A mixed integer linear programming formulation for a multi-stage, multi-Product, multi-vehicle aggregate production-distribution planning problem

In today’s competitive market place, companies seek an efficient structure of supply chain so as to provide customers with highest value and achieve competitive advantage. This requires a broader perspective than just the borders of an individual company during a supply chain. This paper investigates an aggregate production planning problem integrated with distribution issues in a supply chain so as to simultaneously optimize characteristics of these supply chain drivers. The main contribution of this paper is to consider the aggregate production-distribution planning (APDP) problem jointly with multiple stage, multiple product, and multiple vehicle. Moreover, we considered both routing and direct shipment as transportation system which is not considered in APDP literature so far. A mixed-integer linear programming formulation is suggested for two distinct Scenarios: (i) when we have direct shipment in which all shipments are transported directly from manufacturer to customers, and (ii) when we have routing option in which the vehicles can move through routes to deliver products to more than one customer at a trip. A numerical analysis is performed to compare performance of problem in two above Scenarios. Moreover, to assess applicability of problem, some computational experiments are implemented on small, medium and large sized problems.