Java調用cplex求解運輸問題

本文中的課件來自清華大學深圳國際研究生院，物流與交通學部張燦榮教授《生產管理》課程。

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運輸問題(Transportation Problem)描述

運輸問題是一種特殊的最小費用網絡流問題，其中每個節點都是一個純供給節點或一個純需求節點。即所有的流都從供給它的某個源頭節點出發，而后直接到達一個需要它的需求節點，中間不經過其它中間步驟或轉運環節。一個運輸問題中的商品流可能是任何東西，唯一必要的條件就是需要從供給源頭節點流入需求節點。總結一下，運輸問題具有以下的特點：

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運輸問題的數學模型

首先定義運輸問題的參數與決策變量：

目標函數為最小化運輸成本：

約束一為從每個供給節點運出的商品總和等于該節點可用商品的數量：

約束二為每個需求節點流入的商品總和等于該節點需求商品的數量：

最后決策變量的取值范圍：

綜上，1~4式即為運輸問題的數學模型，且為一個線性規劃模型。

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Java調用cplex求解運輸問題

本節介紹如果使用Java語言調用cplex求解器對運輸問題進行求解。問題相關參數如下：Java是一種面向對象的編程語言，故編寫過程中主要涉及以下幾個類：

transportation_node類

package?transportation_problem;

/**
?*?This?class?is?to?define?the?transportation_node
?*?@param?Property?of?node
?*?@return?a?node?object
?*/

public?class?transportation_node?{
?String?NodeName;
?int?quantity;
?int?isSource;??
?int?id;
?public?transportation_node(String?NodeName,int?quantity,int?isSource,int?id)?{
??this.NodeName?=?NodeName;
??this.quantity?=?quantity;
??this.isSource?=?isSource;
??this.id?=?id;
?}?

?public?boolean?isSource()?{
??if(this.isSource?==?1)?{
???return?true;
??}
?return?false;
?}
}

transportation_relation類

package?transportation_problem;

/**
?*?This?class?is?to?define?the?transportation_relation
?*?@param?Property?of?node
?*?@return?a?relation?object
?*/

public?class?transportation_relation?{
?int?[]?distance?;
?public?transportation_relation(int[]?distance)?{
??this.distance?=?distance;
?}
}

讀取數據

package?transportation_problem;

import?java.io.*;
import?java.util.*;

/**
?*?This?class?is?to?read?data?from?txt?file
?*?@param?path:?the?file?path?to?be?read
?*?@return?return?a?data?object
?*?@throws?IOException
?*/
?
public?class?Readfile?{
?List?transportationNodeList?=?new?ArrayList();
?transportation_relation?transportationRelation;public?Readfile(String?path1,String?path2)?throws?IOException?{
??readtransportation_node(path1);
??transportation_relation(path2);
?}public?void?readtransportation_node(String?path)?throws?IOException?{
??BufferedReader?br?=?new?BufferedReader(new?FileReader(path));
??String?line?=?new?String();//讀取變量
?????br.readLine();
?????line?=?br.readLine();
?????String[]?tokens?=?line.split("\\s+");while(tokens.length?>?0)?{
???transportation_node?Temp?=?new?transportation_node(tokens[0],Integer.parseInt(tokens[1]),Integer.parseInt(tokens[2]),Integer.parseInt(tokens[3]));
???transportationNodeList.add(Temp);
??????line?=?br.readLine();??????
??????tokens?=?line.split("\\s+");
??}
??br.close();
?}public?void?transportation_relation(String?path)?throws?IOException?{
??BufferedReader?br?=?new?BufferedReader(new?FileReader(path));
??String?line[]?=?new?String[100];int?row?=?0;
??line[row]?=?br.readLine();while(line[row]?!=?null)?{
???row++;
???line[row]?=?br.readLine();
??}
??String[]?tokens?=?line[0].split("\\s+");int?column?=?tokens.length;int?[]?dis?=?new?int[(row-1)*column];for?(int?i?=?1;?i????tokens?=?line[i].split("\\s+");for?(int?j?=?1;?j?<=?column;?j++)?{
????dis[(column)*(i-1)+j-1]?=?Integer.parseInt(tokens[j]);
???}
??}
??transportationRelation?=?new?transportation_relation(dis);
??br.close();
?}
}

