A Possibility Approach for the Single Item Lot Sizing Problem with Fuzzy Parameters

Abstract

The main objective of this chapter is to deal with a single item lot sizing problem with fuzzy parameters, which is called the fuzzy single item lot sizing problem (F-SILSP). Since F-SILSP does not meet the crisp deterministic assumption, it cannot be solved by traditional mathematical programming. In this chapter, the possibility approach is chosen to convert the fuzzy model to be an equivalent crisp single item lot sizing problem (EC-SILSP). The equivalent crisp model from this transformation procedure is in the form of mixed integer linear programming (MILP). It can be solved by traditional solver to find an optimal solution for each pre-specified possibility level. A numerical example with both trapezoidal and triangular fuzzy parameters is illustrated to demonstrate that an equivalent crisp model can be used. In addition, the equivalent crisp model is employed in inventory planning in a case study of inventory planning for bituminous coal with trapezoidal fuzzy demand and triangular fuzzy unit price in a power plant of an example petrochemical company (Supreme Petro, India).