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In the capacitated production planning problem, quantities of products need to be determined at consecutive periods within a given time horizon when product demands, costs, and production capacities vary through time. We focus on a general formulation of this problem where each product is produced in one step and setup cost is paid at each period of production. Additionally, products can be anticipated or backordered in respect to the demand period. We propose a computationally efficient decentralized approach based on the spillover effect relating to the accumulation of production costs of each product demand through time. The performance of the spillover algorithm is compared against the state-of-the-art mixed integer programming branch-and-bound solver CPLEX 12.8 considering optimality gap and computational time.

A Decentralized Multi-Agent Coordination Method for Dynamic and Constrained Production Planning