Some Studies on the Principles and Mechanisms for Loading and Unloading

LTF works as follows the jobs with total handling time are handled first and completed. The algorithm requires the data pertaining to the number of jobs, the job names, the processing time and the travel time as the input. The second step is sorting out the largest sum of processing time and travel time among the jobs. In the third step, jobs are rescheduled and assigned to the trucks according to the sequence generated through the second step.

µ § Eq ý5.In the end, the makespan is computed by using equations (5-4), (5-5), (5-6) used in FAT.

Table ý5. Schedule obtained using LTF algorithm

Job NumberHandling time (minutes)

Handling time (minutes),in increasing orderJob number according to the new scheduling12+4=612222+10=1210432+5=77342+8=106552+2=461The results of application of LTF algorithm to the 2 truck- 5 jobs problem is presented in Table ý5.. The job sequence as determined by STF is {J2, J4, J3 ,J5 ,J1}. LTF algorithm suggests the following schedules for each truck: T1:{J1, J3,J2} and T2:{J5, J4 }, which results in a makespan of 25 minutes of completion time . This schedule is given in Gantt chart shown in Figure ý5..

 Crane processing time (minutes) 

Truck Travel Time (minutes)

0 2 12 14 1921 25Truck1      J2J3J1 Waiting time 2 412 14 1620Truck2      J4J5Figure ý5. The LTF scheduling algorithm for unloading containers

Model Application to Real World Case Studies

This chapter describes the application of models described in the previous chapter to optimize loading and unloading operations in ICD, Tughlakabad. Four real world case studies based on the data collected from CONCOR for ICD, Tughlakabad are solved using different mechanisms. The mechanisms considered are greedy algorithm, reverse greedy algorithm, shortest time first algorithm, and longest time first algorithm solved on personal computer. Performance of each of the models is evaluated through application to the four real-world case studies as shown in Table ý6.. The model for the greedy algorithms, reverse greedy algorithm and shortest time first and longest time first have been coded using Microsoft Visual C++.

Table ý6. Four different real world case studies

Case study TrainsTrucksJobs11970221214533152104418270

Four different combinations of number of containers, number of trucks and number of trains considered in the computational experiments for each loading and unloading operation are listed in Table ý6.. For the problems considered here, the number of containers (N) to be handled ranges from 70 to 270 and the number of trucks (M) employed ranges from 9 to 18 and number of trains (R) ranges from 1 to 4. The performance of all the four models for each of the problems has been evaluated on the basis of the objective function values achieved and the execution time required. Model runs have been conducted on a personal computer with 2.10 GHz CPU and 2GB RAM.

Case study 1

This section describes the results of application of greedy algorithm model based on FAT principle, reverse greedy algorithm model based on LBT principle, greedy algorithm model based on STF principle, and greedy algorithm model based on LTF principle. In a typical container terminal, trucks travel at the speed of 15 km/h in the terminal area. The time taken by a RMGC to handle a container is typically between 1.5 minutes and 5 minutes. The initial location of each truck and the location of each job’s pick-up/drop-off are randomly generated based on a terminal area of 1500 metres by 1500 metres. The travel time is the time that truck takes to travel from rail-side and return back to the same point. The duration of a job is equal to the sum of the total travel time from its pick-up location to its drop-off location and the total crane handling time. A terminal operations control system is typically used to determine the job ready time and truck ready time. The processing time (s) and travel time (2d) for each job for case study 1 is given in Table ý6..

