1. Scheduling of Rail-mounted Gantry Cranes Based on an Integrated Deployment and Dispatching Approach 15 th Annual International Conference on Industrial Engineering Theory, Applications & Practice 2010. 10. 19. Mingchun Shan, Byung-Hyun Ha Pusan National University, Korea

2. Pusan National University 1 Contents  Introduction  Literature review  Problem definition  Heuristic algorithm  Numerical Experiments  Conclusions

3. Pusan National University 2 I. Introduction  Our goal  Improve the YC scheduling to reduce the vessel turnaround time QC schedulingYT schedulingYC scheduling

4. Pusan National University 3 I. Introduction  RMGC (rail mounted gantry crane)  Moving on rails, limited to certain blocks in one row  Typical layout of RMGCs in the yard

5. Pusan National University  Deployment & Dispatching  Problem  Schedule multiple RMGCs in a row of blocks  Objective  Minimize average waiting time of the trucks with different arrival time in a container yard I. Introduction 4

6. Pusan National University II. Literature review 5 DeploymentDispatchingIntegrated scheduling RMGC Boysen & Fliedner (2010) Froyland et al. (2006) Cao et al. (2008) Kim and Kim (1999) Ng & Mak (2005) Guo et al. (2008) Ng(2005) Petering et al. (2006) Li et al. (2009) RTGC Zhang et al. (2002) Linn et al. (2003) Petering et al. (2009) QC Park & Kim (2003) Lee et al. (2008) Overall Operation Scheduling Murty et al. (2005) Lau & Zhao (2008) Bish (2003) Petering & Murty (2009)

7. Pusan National University II. Literature review 6  Literatures of Multiple RTGCs’ Integrated scheduling  Ng(2005)  This paper develops a dynamic programming-based heuristic to solve the scheduling problem and an algorithm to find lower bounds for benchmarking the schedules found by the heuristic.  Petering et al. (2006)  First a dynamic programming-based scheduling algorithm is presented. Then this paper proposes and evaluates various ways of embedding the algorithm within a real time, dynamic YC routing system, and designs a home-made simulation model of a container terminal to identify which method is the best.  Li et al. (2009)  This paper solves this problem using heuristics and rolling-horizon algorithm.  For our algorithm  We solve the problem using a clustering-based heuristic neither dividing the slots nor considering planning horizon.

8. Pusan National University III. Problem definition 7  Assumptions  RMGCs can only travel in the same row of blocks.  m identical YCs are considered.  The ready time of each truck is known and fixed.  The ready time is denoted by.  Without loss of generality, we assume  The specific slot location for a truck is known and fixed.  The location is denoted by.

9. Pusan National University III. Problem definition 8  Assumptions  All the YCs travel in a same speed.  YC’s travel time between two adjacent slots is one time unit.  The handling time of a job is constant and is denoted by p.  The initial positions of RMGCs are given.  The safety distance is considered that is denoted by s.

10. Pusan National University IV. Heuristic algorithm 9  Deployment & Dispatching  Consider time periods  Ng made a great breakthrough  Only consider the slots  Dynamic programming is employed.

11. Pusan National University  We relax the YC scheduling problem to the assignment problem by supposing that a good schedule can be obtained from a good assignment.  The problem is solved by a two-phase heuristic  Phase 1: a clustering approach is proposed to get initial assignment  Phase 2: the previous result is improved by a neighborhood search technique. IV. Heuristic algorithm 10

12. Pusan National University  Phase 1: a clustering approach  K-means IV. Heuristic algorithm 11. Initial centers AssignmentNew center New assignmentNew center centercluster

13. Pusan National University  Phase 1: a clustering approach  The set of jobs that is assigned to one YC is a “cluster”.  Let be the set.  The expected route of each YC is considered as the “center”.  The distance is defined as IV. Heuristic algorithm 12. p

14. Pusan National University IV. Heuristic algorithm  Solution approach  Step 1. Initial centers  Step 2. Assignment  Step 3. Get new center and test the termination condition  Step 4. Update the center and go to Step 2 13

15. Pusan National University IV. Heuristic algorithm  Step 3. Get new center and test the termination condition 14 P

16. Pusan National University IV. Heuristic algorithm  Step 3. Get new center and test the termination condition  a 15

17. Pusan National University IV. Heuristic algorithm  Step 3. Get new center and test the termination condition 16 P’

18. Pusan National University IV. Heuristic algorithm  Solution approach  Step 1. Initial centers  Step 2. Assignment  Step 3. Get new center and test the termination condition  Step 4. Update the center and go to Step 2  Sequencing method is employed to get the initial schedule. 17

19. Pusan National University  Phase 2: Improvement  A local search technique is employed.  Neighborhood: a new assignment by moving one job from a YC to its adjacent YC. IV. Heuristic algorithm 18

20. Pusan National University IV. Heuristic algorithm  Sequencing Method  FOFO (first off first on) rule is mainly used.  Gives the most priority to the operation that will be completed earliest.  Interference  We propose two interference avoidance approaches:  Active interference avoidance  Passive interference handling method 19

21. Pusan National University IV. Heuristic algorithm 20 An assignment Active interference avoidance Passive interference handling The better one is used

22. Pusan National University IV. Heuristic algorithm  Sequencing Method  Let J’ denote the set of unscheduled jobs, and J-J’ is a set of jobs sche duled already.  y(j) denote the YC that handle job j  Active interference avoidance  Passive interference handling method  Step 1. Sequence the jobs in J’ by the FOFO rule  Step 2. Check interference. Terminate if there is no interference  Step 3. Assign jobs, which cause interference, considering the workloads. Replace J’ by the set of jobs after interference. 21

23. Pusan National University V. Numerical experiments  Input setting  6 YCs serve 360 slots.  cv denote the target coefficient of variation of the minimum length of sides of each triangle generated by Delaunay triangulation algorithm.  We used cv as the measure of well-distributedness as shown in figure.  Result comparison  Our heuristic will be compared with Ng (2005)’s result 22

24. Pusan National University V. Numerical experiments  Performance evaluation 23 Average number of jobs per hour per YC cv Z (average) Average CPU time (sec) Z Ng (average) Average CPU time (sec) Z/ Z Ng 0.32.930.342.800.59104.6% 100.83.720.323.610.58103.0% 1.34.070.454.430.5691.9% 0.34.231.083.921.09107.9% 140.84.550.934.601.0798.9% 1.35.511.006.331.0887.0% Computational result of heuristics: average waiting time, CPU time

25. Pusan National University VI. Conclusions  Consider the problem of schedule multiple RMGCs to handle jobs with different ready times in a straight line of blocks  Especially with the low level of well-distributedness.  Interference avoidance is considered.  Clustering technique is employed.  Sequencing method is presented to get the schedule  The results of the experiment show that our heuristic performs better in low level of well-distributedness case.  Further research:  Apply this approach to the RTGC scheduling problem.  Handling the practical input data, which includes only the workload without the precise information of each job. 24

26. Pusan National University 25