a multi-supplier inventory model with permissible delay in payment and ‎discount

‎this paper proposes a multi-supplier multi-product inventory model in which the suppliers have unlimited production capacity, allow delayed payment, and offer either an all-unit or incremental discount. the retailer can delay payment until after they have sold all the units of the purchased product. the retailer’s warehouse is limited, but the surplus can be stored in a rented warehouse at a higher holding cost. the demand over a finite planning horizon is known. this model aims to choose the best set of suppliers and also seeks to determine the economic order quantity allocated to each supplier. the model will be formulated as a mixed integer and nonlinear programming model which is np-hard and will be solved by using genetic algorithm (ga), simulated annealing (sa) algorithm, and vibration damping optimization (vdo) algorithm. finally, the performance of the algorithms will be ‎compared.‎