An infeasible space exploring matheuristic for the Production Routing Problem

This paper proposes a novel matheuristic algorithm for solving the Production Routing Problem (PRP). The PRP is a hard-to-solve combinatorial optimization problem with numerous practical applications in the field of freight transportation, logistics and supply chain management. A manufacturer is responsible for determining production decisions, as well as the timing and the quantity of replenishment services offered to a set of geographically dispersed customers over a multi-period time horizon. The problem calls for jointly optimizing the production, inventory, distribution and routing decisions. The paper provides a novel two-commodity flow formulation and proposes a two-phase infeasible space matheuristic algorithm for solving the examined problem. The first phase deals with a relaxation of the problem to construct production-distribution plans. In the second phase, these are completed with routing information and optimized via a local search framework which oscillates between the feasible and the infeasible solution space. The framework is equipped with mixed integer programming components for restoring infeasibility and for diversifying the conducted search. Computational experiments demonstrate that the infeasibility space exploration significantly contributes to the quality of the final solutions. The results obtained by the proposed matheuristic out-match the results of state-of-the-art approaches. More specifically, 594 and 55 new best solutions out of 1440 and 90 instances of two well-established benchmark data sets of small-medium and large instances are reported, respectively.