Home health care crew scheduling and routing problem with stochastic service times

The home health care crew scheduling and routing problem with stochastic service times is studied in this paper. A stochastic programming model with recourse is constructed to describe the problem. The approximate formulation for the expected penalty for late arrival at a customer is obtained and analyzed. According to its features, the problem is transformed into a classical set partitioning problem (SPP) and an elementary shortest path problem with resource constraints (ESPPRC). The SPP is solved by the column generation algorithm, and the ESPPRC is solved by an effective label algorithm. To get integer feasible solutions, the column generation procedure is embedded within a branch and bound framework, which is also called branch and price approach. Its effectiveness is validated by the numerical experiment.