Supply Chain Model for Expiring Items Following Ramp-Type Demand With Stochastic Lead Time Under Crisp and Fuzzy Environment

Supply chain models with deteriorating items, season pattern demand, expiration and uncertain lead time, though common in practice; had received little attention from researchers. In this article, the authors proposed a collaborative system with ramp type seasonal pattern demand rate for expiring items with supplier's random lead time under crisp and fuzzy environment considering the effect of inflation and time value of money. For the seasonal kind of items, demand rate follows the combination of increasing-steady-decreasing demand patterns. A supplier's lead time is a stochastic function of his managing cost; thus, the extra costs incurred on the retailer due to the uncertainty in lead time in terms of shortages costs and lost sales costs are owed by the supplier. Numerical examples are cited to illustrate the results and its significant features. Finally, to study the effect of change of parameters sensitivity analysis is presented and necessary observations are made.