Table ý6. Input data for case study 1

Job.s (min)2d(min)Jobs (min)2d(min)JobS(min)2d(min)13.007.00 243.009.00 474.005.00 24.009.00 251.007.00 482.003.00 34.003.00 261.005.00 492.005.00 43.004.00 273.004.00 502.007.00 52.005.00 282.00 5.00 512.004.00 63.007.00 293.007.00 522.003.00 72.009.00 303.0012.00 532.0012.00 83.005.00 313.003.00 542.005.00 93.004.00 323.005.00 552.007.00 102.005.00 335.007.00 564.003.00 113.008.00 343.004.00 574.009.00 124.005.00 353.009.00 582.005.00 134.007.00 36 2.007.00 594.0012.00 143.0010.00 372.0010.00 604.005.00 152.005.00 383.005.00 613.007.00 163.007.00 392.003.00 622.005.00 172.003.00 403.004.00 633.006.00 183.005.00 414.005.00 642.004.00 193.009.00 423.007.00 654.005.00 202.006.00 434.008.00 664.007.00 212.005.00 443.007.00 674.003.00 223.003.00 453.0010.00 685.007.00 232.005.00 463.007.00 693.0010.00 703.504.00 Makespan for unloading operations

Three different models namely greedy algorithm based on FAT, STF, and LTF were used to determine the makespan for the case study 1. Comparison of the makespan obtained using the three models are presented in Figure ý6.. It can be observed from Figure ý6. that the minimum makespan of 201.5 minutes is achieved using the model based on FAT.

Figure ý6. Comparison of makespan for unloading one train

The number of trucks obtained corresponding to the minimum makespan of 201.5 is 5. For the existing situation, the minimum makespan with 9 trucks is 214.5 minutes. Therefore, there is a saving of 13 minutes and 4 trucks when the model based on FAT principle is used. In terms of makespan, the worst performance was obtained by using the STF model. The minimum makespan and the corresponding number of trucks for the three models and for the existing situation are shown in Table ý6..

Table ý6. Minimum makespan and the corresponding number of trucks of unloading operation

STFLTFFATExistingMakespan (minutes)214.5201.5201.5214.5Number of trucks5959Computation of makespan for loading operations

Three different models namely greedy algorithm based on LBT, STF, and LTF were used to determine the makespan for case study 1. Comparison of makespan obtained using the three models is presented in Figure ý6.. It can be observed from Figure ý6. that the minimum makespan of 204.5 minutes is achieved using the model based on STF.

Figure ý6. Comparison of makespan for loading one train

The number of trucks obtained corresponding to the minimum makespan of 204.5 is 6. For the existing situation, the minimum makespan with 9 trucks is 213.5 minutes. Therefore, there is a saving of 9 minutes and 3 trucks when the model based on STF principle is used. In terms of makespan, the worst performance was obtained by using the LTF model. The minimum makespan and the corresponding number of trucks for the three models and for the existing situation are shown in Table ý6.

Table ý6. Minimum makespan and the corresponding number of trucks for loading operation

STFLTFLBTExisting Makespan (minutes)204.5213.5208.5213.5Number of trucks6759Cost of unloading operations

The cost of unloading a container from a train and transporting it to its location in the storage yard depends upon the travel time of the truck, processing time taken by the crane, and waiting time for the truck. The following equation ( Eq ý6. )has been used to compute the cost µ §of unloading a single container.

µ § i=1,...n and j=1,...mEq ý6.Where µ § is arrival time of job i on truck j, µ § is departure time of job i on truck j,µ § is waiting time of job i on truck j, and µ §is the processing time of job i to be loaded on truck j.

Figure ý6. gives the comparisons of the cost obtained through three models based on the SFT, LFT, and FAT principle. It can be seen from Figure ý6. that the lowest cost of operation is obtained using the model based on FAT principle while the SFT model produces the worst results in terms of cost.

Figure ý6. Comparison of cost of unloading one train

Table ý6. shows the cost of operation corresponding to minimum makespan obtained through three different models. The existing operation cost is also given in Table ý6..

