Risk-cost optimization for procurement planning in multi-tier supply chain by Pareto Local Search with relaxed acceptance criterion

We address a 2-objective optimization problem to minimize a retailer's procurement cost and risk that is evaluated as recovery time of the retailer's business after the procurement is suspended by a catastrophic event. In order to reduce the recovery time, the retailer needs to decentralize ordering to multiple suppliers and have contingency stock, which costs the retailer. In multi-tier supply chains, not only the retailer's procurement plan but also their suppliers' procurement plans affect the retailers' risk and cost. Due to the huge combinations of their plans, it is difficult to find Pareto optimal solutions of the 2-objective optimization problem within a short space of time. We apply Pareto Local Search (PLS) based on heuristics to generate neighbors of a solution by changing suppliers' plans in the closer tier to the retailer. The original PLS accepts the solutions that are nondominated neighbor solutions for the next search, but the acceptance criterion is too strict to find all Pareto optimal solutions. We relax the acceptance criterion in order to include dominated solutions whose Pareto rank is equal to or less than a threshold. The threshold is updated based on changes of Pareto rank during local searches.