service time can be reduced. Another observation is that if crane service time can be reduced to 90%, straddle carriers can increase crane productivity by more than 10%. However, if 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

31 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 if 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, if cranes can work faster, crane starving will 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 if the crane service time is different. First, the T/T model was tested with 80% crane service time to check if 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 if 3 straddle carriers per crane is still better than 5 T/Ts. The results are listed in Table

32 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 % 31: % % ', % % % % " % % '32: % % ', % >- -. c c % ' f % % 127' % % > , % % , % * ' IP, D, % % % % % % *: 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 usingfivetractor/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 % % ' % % % % % % ' % D % % % ^ %, % ' % % ~ % % c % % % % ""' % «, % % %, % % 29:97 7,02% % D % % % % % % % % % 26