Supply chain model with stochastic lead time under imprecise partially backlogging and fuzzy ramp-type demand for expiring items

The objective of this research is to develop a multi-echelon supply chain model with fuzzy ramp-type demand rate and imprecise partial backlogging rate of unsatisfied demand, considering the effect of inflation and time value of money. Supplier's lead time is a stochastic function of his managing cost. The extra costs incurred on retailer, due to the uncertain lead time in terms of shortages costs or lost sales costs are owed by the supplier. The items have a certain expiration date, due to the fact there is decline in the demand rate with time, but after a period of time it becomes steady. A numerical example is cited to illustrate the results and its significant features. Finally, to study the effect of changes of demand parameters, deterioration, inflation and partially backlogging rate on supplier's and the retailer's profit, a sensitivity analysis is presented numerically.