Table ý6. Comparison of costs for unloading operations

STFLTFFATExistingCost(Rupees)2146.5273221642674Number of trucks5959Cost of loading operation

The cost of loading a container onto a train after bringing container from its location in the storage yard depends upon the travel time of the truck, processing time taken by the crane, and waiting time for the truck. The Eq ý6. is used to compute the cost µ §of loading a single container

Figure ý6. gives the comparisons of the cost obtained through three models based on the SFT, LFT, and LBT principles. It can be seen from Figure ý6. that the lowest cost of operation is obtained using the model based on LBT principle while the LTF model produces the worst results in terms of cost.

Figure ý6. Comparison of cost of loading one train

Table ý6. shows the cost of operation corresponding to minimum makespan obtained through three different models. The existing operation cost is also given in Table ý6.

Table ý6. Comparison of costs for loading operations

STFLTFLBTExisting Cost (Rupees)1684186915632176Number of Truck6759Waiting time of unloading operation

A truck might have to wait before loading could start on it if there are other trucks in the rail side on which the jobs are being processed. The waiting time of truck depends upon the arrival time and departure time of a truck. The following equation (Eq ý6.) has been used to compute the waiting time µ § of unloading a single container

µ § i=1,...n and j=1,...mEq ý6.where µ § is the minimum arrival time value among set a=i-m, and µ § is the maximum departure time value within a set a=i-m.

Figure ý6. gives the comparisons of the waiting time obtained through three models based on the SFT, LFT, and FAT principles. It can be seen from Figure ý6. that the lowest waiting time of operation is obtained using the model based on FAT principle while the LTF model produces the worst results in terms of waiting time

Figure ý6. Comparison of waiting time for unloading one train

Table ý6. shows the waiting time of unloading operation corresponding to minimum makespan obtained through three different models. The existing waiting time for unloading operation is also given in Table ý6..

Table ý6. Comparison of waiting time for unloading operations

STFLTFFATExistingWaiting time (minutes)39711653221165Number of trucks5959Waiting time of loading operation

The waiting time of truck to load a container to a train after coming back from the storage yard depends upon the arrival time and departure time of a truck. The Eq ý6. is used to compute the waiting time µ §of loading a single container

Figure ý6. gives the comparisons of the waiting time obtained through three models based on the SFT, LFT, and LBT principles. It can be seen from Figure ý6. that the lowest waiting time of operation is obtained using the model based on LBT principle while the LTF model produces the worst results in terms of waiting time.

Figure ý6. Comparison of waiting time for loading one train

Table ý6. shows the waiting time of loading operation corresponding to minimum makespan obtained through three different models. The existing waiting time for loading operation is also given. It is found that LBT gives a minimum waiting time of 333 minutes while LTF gives a worst waiting time of 838 minutes.

Table ý6. Comparison of waiting time for loading operations

STFLTFLBTExistingWaiting time(Minutes)562.5 838 3331235Number of trucks6759Case study 2

In this case study, as shown in Table ý6., there are two trains, 12 trucks and 145 jobs to be processed. The processing time (s) and travel time (2d) for each job is given in Table ý6..

Table ý6. Input data for case study 2

Job.s(min)d (min)Job.s(min)d (min)Jobs(min)d(min)13.003.50492.002.50972.002.5024.002.50502.003.50982.503.0034.001.50512.002.00992.003.5043.002.00522.001.501002.002.5052.002.50532.006.001013.003.5063.003.50542.002.501022.001.5072.004.50552.003.501033.004.5083.002.50564.001.501043.004.0093.002.00574.004.501052.002.50102.002.50582.002.501062.002.00113.004.00594.006.001074.004.50124.002.50604.002.501086.002.50134.003.50613.003.501093.003.00143.005.00622.002.501103.002.50152.002.50633.003.001115.006.00163.003.50642.002.001121.503.00172.001.50654.002.501133.003.50183.002.50664.003.501145.004.00193.004.50674.001.501153.002.00202.003.00685.003.501165.003.50212.002.50693.005.001174.004.50223.001.50703.502.001181.503.00232.002.50713.003.501192.003.50243.004.50723.001.501202.002.50251.003.50733.002.001212.004.00261.002.50742.002.501222.503.50273.002.00752.503.001236.002.50282.002.50762.003.501245.003.50293.003.50772.002.501252.003.00303.006.00782.501.501264.003.50313.001.50793.003.501272.004.00323.002.50802.002.501284.002.50335.003.50812.002.001294.003.50343.002.00823.004.001302.002.50353.004.50833.002.001313.002.00362.003.50843.002.501325.003.00372.005.00852.006.001332.002.50383.002.50863.002.001342.003.00392.001.50872.004.501353.003.50403.002.00881.502.501364.004.00414.002.50891.501.501372.002.50423.003.50902.002.501384.003.00434.004.00912.503.001396.002.50443.003.50925.003.501403.004.00453.005.00933.002.001413.001.50463.003.50942.003.501424.003.00474.002.50951.504.501434.002.50482.001.50962.005.001443.003.001452.003.5Makespan for unloading operations

