Using Stepping Stone and Modi Methods to Solve Transportation Problems

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USING STEPPING STONE AND MODI METHODS TO SOLVE TRANSPORTATION PROBLEMS

BY

ABDUSSALAM MUHAMMAD MUSTAPHA

09/211306009

A SEMINAR PAPER PRESENTED TO THE DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, USMANU DANFODIYO UNIVERSITY, SOKOTO IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF THE DEGREE OF MASTER OF SCIENCE (MATHEMATICS)

SUPERVISORY TEAM:
MAJOR SUPERVISOR: DR. U. A. ALI
CO – SUPERVISOR I: DR. I. J. UWANTA
CO – SUPERVISOR II:DR. MU’AZU MUSA

DATE:07TH NOVEMBER, 2012
TIME:10:00 AM
VENUE:U.G. COMPUTER LABORATORY
Abstract
This research is posed with investigation of transportation problems of a bus transit company considering the importance derived from the transport sector of the economy to the leaders and the led. The research considered the balanced type of transportation problems and showed how the initial solutions can be obtained as well as the optimal solution which is of great importance. The Vogel’s approximation method (VAM) was used to determine the initial solution while the Stepping stone (SS) and the Modified Distribution (MODI) methods were used to test for optimality. The algorithms for obtaining the VAM, SS and MODI methods are presented and used to maximize the transportation problem of Katsina State Transport Authority for four busiest routes selected. The optimal solution obtained yielded an increase of about 1.4% of the daily income generated by the routes. Finally it was observed that the problem has multiple optimal solution and suggestions were made on allocations that will yield optimal profit.

1.0 Introduction:
1. Introduction:
Transportation is an important domain of human activity. It supports and makes possible most other social and economic activities and exchanges. Transportation is also a complex domain, with several players and levels of decision, where investments are capital-intensive and usually require long implementation delays. (Crainic, 1998) According to Enyi (2007), “The primary objective of a business entity is to maximize owners’ equity”. A passenger transport service company maximizes profit from its operations by taking advantage of all situations by applying operational research techniques to aid decision making tend to perform better than those that do not apply them. Passenger transport service business in Nigeria is the most competitive, most vulnerable and most volatile of all sectors in the Nigerian economy. The reasons for these are not too difficult to discern. Nigerians are highly mobile people willing to travel at short notice, apart from road transportation which is even characterized by lack of effective government coordination, other forms of transport are still highly underdeveloped and most transport operators in Nigeria are still “traditional” in their approach to doing business due to the virtually low level of intellectual development prevailing amongst them. Furthermore, the transport business brings in very high and quick returns than other forms of business especially during festivity periods. (Enyi, 2007) The objective of an efficient system is to meet the diverse demands and minimize operator’s loss. This requires that the optimizing, routing, scheduling and synchronizing problems are given special attention, while designing an efficient bus system. 1.2 Background to the study:

During the colonial days when cars and buses are relatively scarce, the major systems of mass transport of people and cargo are the Nigerian Railway (now in moribund state) and the popular gwon-gworo or mammy wagon. These modes of transportation, though, still very much in existence were complimented with the introduction of the luxury bus system by the then Midwestern state towards the tail end of the 60s. This luxury bus system called Mid West Line operated from Benin- City to Lagos and from Lagos to Kaduna, Kano and Jos. The Mid West Line was later joined by such other transport services like Oriental line...
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