Experimental Analysis of Some Variants of Vogel's Approximation Method

Abstract

This paper presents a variant of Vogel's approximation method (VAM) for transportation problems. The importance of determining efficient solutions for large sized transportation problems is borne out by many practical problems in industries, the military, etc. With this motivation, a few variants of VAM incorporating the total opportunity cost (TOC) concept were investigated to obtain fast and efficient solutions. Computational experiments were carried out to evaluate these variants of VAM. The quality of solutions indicates that the basic version of the VAM coupled with total opportunity cost (called the VAM–TOC) yields a very efficient initial solution. In these experiments, on an average, about 20% of the time the VAM–TOC approach yielded the optimal solution and about 80% of the time it yielded a solution very close to optimal (0.5% loss of optimality). The CPU time required for the problem instances tested was very small (on an average, less than 10 s on a 200 MHz Pentium machine with 64 MB RAM).

Material flow optimisation in a multi-echelon and multi-product supply chain

“…Kirca and Satir (1990) developed a heuristic, called total opportunity-cost method (TOM), for obtaining an initial feasible solution for the transportation problem. Mathirajan and Meenakshi (2004) presented two variants of VAM for transportation problems by coupling the idea of TOM (Kirca and Satir, 1990) with VAM. These variants are: VAM, applied on the TOC matrix [VAM-TOC] and VAM with tie breakers applied on the TOC matrix [VAMT-TOC] [refer to Das and Heragu (1988), Gass (1990), Goyal (1984), Lee (1986), Ramakrishnan (1988), Russel (1969) and Shimshak et al (1981) for more work on transportation problems].…”

“…We also mention here that a similar method known as VAM-TOC was proposed by Mathirajan and Meenakshi (2004). The steps for the TOPCM solution are given below:…”

A heuristic based on Vogel's approximation method for sequencing mixed-model assembly lines

“…In literature, the VAM approach has been extended and is also used as construction heuristic for other transportation problems (cf. Larson 1972, Sharma and Prasad 2003, Mathirajan and Meenakshi 2004.…”

A New Approach to Solve Transportation Problems

“…This problem has been studied since long and is well known by Abdur Rashid et al [4], Aminur Rahman Khan et al [5]- [8], Hamdy A. T. [9], Kasana & Kumar [10], Kirca and Satir [11], M. Sharif Uddin et al [12], Mathirajan, M. and Meenakshi [13], Md. Amirul Islam et al [14] [15], Md.…”

“…Again, some of the well reputed methods for finding an initial basic feasible solution of transportation problems developed and discussed by them are North West Corner Method (NWCM) [9], Row Minimum Method (RMM) [6] [26], Column Minimum Method (CMM) [6] [26], Least Cost Method (LCM) [9], Vogel's Approximation Method (VAM) [9] [24], Extremum Difference Method (EDM) [10], Highest Cost Difference Method (HCDM) [5] [6], Average Cost Method (ACM) [4], TOCM-MMM Approach [11], TOCM-VAM Approach [13], TOCM-EDM Approach [15], TOCM-HCDM Approach [14], TOCM-SUM Approach [7] etc.…”