Intuitionistic fuzzy T-sets based optimization technique for production-distribution planning in supply chain management

Abstract

Technique to find optimal solutions for production-distribution planning in supply chain management under imprecise environment is discussed in this paper. In 1997, Angelov first introduced an optimization technique under intuitionistic fuzzy environment. Several other researchers have worked on it in recent years. In 2015, Wu, Liu and Lur redefined membership functions of fuzzy set theory and proposed another two phase technique. In optimization problem under uncertainty, it is observed that prime intention to maximize up-gradation of most misfortunate is better served if some constraints present in existing, established techniques are removed. It is also observed that membership functions and non-membership functions are not utilized in the way they are defined in existing techniques. And in some cases, constraints in existing techniques may make model infeasible. Hence in this paper, new functions: T⁽⁺⁾-characteristic functions and T^(-)-characteristic functions, are introduced to supersede membership functions and non-membership functions respectively; and subsequently new set: Intuitionistic fuzzy T-set is introduced to supersede intuitionistic fuzzy set to represent uncertainty. Moreover in this paper, one general algorithm has been developed to find optimal solutions to optimization problems under uncertainty. One standard production-distribution model is taken not only to allocate limited available resources and equipment to produce the products over time periods but also to determine economic distributors for dispatching product to the retailers. Real life numerical applications of this model further illustrate the limitations of existing techniques as well as advantages of using proposed technique. Finally conclusions are drawn.