Three different models based on FAT, STF, and LTF principles were used to determine the makespan for the case study 2. Comparison of the makespan obtained using the three models is presented in Figure ý6.. It can be observed from Figure ý6. that the minimum makespan of 421 minutes is achieved using the model based on FAT. The number of trucks obtained corresponding to the minimum makespan of 421 is 7. For the existing situation, the minimum makespan with 12 trucks is 437 minutes. Therefore, there is a saving of 16 minutes and 5 trucks when the model based on FAT principle is used. In terms of makespan, the worst performance was obtained by using the LTF model. The minimum makespan and the corresponding number of trucks for the three models and for the existing situation are shown in Table ý6..

Figure ý6. Comparison of makespan for unloading two trains

Table ý6. Minimum makespan and the corresponding number of trucks for unloading operations

STFLTFFATExisting Makespan (minutes) 434 422.5 421 437Number of trucks56712Makespan for loading operations

Three different models namely greedy algorithm based on LBT, STF, and LTF were used to determine the makespan for the case study 2. Comparison of the makespan obtained using the three models to load two trains is presented in Figure ý6.. It can be observed from Figure ý6. that the minimum makespan of 423.5 minutes is achieved using the model based on STF. The number of trucks obtained corresponding to the minimum makespan of 423.5 is 5. For the existing situation, the minimum makespan with 12 trucks is 432.5 minutes. Therefore, there is a saving of 9 minutes and 7 trucks when the model based on STF principle is used. In terms of makespan, the worst performance was obtained by using the LTF model. Also, there is no decrease in the makespan even the number of trucks are increased beyond 7. The minimum makespan and the corresponding number of trucks for the three models and for the existing situation are shown in Table ý6.

Figure ý6. Comparison of makespan of unloading two trains

Table ý6. Minimum makespan for loading two trains

STFLTFLBTExistingWaiting time (minutes)423.5 432.5 427.7 432.5Number of trucks56712Cost of unloading operations

The cost of unloading a containers from trains and transporting it to its location in the storage yard depends upon the travel time of the truck, processing time taken by the crane, and waiting time for the truck. The Eq ý6. used to compute the cost µ §of unloading a single container.

Figure ý6. gives the comparisons of the cost obtained through three models based on the SFT, LFT, and FAT principles. It can be seen from Figure ý6. that the lowest cost of operation is obtained using the model based on STF principle while the FAT model produces the worst results in terms of cost.

Figure ý6. Comparison of cost for unloading two trains

Table ý6. shows the cost of operation corresponding to minimum makespan obtained through three different models. The existing operation cost is also given in Table ý6..

Table ý6. Operation cost for unloading two trains

STFLTFFATExistingCost (Rupees)4400 4695 48616375 Number of trucks56712Cost of loading operations

The cost of loading a container onto a train after bringing it from its location in the storage yard depends upon the travel time of the truck, processing time taken by the crane, and waiting time for the truck. The Eq ý6. used to compute the cost µ §of loading a single container.

