Transportation model

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Lokesh Payasi

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Formation

GYAN GANGA INSTITUTE OF TECHNOLOGY AND MANAGEMENT, BHOPAL Transportation Problem Presented by: ,[object Object]

Rahul JainGuided by: Prof. Lokesh Payasi

Definition ,[object Object],[object Object]

Application of Transportation Problem ,[object Object]

Military distribution system,[object Object]

Vogle Approximation Method (VAM),[object Object]

Row Minima Method ,[object Object],Supply Minimum cost in the Row Demand

Column Minima Method ,[object Object],Supply Minimum cost in the Column Demand

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This paper aims at identifying an effective and appropriate method of calculating the cost of transporting goods from several supply centers to several demand centers out of many available methods. Transportation algorithms of North-West corner method (NWCM), Least Cost Method (LCM), Vogel’s Approximation Method (VAM) and Optimality Test were carried out to estimate the cost of transporting produced newspaper from production center to ware-houses using Statistical software called TORA. The results revealed that: NWCM = 36,689,050.00, LCM = 55,250,034.00, VAM = 29,097,700.00 and Optimal solution = 19,566,332.00. It was discovered that Vogel’s Approximation method gives the transportation cost that closer to optimal solution. Also, the study revealed that a production center should be created at northern part of Nigeria to replace the dummy supply center used in the analysis, so as to make production capacity equal to requirement.

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Transportation Problem (TP) is an important network structured linear programming problem that arises in several contexts and has deservedly received a great deal of attention in the literature. The central concept in this problem is to find the least total transportation cost of a commodity in order to satisfy demands at destinations using available supplies at origins in a crisp environment. In real life situations, the decision maker may not be sure about the precise values of the coefficients belonging to the transportation problem. The aim of this paper is to introduce a formulation of TP involving Triangular fuzzy numbers for the transportation costs and values of supplies and demands. We propose a two-step method for solving fuzzy transportation problem where all of the parameters are represented by non-negative triangular fuzzy numbers i.e., an Interval Transportation Problems (TPIn) and a Classical Transport Problem (TP). Since the proposed approach is based on classical approach it is very easy to understand and to apply on real life transportation problems for the decision makers. To illustrate the proposed approach two application examples are solved. The results show that the proposed method is simpler and computationally more efficient than existing methods in the literature.

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Transportation is defined as the movement of passengers and freight from one place to another. Passenger is an important part of the overall development problem of the nation and it affects mostly all the aspects of mobility. The Transportation problem is one of the sub classes of LPP in which the objective is to transport various amount of a single homogeneous commodity, that are initially stored at various origins, to different destinations in such a way that the total transportation cost is minimum. Although the name of the problem is derived from transport to which it was first applied, the problem can also be used for machine allocation, plant location, product mix problem, and many others, so that the problem is not confined to transportation or distribution only. Data Envelopment Analysis (DEA) is a very powerful service management and benchmarking technique originally developed by Charnes et al (1) to evaluate nonprofit and public sector organizations. Linear programming problem (LPP) is the underlying methodology that makes DEA particularly powerful compared with alternative productivity management tools. A Transportation Problem can be solved very easily by different methods (NWC RULE, LCM & VAM) by recognizing and formulating into LPP. The IBFS obtained in Transportation Algorithm can be tested also by MODIFIED DISTRIBUTION METHOD. After studying this paper, we will be able to achieve the following objectives of Transportation System - a major problem of the metropolitan cities. 1- Recognize and formulate the transportation problem as a linear programming problem. 2- Build a transportation table and describe its components. 3- Find an initial basic feasible solution of the transportation problem by using various methods. 4- Know in detail all the steps involved in solving a transportation problem by MODI problem. 5- Solve the unbalanced transportation problems by MODI method. 6- Identify the special situation in transportation problems; such as degeneracy and alternative optimal solution. 7- Resolve the special cases in transportation problems, where the objective may be of maximization or some transportation route may be prohibited.

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