A New Approach to Find the Initial Basic Feasible Solution of a Transportation Problem

Abstract

Transportation problem (TP) in operations research is a widely used optimization technique to study the problems concerned with transporting goods from production places to sale points. The TP may have one or more objectives such as minimization of transportation cost, minimization of distance with respect to time, and so on. There is a systematic method to solve such problems. For this, we find the Initial Basic Feasible Solution (IBFS) to the given problem. North West corner method, least cost method, Vogel’s approximation method are the standard methods one uses to find the IBFS. In recent years, there are several other methods are proposed to solve such problems. In this paper, we propose a new technique named as Direct Sum Method (DSM) and its effectiveness is compared with the standard methods. The result shows that it is easy to compute and near to the optimum solution of the problem.

Analysis of IBFS for Transportation Problem by Using Various Methods

“…The main advantage of this method it is very easy to use but finding the solution by this method takes some time. Kumar et al [7] suggested the transportation problem have many objectives such as minimize the transportation cost, with respect to time we minimize the distance, find the past having lowest cost etc. Sharma [8] also suggested an analysis for solving the different types of problems in real.…”

An Improved Algorithm for Optimal Solution of Unbalanced Transportation Problems

“…M. Palanivel, et al [15] analyzed an innovative procedure for solving problems of transportation by using Harmonic Mean Approach. Ravi Kumar R, et al [16] they proposed a new technique named Direct Sum Method using VAM, to discover the I.B.F.S of transportation problems. A. Seethalakshmy & N. Srinivasan [17] proposed a different technique to resolve of unbalanced transportation assignment problems, based on finding the position of '1' by using systematic procedure.…”

A Proposed Method for Finding Initial Solutions to Transportation Problems

“…The Total Opportunity Cost Matrix-Minimal Total (TOCM-MT) method (Amalia et al , 2019) was compared to Hosseini's methods and the VAM for which it was claimed to have performed better than the other methods. Similarly, Ravi et al (2018) proposed the Direct Sum Cost method in comparison to the Vogel's method (i.e VAM), NCR and the LCM to evaluate its effectiveness in solving the transportation problem. Hanif and Rafi (2018) also suggested a new methodology which requires arithmetic and logical calculations to yield an IBFS in comparison to VAM; even so, the proposed method could not outperform the VAM in such cases.…”