Scheduling of Rail-mounted Gantry Cranes Based on an Integrated Deployment and Dispatching Approach

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Scheduling of Rail-mounted Gantry Cranes Based
onan Integrated Deployment and Dispatching
Approach

• 15th Annual International Conference on
  Industrial Engineering Theory, Applications
  Practice 

Mingchun Shan, Byung-Hyun Ha Pusan National
University, Korea
2010. 10. 19.
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Contents

• Introduction
• Literature review
• Problem definition
• Heuristic algorithm
• Numerical Experiments
• Conclusions

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I. Introduction
QC scheduling
YT scheduling
YC scheduling
YC scheduling

• Our goal
• Improve the YC scheduling to reduce the vessel
  turnaround time

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I. Introduction

• RMGC (rail mounted gantry crane)
• Moving on rails, limited to certain blocks in one
  row
• Typical layout of RMGCs in the yard

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I. Introduction

• 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

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II. Literature review
Deployment Dispatching Integrated 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)
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II. Literature review

• 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.

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III. Problem definition

• 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 .

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III. Problem definition

• Assumptions
• All the YCs travel in a same speed.
• YCs 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.

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IV. Heuristic algorithm

• Deployment Dispatching
• Consider time periods
• Ng made a great breakthrough
• Only consider the slots
• Dynamic programming is employed.

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IV. Heuristic algorithm

• 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.

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IV. Heuristic algorithm
.

• Phase 1 a clustering approach
• K-means

center
cluster
Initial centers
Assignment
New center
New assignment
New center
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IV. Heuristic algorithm
.

• 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

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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

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IV. Heuristic algorithm

• Step 3. Get new center and test the termination
  condition

P
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IV. Heuristic algorithm

• Step 3. Get new center and test the termination
  condition
• a

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IV. Heuristic algorithm

• Step 3. Get new center and test the termination
  condition

P
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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.

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IV. Heuristic algorithm

• Phase 2 Improvement
• A local search technique is employed.
• Neighborhood a new assignment by moving one job
  from a YC to its adjacent YC.

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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

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IV. Heuristic algorithm
An assignment
Active interference avoidance
Passive interference handling
The better one is used
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IV. Heuristic algorithm

• Sequencing Method
• Let J denote the set of unscheduled jobs, and
  J-J is a set of jobs scheduled 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.

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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

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V. Numerical experiments

• Performance evaluation

Computational result of heuristics average
waiting time, CPU time
Average number of jobs per hour per YC cv Z (average) Average CPU time (sec) ZNg (average) Average CPU time (sec) Z/ ZNg
0.3 2.93 0.34 2.80 0.59 104.6
10 0.8 3.72 0.32 3.61 0.58 103.0
1.3 4.07 0.45 4.43 0.56 91.9
0.3 4.23 1.08 3.92 1.09 107.9
14 0.8 4.55 0.93 4.60 1.07 98.9
1.3 5.51 1.00 6.33 1.08 87.0
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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.

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Thank you for your attention