On optimization of a Multi-Retailer Multi-Product VMI Model with Variable Replenishment Cycle

This paper discusses how a vendor manages multiple products within its multiple non-identical retailers operating under a vendor managed inventory (VMI) contract that allows unequal shipment frequencies to the retailers. The vendor replenishment cycle for each product is taken to be an integer multiple of the retailer replenishment cycle where vendor is penalized for exceeding the upper stock limits at the retailer premises for each product. A mixed-integer nonlinear model is developed to address the replenishment problem among multiple retailers for multiple products that minimizes the joint relevant inventory costs under unequal shipment frequency. A particle swarm optimization (PSO) and simulated annealing (SA) algorithm along with a numerical illustration is also provided to demonstrate the proposed model. Results show that PSO algorithm finds optimal or near optimal solutions for the total system cost, and it proposes substantial savings compared to the solution obtained in SA and traditional optimizer software.