A goal programming model for joint decision making of inventory lot-size,supplier selection and carrier selection

In this paper, we address a problem in which a storage space constrained buyer procures a single product in multiple periods from multiple suppliers. The production capacity constrained suppliers offer all-unit quantity discounts. The late deliveries and rejections are also incorporated in sourcing. In addition, we consider transportation cost explicitly in decision making which may vary because of freight quantity and distance of shipment between the buyer and a supplier. We propose a multi-objective integer linear programming model for joint decision making of inventory lot-sizing, supplier selection and carrier selection problem. In the multi-objective formulation, net rejected items, net costs and net late delivered items are considered as three objectives that have to be minimized simultaneously over the decision horizon. The intent of the model is to determine the timings, lot-size to be procured, and supplier and carrier to be chosen in each replenishment period. We solve the multi-objective optimization problem using three variants of goal programming (GP) approaches: preemptive GP, non-preemptive GP and weighted max–min fuzzy GP. The solution of these models is compared at different service-level requirements using value path approach.