Least-looping stepping-stone-based ASM approach for transportation and triangular intuitionistic fuzzy transportation problems

Abstract

Transportation problem (TP) is a popular branch of Linear Programming Problem in the field of Transportation engineering. Over the years, attempts have been made in finding improved approaches to solve the TPs. Recently, in Quddoos et al. (Int J Comput Sci Eng (IJCSE) 4(7): 1271–1274, 2012), an efficient approach, namely ASM, is proposed for solving crisp TPs. However, it is found that ASM fails to provide better optimal solution in some cases. Therefore, a new and efficient ASM appoach is proposed in this paper to enhance the inherent mechanism of the existing ASM method to solve both crisp TPs and Triangular Intuitionistic Fuzzy Transportation Problems (TIFTPs). A least-looping stepping-stone method has been employed as one of the key factors to improve the solution quality, which is an improved version of the existing stepping-stone method (Roy and Hossain in, Operation research Titus Publication, 2015). Unlike stepping stone method, least-looping stepping-stone method only deals with few selected non-basic cells under some prescribed conditions and hence minimizes the computational burden. Therefore, the framework of the proposed method (namely LS-ASM) is a combination of ASM (Quddoos et al. 2012) and least-looping stepping-stone approach. To validate the performance of LS-ASM, a set of six case studies and a real-world problem (those include both crisp TPs and TIFTPs) have been solved. The statistical results obtained by LS-ASM have been well compared with the existing popular modified distribution (MODI) method and the original ASM method, as well. The statistical results confirm the superiority of the LS-ASM over other compared algorithms with a less computationl effort.