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Solving Transportation Problem Using Object-Oriented Model

Taghrid Imam Gaber Elsharawy Mohamed Gomah Iman Samy

Department of mathematics, Faculty of science El Azhar Unversity , Egypt We design Object-Oriented Model as decision support tool to evaluate the solution for the five methods using C++ language. After designing the five models (the five programs) we compare between each solution using C++programs and LP solution which have the same result. Comparison between different solutions is done for choosing less value of the objective function so that the user will be able to make decision.

Summary

This paper is about solving transportation problem using Operation Research (OR) approach in analysis and design phases and we use C++ programming language to model the problem. The results obtain from both solutions are compared in order to make analysis and prove the object-oriented model correctness. We proved that both results are identical and have the same results when solving the problem using the five methods: northwest corner method; minimum cost method; row minimum cost method; column minimum cost method, and Vogel’s approximation method.

TRANSPROTATION MODEL

Transportation model is a special type of networks problems that for shipping a commodity from source (e.g., factories) to destinations (e.g., warehouse). Transportation model deal with get the minimum-cost plan to transport a commodity from a number of sources (m) to number of destination (n). Let si is the number of supply units required at source i (i=1, 2, 3……. m), dj is the number of demand units required at destination j (j=1, 2, 3….. n) and cij represent the unit transportation cost for transporting the units from sources i to destination j. Using linear programming method to solve transportation problem, we determine the value of objective function which minimize the cost for transporting and also determine the number of unit can be transported from source i to destination j. If xij is number of units shipped from source i to destination j. the equivalent linear programming model will be [5] The objective function

Key words:

Transportation problem, Linear Programming (LP), objectoriented programming

1. Introduction

The first main purpose is solving transportation problem using five methods of transportation model by linear programming (LP). The second main purpose is solving transportation problem by object-oriented programming. C++ programming language is used to get the solution. The results obtain from both LP and objectoriented programming solutions are compared. The five methods for solving Transportation problem are: 1. Northwest Corner method 2. Minimum cost method 3. Vogel’s approximation method 4. Row Minimum Method 5. Column Minimum Method. This paper introduces methods for solving transportation problem by C++ programming language; we use flow chart, algorithms and consider the importance of defining a problem sufficiently and what assumptions we may consider during the solution. Solving transportation problem by computer involves serves of steps: define the problem, analysis the problem and formulate a method to solve it, describe the solution in the form of an algorithm, draw a flow chart of the algorithm, write the computer program, compile and run the program, test the program and interpretation of results.

Subject to for i=1,2,…………..m. for j=1,2,…..……….,n. And xij 0 for all i to j.

Manuscript received February 5, 2009 Manuscript revised February 20, 2009

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IJCSNS International Journal of Computer Science and Network Security, VOL.9 No.2, February 2009

Fig.4.1 Network representation of the transportation problem A transportation problem is said to be balanced if the total supply from all sources equals the total demand in all destinations made in that row or column. If both a row and a column net to...