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

Scheduling of Rail-mounted Gantry Cranes Based on

an Integrated Deployment and Dispatching Approach

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

2010. 10. 19.

Mingchun Shan, Byung-Hyun Ha

Pusan National University, Korea

Pusan National University2

Contents

Introduction

Literature review

Problem definition

Heuristic algorithm

Numerical Experiments

Conclusions


I. Introduction

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

QC scheduling YT scheduling YC schedulingYC scheduling


I. Introduction

RMGC (rail mounted gantry crane) Moving on rails, limited to certain blocks in one row

Typical layout of RMGCs in the yard

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

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II. Literature review

6

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)


II. Literature review

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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.


III. Problem definition

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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 .

𝑟1 < 𝑟2 < ⋯ < 𝑟𝑛

𝑟𝑗

𝑏𝑗


III. Problem definition

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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.


IV. Heuristic algorithm

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Deployment & Dispatching Consider time periods Ng made a great breakthrough

Only consider the slots Dynamic programming is employed.


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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Phase 1: a clustering approach K-means


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.

Initial centers Assignment New center

New assignmentNew center

center cluster


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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𝐽𝑖

.

𝑑𝑗𝑖 = ቚ𝐶𝑟𝑗𝑖 − 𝑏𝑗ቚ+ 𝑤𝑟𝑗𝑖

p



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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Step 3. Get new center and test the termination condition

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P



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

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Let 𝐽1𝑖,𝐽2𝑖 ,…,𝐽𝑔𝑖𝑖 be the groups of jobs assigned to YC 𝑖,where 𝑔𝑖 is the number of the groups. 𝐽𝑘𝑖 ’s are a partition of 𝐽𝑖.



Step 3. Get new center and test the termination condition

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P’min. ห𝑐𝑘𝑖 − 𝑏𝑗ห+ 𝑤𝑟𝑗𝑖𝑗∈𝐽𝑘𝑖𝑔𝑖

𝑘=1𝑚

𝑖=1

s.t. ห𝑐𝑘𝑖 − 𝑐𝑘−1𝑖 ห≤ 𝛼𝑘𝑖 − 𝛽𝑘−1𝑖 ∀𝑘 ∀𝑖 𝑐𝑘𝑖 + 𝑠ሺ𝑖′ − 𝑖ሻ≤ 𝑐𝑘′𝑖′ for 𝑖,𝑖′,𝑘,𝑘′ such that 𝑖 < 𝑖′ 𝑎𝑛𝑑 ൣ �𝛼𝑘𝑖 ,𝛽𝑘𝑖൧∩ቂ𝛼𝑘′𝑖′ ,𝛽𝑘′𝑖′ ቃ≠ ∅

𝑐𝑘𝑖 + 𝑠ሺ𝑖′ − 𝑖ሻ≤ 𝑐𝑘′𝑖′ + 𝛼𝑘𝑖 − 𝛽𝑘′𝑖′ for 𝑖,𝑖′,𝑘,𝑘′ such that 𝑖 < 𝑖′ 𝑎𝑛𝑑 𝛽𝑘−1𝑖 < 𝛽𝑘′𝑖′ ≤ 𝛼𝑘𝑖 𝑐𝑘′𝑖′ + 𝑠ሺ𝑖 − 𝑖′ሻ≤ 𝑐𝑘𝑖 + 𝛼𝑘𝑖 − 𝛽𝑘′𝑖′ for 𝑖,𝑖′,𝑘,𝑘′ such that 𝑖′ < 𝑖 𝑎𝑛𝑑 𝛽𝑘−1𝑖 < 𝛽𝑘′𝑖′ ≤ 𝛼𝑘𝑖



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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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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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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21

An assignment

Active interference avoidance

Passive interference

handlingThe better one

is used



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

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Average number of jobs per hour per YC

cvZ

(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%

Computational result of heuristics: average waiting time, CPU time


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

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