The Large-Scale Periodic Home Health Care Server Assignment Problem: A Region-Partition-Based Algorithm

Abstract

This article addresses the periodic home health care (HHC) server assignment problem in HHC companies. This problem is a variant of the periodic vehicle routing problem with specific constraints for customers and servers (e.g., customers’ requirements for multiple medical skills and continuous care offered by a given number of servers and servers’ requirements for workload balance). Solving large-scale problems from practical applications of HHC companies within an acceptable computation time is challenging. Consequently, we develop an efficient region-partition-based algorithm to solve these large-scale problems. First, the algorithms assign customers and servers to many independent regions. Second, four different tabu search (TS) algorithms are designed to solve the optimization problem of each region. Finally, the algorithms iteratively adjust the assignment of customers and servers to regions and solve the problems of each region. The performances of different TS algorithms are discussed. The effectiveness of the proposed region-partition-based algorithm for large-scale problems is validated. Note to Practitioners —This article is motivated by our collaboration with an HHC company in Shanghai, China. The company delivers medical, paramedical, and social services to customers in their homes to help them improve their clinical and psychological conditions without hospital stays. In practice, customers require long-term and periodic service (e.g., weekly), which may last many months or even years. HHC companies have to assign a combination of service days and at least one server to each customer. Due to specific constraints in practical operations and the large scale of the practical problems (e.g., 1000–2000 customers) of the HHC in this article, the server assignment problem is challenging to the HHC company. The algorithm presented in this article takes into account the special constraints of the HHC and is able to solve the large-scale problem in a reasonable time span. The algorithm can be used to help decision-makers assign combinations of service days and servers to customers with the objective of balancing the workloads among servers.