A dual-objective vendor-managed inventory model for a single-vendor multi-retailersupply chain with fuzzy random demand.

This paper develops a dual-objective vendor-managed inventory model with a single supplier and multiple retailers in a supply chain in which the retailer's demand is assumed as a fuzzy random variable and the supplier incurs a constant deterioration rate. The model is optimized to simultaneously minimize the total cost and maximize the service level under capital budget and storage constraints, in which ordering cost, holding cost, deterioration cost and transportation cost are considered in the total cost of the vendor. To solve the proposed model in an imprecise environment, the expected value and pessimistic value are used to change the fuzzy random model into a determined model. Three fuzzy random simulations are presented to obtain the optimal replenishment quantities of the expectation model and the pessimistic model. A numerical study with a single vendor and three retailers in the supply chain is provided to demonstrate the efficiency of the models and algorithms, which gives the optimal results for the expectation model and pessimistic model. Furthermore, recommendations for the replenishment policy for different types of decision makers in the pessimistic model are provided based on the analysis of inventory costs with different parameter values.