A genetic algorithm to optimize a multi-product EOQ model with limited warehouse-space and capital limitation under VMI

Vendor-managed inventory (VMI) system is a mechanism where the supplier creates the purchase orders based on the demand information exchanged by the retailer/customer. In this paper, the performance of the traditional and VMI system is compared by using EOQ model. Mathematical modeling is applied and total inventory cost in the supply chain is used as the performance measure. The supply chain is considered in two levels, i.e., buyer and supplier, with the assumption that the supplier faces n buyers and more products as the contract party. Results of proposed model of VMI are clearly better than traditional model. In order to make the model more applicable to real-world production and inventory control problems, we expand this model by assuming a multi-product economic order quantity problem with limited warehouse-space and capital limitation. Under this condition, we formulate the problem as a non-linear integer programming model and propose a genetic algorithm to solve it. Moreover, design of experiments is employed to calibrate the parameters of the algorithm for different problem sizes. At the end, we present a numerical example to demonstrate the application of the proposed methodology.