集装箱堆场问题的一个数学模型及其算法_英文

第28卷　增刊大连海事大学学报Vol.28,Suppl. 2002年8月Journal of Dalian Maritime U niversity Aug.,2002

文章编号:100627736(2002)增20115203

集装箱堆场问题的一个数学模型及其算法

杨淑芹,张运杰,王志强

(大连海事大学数理系,辽宁大连　116026)

摘要:讨论了集装箱堆场中一个常见的问题,即若干个不同重量的集装箱按一定顺序到达,要将这些箱子三个一垛码好,先到先码,后到后码,尽量轻箱在下,重箱在上,以保证装船时重箱在下,轻箱在上。因为在大多数情况下,无论怎样码放,都免不了捣箱。因此,如何码放才能使捣箱数最小是值得研究的问题,此问题可能是N2P难的问题,所以本文给出了这一问题的一个启发式算法。

关键词:堆场;集装箱移动数量

中图分类号:U492.315 文献标识码:A

A model and its algorithm on container yard problem

YAN G Shu2qin,ZHAN G Yun2jie,WAN G Zhi2qiang

(M ath.&Phys.Dept.,Dalian Maritime Univ.,Dalian116026,China)

Ξ

Abstract:There is a problem in container yard,a series of containers is transformed to the gate of yard waiting for being assigned a location.The containers are stacked in three with the lighter below and the heavier above in order that the lighter container is above when loading the ship.

For the random of arrivals of the containers,it is inevitable to shift containers(if a lighter container is above a heavier one,then we move the lighter aside to load the heavier,then load the lighter).How to as2 sign a location to the container to minimize the number of shifting containers maybe a NP problem.There is no precise solution.So we give a heuristic algorithm to the solution.

K ey w ords:yard;number of container2shifting

1　Introduction

Three days before a ship departs,the contain2 ers of the ship are sent to the container wharf which is called“collection”[1].All containers of the same ship are stacked up in the same yard.We are required to pile the containers three in a stack and let the lighter below and the heavier above as much as possible so that the heavier is loaded firstly.Be2 cause the containers arrive at the yards gate ran2 domly,the workers assign a location number to the containers according to the sequence.It is unavoid2 able to locate the heavier below and the lighter above.In this case,we must put the lighter aside

Ξ收稿日期:20022072181

作者简介:杨淑芹(19632),女,辽宁大连人,副教授,主要从事优化问题的研究1

and load the heavier,then load the lighter.This is called“shifting”.The numbers of shifting can low2 er the loading speed,prolong the parking time,so influence the working efficiency.In order to reduce the rate of shifting,we find a method to assign the locations for a group of containers.

2　Constructing a model

According to the yard problem,we construct a mathematical model.

For a sequence of n containers with a weight number,we pile them up three in one stack one above another.Then the number of stacks is

k=

n

3

n

3

+1

n is integer times of3

n is not integer times of3

We let the lighter container above and the

heavier below.The container with the same num2 ber can be piled up in one stack.So the three weight numbers of one stack make a sequence from the bottom to top.There is an inverse number for every stack.The problem becomes that how to as2 sign a location to every container so that the sum of the inverse numbers of k stacks is minimum.

The number in a containers represents the weight of the ually,the containers are divided into several groups according to their weight.The containers in the same group can be piled up in the same stack in which the inverse number is zero.For example,at the yard gate,the containers are divided into three groups,one group with the weight0～10tons;another with11～17 tons;else another with17tons or above.Consider2 ing the weight of a container is not an integer,it is difficult to make a computer program,and it’s im2 possible to arrange the containers strictly by their weights.We divide the containers into nine groups by their weight.So every container has a number from1to9.The bigger the number is,the heavier the container is.The containers with the same number have the same weight and the inverse num2 ber of three containers of them is zero.

The minimum of the inverse number is corre2 sponding to that of the shifting number.

The problem is complicated because

(1)the method to pile n containers in k stacks with the minimizing shifting number is not unique. This problem maybe N2P difficult problem,that is,the optimal solution is not found by the comput2 er[3].

(2)a container arrives at the container yard randomly.We assign a position to the container only by the preceding containers’positions.So the shifting is not avoidable.

This paper gives an approximate algorithm to assign positions to a group of containers.Firstly it derives a rough solution,then improves it step by step.

3　The algorithm

Set up a two2dimensional rectangular2coordi2 nate system,let a point in the plane represent a container.The x2coordinate represents its order number,the y2coordinate represents its weight number.We obtain many points in the coordinate system.

Firstly rough division:let the point with the smallest x2coordinate be the first point,scan the area which is a infinite rectangle with the first point be the most left and lowest point,find the nearest point according to the x2coordinate in the area,let it be the second point,link the second point into the first point by a line segment.Then repeat the steps above.Scan the area which is a in2 finite rectangle with the second point be the most left and lowest point,find the nearest point accord2 ing to the x2coordinate in the area,let it be the third point,link this point into the second point by a line segment.The process continues until there is not any point in the right and above area.Then we obtain a group of point linked by line segments. This group of containers can be piled up in a stack in which the inverse number is zero.Let the point with the smallest x2coordinate in the remaining points be the first point,scan its right2above area, find the point which is nearest to the first point ac2 cording to x2coordinate,let it be the second point, link the two points.Repeat the above steps to get

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大连海事大学学报 第28卷