Mixed Integer Programming with Decomposition to Solve a Workforce Scheduling and Routing Problem

Abstract

Abstract:We propose an approach based on mixed integer programming (MIP) with decomposition to solve a workforce scheduling and routing problem, in which a set of workers should be assigned to tasks that are distributed across different geographical locations. This problem arises from a number of home care planning scenarios in the UK, faced by our industrial partner. We present a mixed integer programming model that incorporates important real-world features of the problem such as defined geographical regions and flexibility in the workers' availability. Given the size of the real-world instances, we propose to decompose the problem based on geographical areas. We show that the quality of the overall solution is affected by the ordering in which the sub-problems are tackled. Hence, we investigate different ordering strategies to solve the sub-problems and show that such decomposition approach is a very promising technique to produce high-quality solutions in practical computational times using an exact optimization method.

A Heuristic for a Mixed Integer Program using the Characteristic Equation Approach

“…In many cases the resulting MIP can either be too weak or too large to be solved effectively by the state-of-the-art solvers (Vielma, 2015). Mathematical programming has been used in the literature to tackle some problems as a LP model (Yildiz and Vielma, 2013); some as a PIP model (Laesanklang et al, 2015); and some as a MIP model (Borsani et al, 2006;Bredstrom and Rönnqvist, 2007;Dohn et al, 2009;Rasmussen et al, 2012). Mixed integer conic programming (MICP) is a generalization of mixed integer linear programming.…”

“…This technique has been applied in various problem domains. For example, Benders' (1962) decomposition was used to produce solutions for large instances of the aircraft routing and crew scheduling problems (Laesanklang et al, 2015). Decomposition techniques have also been applied within heuristic approaches using some form of clustering.…”

Mixed Integer Programming with Decomposition for Workforce Scheduling and Routing with Time-dependent Activities Constraints

“…A key difference with our previous work in (Laesanklang et al, 2015) is that the WSRP scenarios tackled here include a special set of constraints called timedependent activities constraints that establish some inter-dependence between activities as denoted by (11). These constraints reduce the flexibility in the assignment of visits to employees because for example, a pair of visits might need to be executed in a given order.…”

“…This section describes the Repeated Decomposition with Conflict Repair (RDCR) approach used to tackle the WSRP with time-dependent activities constraints. In a previous paper (Laesanklang et al, 2015) we presented a method called Geographical Decomposition with Conflict Avoidance (GDCA). In that work, conflicting paths and conflicting assignments as described above were not allowed to happen.…”

“…A mixed integer programming decomposition method, called Geographical Decomposition with Conflict Avoidance (GDCA), was proposed in (Laesanklang et al, 2015) to tackle a home care scheduling problem which is a type of WSRP. Those home care problem instances tackled with GDCA had a fixed time for the visits (instead of a time window) and no time-dependent activities constraints.…”