Optimal Planning of Closed Loop Supply Chains: A Discrete versus a Continuous-time formulation

In this paper the planning of closed loop supply chains is studied where both. forward and return flows are integrated considering their simultaneous coordination. The product supply and returns are then considered explicitly at the planning level of the supply chain optimization. Two different approaches are developed and implemented to model the supply chain optimal planning problem: a discrete and a continuous-time formulation. The former considers an uniform discretization of the planning horizon while the continuous-time counterpart considers the time space domain modeled through the definition of a set of time instances called slots of unknown duration. Each slot dimension is optimized simultaneously with the planning events. Both approaches account explicitly for the integration of topological, operational and market supply-demand constraints and requirements (Amaro and Barbosa-Póvoa, 2006). The proposed formulations results both into Mixed Integer Linear Programming (MILP’s) models that are solved using a standard Branch and Bound (B&B) procedure. A detailed plan is obtained, at each formulation approach, that allows the improvement of the supply chain operability by exploiting general resource capacities (e.g. transforming, storage and transportation) and resource sharing policies based on equipment/tasks suitability’s, economical performances and operational restrictions. 2 A.C.S. Amaro et al. The applicability of the proposed formulations is illustrated by its implementation on the solution of an industry-oriented case study involving an international pharmaceutical supply chain.