Heuristic decomposition and mathematical programming for workforce scheduling and routing problems

This thesis presents a PhD research project using a mathematical programming approach to solve a home healthcare problem (HHC) as well as general workforce scheduling and routing problems (WSRPs). In general, the workforce scheduling and routing problem consists of producing a schedule for mobile workers to make visits at different locations in order to perform some tasks. In some cases, visits may have time-wise dependencies in which a visit must be made within a time period depending on the other visit. A home healthcare problem is a variant of workforce scheduling and routing problems, which consists of producing a daily schedule for nurses or care workers to visit patients at their home. The scheduler must select qualified workers to make visits and route them throughout the time horizon. We implement a mixed integer programming model to solve the HHC. The model is an adaptation of the WSRP from the literature. However, the MIP solver cannot solve a large-scale real-world problem defined in this model form because the problem requires large amounts of memory and computational time. To tackle the problem, we propose heuristic decomposition approaches which split a main problem into sub-problems heuristically and each sub-problem is solved to optimality by the MIP solver. The first decomposition approach is a geographical decomposition with conflict avoidance (GDCA). The algorithm avoids conflicting assignments by solving sub-problems in a sequence in which worker’s availabilities are updated after a sub-problem is solved. The approach