A fuzzy random periodic review system with variable lead-time and negative exponential crashing cost

In the present model a fuzzy random periodic review system has been investigated with the annual demand assumed to be a discrete fuzzy random variable with associated imprecise probabilities. Keeping in mind the widespread application of the Just-In-Time manufacturing philosophy and lead-time management being one of its most effective methods of implementation, the lead-time has been assumed to be an added control parameter. Also as it may not be always possible to resolve the lead-time into all its components and estimate their individual crashing costs, the crashing cost has been introduced as a negative exponential function of the lead-time. A methodology has been developed in this regard such that the total inventory cost is minimized and the optimal period of review, the optimal target inventory level and the optimal lead-time are determined in the process. An algorithm has been provided to encapsulate the methodology and it has been illustrated by way of a numerical example.