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

• A chance-constraint joint single vendor-single buyer supply chain problem with stochastic demand and fuzzy lead-time is investigated.
• The goal is to determine the re-order point and the order quantity of the products such that the total cost is minimized.
• Hybrid procedures of artificial bee colony and with fuzzy simulation and approximate simulation methods are developed.
• We demonstrate the applicability of the proposed methodologies in a real world supply chain problem.

This study solves a chance–constraint supply chain problem with stochastic demand which follows a uniform distribution. Fuzzy delay times (moving, waiting and setup time) are assumed to be lot size dependent and shortage is partially backordered. The buyer is responsible for the costs incurred in ordering, holding, shortage and transportation, while the vendor is responsible for setup and holding costs. The service rate of each product has a chance constraint and the buyer has a budget constraint. Our objective is to determine the re-order point and the order quantity of the products such that the total cost is minimized. Since the problem is uncertain integer–nonlinear, two hybrid procedures of Artificial Bee Colony (ABC) and Particle Swarm Optimization (PSO) with fuzzy simulation and approximate simulation methods are developed to solve the problems. Three numerical case examples are given to demonstrate the applicability of the proposed methodologies in a real world supply chain problem.