Analytic network process and multi-period goal programming integration in purchasing decisions

This paper presents a multi-period inventory lot sizing scenario, where there is single product and multiple suppliers. By considering multi-period planning horizon, an integrated approach of Archimedean Goal Programming (AGP) and Analytic Network Process (ANP) is suggested. This integrated approach proposes a two-stage mathematical model to evaluate the suppliers and to determine their periodic shipment allocations given a number of tangible and intangible criteria. In the evaluation stage, the suppliers are evaluated according to 14 criteria that are involved in four control hierarchies; benefit, opportunity, cost and risk (BOCR). In the shipment stage, a multi objective mixed integer linear programming (MOMILP) model is described to solve the order allocation problem. This MOMILP model is suggested to achieve target values of periodic goals: budget, aggregate quality, total value of purchasing (TVP) and demand over the planning horizon, without exceeding vendor production capacities. This multi-period model is solved by using AGP. Finally some computational experiments are conducted to test the performance of the proposed method.