在cplex中建立運輸問題模型

package?transportation_problem;

import?java.util.List;
import?ilog.concert.IloException;
import?ilog.concert.IloNumExpr;
import?ilog.concert.IloNumVar;
import?ilog.cplex.IloCplex;

/**
?*?This?class?is?to?conduct?a?model?in?cplex?and?solve
?*?@param?problem?parameter
?*?@return?return?solve?result
?*?@throws?IloException
?*/

public?class?model_transportation?{
?IloCplex?cplex?;
?double?objectiveValue;
?IloNumVar?x[];
?int?numOfPlants?=?0;
?int?numOfdestination?=?0;
?/**
??*?This?method?is?to?bulidModel
??*?@param?transportation_problem's?data
??*?@return?transportation_problem's?model
??*?@throws?IloException
??*/
?public?void?bulidModel(List?transportationNodeList,transportation_relation?transportationRelation)throws?IloException?{
??this.cplex?=?new?IloCplex();
??for(transportation_node?tsNode?:?transportationNodeList){
???if?(tsNode.isSource())?{
????numOfPlants++;
???}else?{
????numOfdestination++;
???}
??}
??CreatDecisionVariab();
??CreatObjFunc(transportationRelation);
??CreatConstraints(transportationNodeList);
??Solve(transportationNodeList);
?}
?/**
??*?This?method?is?to?create?decision?variables
??*?@throws?IloException
??*/
?public?void?CreatDecisionVariab()?throws?IloException{
??x?=?new?IloNumVar[numOfPlants*numOfdestination];
??for?(int?i?=?0;?i????for?(int?j?=?0;?j?????x[i*numOfdestination+j]?=?cplex.numVar(0,?Double.MAX_VALUE,"x"+(i+1)+(j+1));
???}
??}
?}
?/**
??*?This?method?is?to?create?objective?function
??*?@throws?IloException
??*/
?public?void?CreatObjFunc(transportation_relation?transportationRelation)?throws?IloException{
??cplex.addMinimize(cplex.scalProd(x,transportationRelation.distance));
?}
?/**
??*?This?method?is?to?add?constraints
??*?@throws?IloException
??*/
?public?void?CreatConstraints(List?transportationNodeList)?throws?IloException?{
??for(transportation_node?tsNode?:?transportationNodeList){
???IloNumExpr?left?=?cplex.linearNumExpr();
???if?(tsNode.isSource())?{
????for(int?i?=?0;i?????left?=?cplex.sum(left,cplex.prod(1,x[tsNode.id*numOfdestination+i]));
????}
????cplex.addEq(left,tsNode.quantity);
???}else?{
????for(int?i?=?0;i?????left?=?cplex.sum(left,cplex.prod(1,x[tsNode.id+i*numOfdestination]));
????}
????cplex.addEq(left,tsNode.quantity);
???}
??}
?}
?/**
??*?This?method?is?to?solve?model
??*?@return?values?of?objective?function?and?decision?variables
??*?@throws?IloException
??*/
?public?void?Solve(List?transportationNodeList)?throws?IloException{
??cplex.setOut(null);
??if?(cplex.solve())?{
???cplex.exportModel("111.lp");
???objectiveValue?=?cplex.getObjValue();
???System.out.println("最小運費為："?+?objectiveValue);
???for?(int?i?=?0;?i?????for?(int?j?=?0;?j??????System.out.print(transportationNodeList.get(i).NodeName+"?to?"+transportationNodeList.get(numOfPlants+j).NodeName+"?:?");
?????System.out.println(cplex.getValue(x[i*numOfdestination+j]));
????}
???}
??}
?}
}

主函數main

package?transportation_problem;

import?java.io.IOException;
import?java.util.List;
import?ilog.concert.IloException;

public?class?Main?{
?public?static?void?main(String[]?args)?throws?IOException,?IloException?{
??Readfile?file?=?new?Readfile("transportation_node.txt","transportation_relation.txt");
??List?transportationNodeList?=?file.transportationNodeList;
??transportation_relation?transportationRelation?=?file.transportationRelation;
??model_transportation?model?=?new?model_transportation();
??model.bulidModel(transportationNodeList,?transportationRelation);
?}
}

求解結果

導出模型：

這樣就完成了，感謝大家的閱讀。

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作者：夏旸，清華大學，工業工程系/深圳國際研究生院 (碩士在讀)?

郵箱：xia970201@gmail.com

完整Project文件請在后臺回復【運輸問題】獲取。

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