Figure ý6. gives the comparisons of the cost obtained through three models based on the SFT, LFT, and LBT principles. It can be seen from Figure ý6. that the lowest cost of operation is obtained using the model based on LBT principle while the LTF model produces the worst results in terms of cost.

Figure ý6. Comparison of cost for loading two trains

Table ý6. shows the cost of operation corresponding to minimum makespan obtained through three different models. The existing operation cost is also given in Table ý6..

Table ý6. Operation cost for loading two trains

STFLTFLBTExistingCost (Rupees)3574 3935.533845059.5 Number of trucks78612Waiting time for unloading operations

The waiting time of truck to unload a container from a train after return back to the rail yard depends upon the arrival time and departure time of a truck. The equation 6-2 has been used to compute the waiting time µ § of unloading a single container

Figure ý6.which give the comparisons of the waiting time obtained through three models based on the SFT, LFT, and FAT principles. It can be seen from Figure ý6. that the lowest waiting time of operation is obtained using the model based on STF principle while the FAT model produces the worst results in terms of waiting time.

Figure ý6. Comparison of waiting time for unloading two trains

Table ý6. shows the waiting time of unloading operation corresponding to minimum makespan obtained through three different models. The existing waiting time for unloading operation is also given in Table ý6..

Table ý6. Waiting time for unloading two trains

STFLTFFATExistingWaiting time (minutes)81412341525.53856Number of trucks56712Waiting time for loading operations

The waiting time of truck to load a container to a train after coming back to the storage yard depends upon the arrival time and departure time of a truck. The Eq ý6. is used to compute the waiting time µ §of loading a single container.

Figure ý6. presents the comparisons of the waiting time obtained through three models based on the SFT, LFT, and LBT principles. It can be seen from Figure ý6. that the lowest waiting time of operation is obtained using the model based on LBT principle while the LTF model produces the worst results in terms of waiting time.

Figure ý6. Comparison of waiting time for loading two trains

Table ý6. shows the waiting time of unloading operation corresponding to minimum makespan obtained through three different models. The existing waiting time for unloading operation is also given in Table ý6..

Table ý6. Waiting time for loading two trains

STFLTFLBTExistingWaiting time (minutes)1576.5211711513779Number of trucks78612Case study 3

This section describes the results of application of greedy algorithm model based on FAT principle, reverse greedy algorithm model based on LBT principle, greedy algorithm model based on STF principle, and greedy algorithm model based on LTF principle. In this case study, as given in Table ý6. there are three trains, 15 trucks and 210 jobs to be processed. The processing time (s) and travel time (2d) for each job for case study 3 is given in Table ý6.

