An optimal inventory model with interaction of lot size, production rate and lead-time in a fuzzy back-order system

Abstract

This paper examines the decision-making about the interaction of lot size, production rate and lead time between a vendor and a buyer with the consideration of trade credit and fuzzy back-order rate. We assume that the lead time demand is distribution free and the back-order rate is triangular fuzzy number. An economic model is design to determine the optimal lot-size, production rate and lead time while minimizing system total cost. A minimax approach is applied to tackle the model and designed an iterative algorithm to obtain the optimal strategy. Numerical example and sensitivity analyses are given to demonstrate the performance of the proposed methodology and to highlight the differences between crisp and the fuzzy cases. This paper provides optimal decision support tools for managers in the form of mathematical model that improve operational, tactical, and strategic decision making in the fuzzy system. This paper aims to raise the awareness of managers with regard to realistic inventory problems.