Supply chains planning with reverse flows: Optimal alternative time formulations

In this paper the optimal planning of supply chains is studied. Two alternative formulations are developed to model the supply chain optimal planning: a discrete and a continuous-time formulation. The former considers the uniform split of the planning horizon into equal time intervals while the continuous-time counterpart involves the definition of a set of time 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. The supply of final products ( forward flows ) and the return of nonconform products ( reverse flows ) are simultaneously coordinated at the planning level of the supply chain optimization. The proposed formulations result into mixed integer linear programming (MILP’s) models. A detailed plan is obtained for each formulation approach, which improves the supply chain operability by exploiting general resource capacities (e.g., transforming, storage, and transportation) and resource sharing policies based on the suitability of equipment/tasks, economical performances, and operational conditions. The applicability of the proposed formulations is illustrated through the solution of an industry-oriented case study.