Joint single vendor-single buyer supply chain problem with stochastic demand and fuzzy lead-time

In this paper, a chance-constraint joint single vendor, single buyer supply chain problem with stochastic demand and fuzzy lead-time is investigated. The lead-time is lot size dependent; and delay times such as moving, waiting and setting time are fuzzy. The shortage costs result from backorder and/or lost sale, and the uncertain demand follows a uniform distribution. The buyer’s cost function consists of fixed ordering, holding, shortage and transportation costs, while the vendor is responsible for the set up and holding costs. The service rate of each product has a chance constraint and the buyer has a limited budget. The goal is to determine the re-order point and the order quantity of the products such that the total cost is minimized. The mathematical formulation of the problem is shown to be uncertain integer-nonlinear; hence two hybrid procedures of artificial bee colony and particle swarm optimization, with fuzzy simulation and approximate simulation methods are developed to solve the problems. Finally, three numerical examples are given to demonstrate the applicability of the proposed methodologies in a real world supply chain problem.