An Algorithm Framework for Facility Service Districting Problem

  Objectives  Facility service districting problem(FSDP) refers to the design of facility service areas according to the facility locations and service capacities in a geographical region. The design criteria for service areas include the balance of service demand and supply, the highest service accessibility, and the spatial contiguity. The spatial contiguity is a necessity for satisfying some policies on public services, such as school districting and medical districting. However, solving the FSDP with contiguity constraints is challenging. We present a hybrid algorithm framework for solving the FSDP.

  Methods  The algorithm is proposed based on the general local search algorithm and furtherly enhanced by multi-start, ruin-recreate, set-partitioning and other optimization strategies. The basic modules such as initial solution generation method, local search operators, solution perturbation, model building and solving, and search strategies, are provided in the framework. Using these building blocks, some exact, metaheuristic and hybrid algorithms could be implemented effectively. Five algorithms are implemented for the FSDP: Exact method by solving a mixed integer linear programming model, simulated annealing (SA) algorithm, iterative local search (ILS) algorithm, SA with set-partitioning, and ILS with set-partitioning. In addition, four instances are designed to test the algorithms. The instance size, supply-demand ratio, and geographic environment are considered in the instance design.

  Results  There are several findings from computing experimentation: Optimal or near-optimal solutions of the instances could be obtained by CPLEX optimizer; high-quality solutions could be found by SA and ILS algorithms much more efficiently; the set-partitioning procedure is capable of improving the solution quality.

  Conclusions  Based on the proposed algorithm framework, it is easy and flexible to design local-search based matheuristics and hybrid algorithms for the FSDP. High quality solutions could be obtained by coupling the local search with ruin-recreate perturbation and set-partitioning.