Integrated Production, Location, and Distribution Problems: Models and Hybrid Heuristic

Abstract We propose three models and a hybrid heuristic that integrates objective relaxation, fix‐and‐optimize, relax‐and‐fix, and a relaxation and incumbent solution‐empowered constructive search to tackle the integrated production, location, and distribution (IPLD) problem, which involves making production, location, inventory, and distribution decisions. The objective relaxation technique is used to generate initial solution values, allowing a subset of binary variables to be fixed, thereby reducing the problem size and enabling the relax‐and‐fix algorithm to solve manageable subproblems. Additionally, the hybrid heuristic incorporates a constructive search method, leveraging both relaxation and incumbent solutions to progressively improve solution quality by generating high‐quality subproblems. The performance of this hybrid heuristic is evaluated against a benchmark algorithm and a general mixed‐integer linear programming (MILP) solver using benchmark test instances. The computational results show that our models can enforce tighter constraints and contain fewer integer and continuous decision variables and constraints, and the hybrid heuristic can lower the system costs compared to the benchmark algorithm. Further, we extend the models and heuristic for an IPLD problem with setup carryover, and their efficacies are evaluated by comparing them to the general MILP solver.