Table ý6. Input data for case study 3

jobs(min)2d(min)jobs(min)2d(min)job.s(min)2d(min) 14.00 5.00 713.007.00 1412.007.00 22.007.00 722.009.00 1422.005.00 32.008.00 733.005.00 1432.503.00 42.004.00 743.004.00 1443.007.00 52.506.00 752.005.00 1452.005.00 62.005.00 763.008.00 1462.004.00 72.006.00 774.005.00 1473.008.00 82.005.00 784.007.00 1483.004.00 92.0010.00 793.0010.00 1493.005.00 103.005.00 802.005.00 1502.0012.00 113.006.00 813.007.00 1513.00 4.00 125.007.00 822.003.00 1522.009.00 134.003.00 833.005.00 1531.505.00 143.007.00 843.009.00 1541.503.00 153.006.00 852.006.00 1552.005.00 162.005.00 862.005.00 1562.506.00 172.004.00 873.003.00 1575.007.00 183.008.00 882.005.00 1583.004.00 192.005.00 893.009.00 1592.007.00 203.004.00 901.007.00 1601.509.00 213.506.00 911.005.00 1612.0010.00 223.00 7.00 923.004.00 1622.005.00 232.508.00 932.005.00 1632.506.00 242.005.00 943.00 7.00 1642.007.00 253.003.00 953.0012.00 1652.005.00 262.005.00 963.003.00 1663.007.00 273.008.00 973.005.00 1672.003.00 281.504.00 985.007.00 1683.009.00 293.007.00 993.004.00 1693.008.00 302.005.00 1003.009.00 1702.005.00 314.007.00 1012.007.00 1712.004.00 323.004.00 1022.0010.00 1724.009.00 332.005.00 1033.005.00 1736.005.00 343.008.00 1042.003.00 1743.006.00 352.004.00 1053.004.00 1753.005.00 363.007.00 1064.005.00 1765.0012.00 372.004.00 1073.007.00 1771.506.00 383.0010.00 1084.008.00 1783.007.00 393.504.00 1093.007.00 1795.008.00 402.005.00 1103.0010.00 1803.004.00 413.006.00 1113.007.00 1815.007.00 424.005.00 1124.005.00 1824.009.00 434.008.00 1132.003.00 1831.506.00 443.007.00 1142.005.00 1842.007.00 452.004.00 1152.007.00 1852.005.00 462.0010.00 1162.004.00 1862.008.00 472.005.00 1172.003.00 1872.507.00 483.004.00 1182.0012.00 1886.005.00 493.009.00 1192.005.00 1895.007.00 502.005.00 1202.007.00 1902.006.00 513.006.00 1214.003.00 1914.007.00 522.005.00 1224.009.00 1922.008.00 532.004.00 1232.005.00 193 4.005.00 543.007.00 1244.0012.00 1944.007.00 554.005.00 1254.005.00 1952.005.00 562.004.00 1263.007.00 1963.004.00 573.007.00 1272.005.00 1975.006.00 583.005.00 1283.006.00 1982.005.00 592.0010.00 1292.004.00 1992.006.00 605.007.00 1304.005.00 2003.007.00 613.005.00 1314.007.00 2014.008.00 624.004.00 1324.003.00 2022.005.00 631.506.00 1335.007.00 2034.006.00 642.005.00 1343.0010.00 2046.005.00 652.007.00 1353.504.00 2053.008.00 663.007.00 1363.007.00 2063.003.00 674.005.00 1373.003.00 2074.006.00 684.003.00 1383.004.00 2084.005.00 693.004.00 1392.005.00 2093.006.00 702.005.00 1402.506.00 2102.007.00 Makespan for unloading operations

A comparison of the makespan obtained using the three models STF, LTF, and FAT is presented in Figure ý6. It can be observed from Figure ý6. that the minimum makespan of 598.5 minutes is achieved using the model based on LTF. The number of trucks obtained corresponding to the minimum makespan of 598.5 is 8. For the existing situation, the minimum makespan with 15 trucks is 622 minutes. Therefore, there is a saving of 23.5 minutes and 7 trucks when the model based on LTF principle is used. In terms of makespan, the worst performance was obtained by using the STF model.

Figure ý6. Comparison of makespan for unloading three trains

The minimum makespan and the corresponding number of trucks for the three models and for the existing situation are shown in Table ý6..

Table ý6. Minimum Makespan for unloading three trains

STFLTFFATExisting Makespan(minutes)610.5 598.5601622Number of trucks58715Makespan for loading operations

A Comparison of the makespan obtained using the three models STF, LTF, and LBT is presented in Figure ý6. It can be observed from Figure ý6. that the minimum makespan of 599.5 minutes is achieved using the model based on STF. The number of trucks obtained corresponding to the minimum makespan of 599.5 is 8. For the existing situation, the minimum makespan with 15 trucks is 608.5 minutes. Therefore, there is a saving of 9 minutes and 7 trucks when the model based on STF principle is used. In terms of makespan, the worst performance was obtained by using the LTF model. The minimum makespan and the corresponding number of trucks for the three models and for the existing situation are shown in Table ý6..