Using Stepping Stone and Modi Methods to Solve Transportation Problems
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
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
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