Application Of Minimax Distribution Free Procedure And Chebyshev Approach In Mixed Inventory Model Involving Reducible Lead-Time And Setup Cost With Imprecise Demand

In this paper, we extend Lin [Lin, YJ (2008). Minimax distribution free procedure with backorder price discount. International Journal of Production Economics, 111, 118–128] model by fuzzifying the demand rate, based on triangular fuzzy number to increase its applicability and solve the problem by using an alternative approach i.e., Chebyshev approach. We prove the concavity and convexity of the estimate of total variable cost per unit time in fuzzy sense. To compare the expected annual cost of proposed model, defuzzification is performed by two different methods namely signed distance and centroid method. We provide a solution procedure to find the optimal values of lead-time, the order quantity and the backorder price discount by using minimax distribution free procedure and Chebyshev approach. Through numerical example it is shown that there is a significant saving in cost due to crashing cost to reduce the lead-time and the setup cost. We also compare our results with Cheng et al. [Cheng, TL, CK Huang and KC Chen (2004). Inventory model involving lead-time and setup cost as decision variables. Journal of Statistics and Management Systems, 7, 131–141] model and show that Ben-Daya and Raouf's [Ben-Daya, M and A Raouf (1994). Inventory model involving lead-time as a decision variable. Journal of the Operational Research Society, 45, 579–582] model is the special case of our proposed model.