Application of minimax distribution free procedure and Chebyshev inequality for backorder discount inventory model with effective investment to reduce lead‐time and defuzzification by signed distance method

This paper considers the mixture inventory model involving variable lead‐time with discounted backorder model. We first fuzzify the demand rate, based on triangular fuzzy number and obtain the total cost in the fuzzy sense. Defuzzification of expected annual cost is performed by signed distance. We provide a solution procedure to find the optimal values of lead‐time, order quantity and backorder price discount by using minimax distribution free approach and Chebyshev inequality. We also prove the concavity and convexity of the estimate of total variable cost per unit time in fuzzy sense. Through numerical example, it is shown that there is a significant saving in cost due to crashing cost to reduce the lead‐time.