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

Abstract

We present a mixed integer programming decomposition approach to tackle workforce scheduling and routing problems (WSRP) that involve time-dependent activities constraints. The proposed method is called repeated decomposition with conflict repair (RDCR) and it consists of repeatedly applying a phase of problem decomposition and sub-problem solving, followed by a phase dedicated to conflict repair. Five types of timedependent activities constraints are considered: overlapping, synchronisation, minimum difference, maximum difference, and minimum-maximum difference. Experiments are conducted to compare the proposed method to a tailored greedy heuristic. Results show that the proposed RDCR is an effective approach to harness the power of mixed integer programming solvers to tackle the difficult and highly constrained WSRP in practical computational time.

A genetic algorithm for a workforce scheduling and routing problem

“…That study revealed that tackling instances with 50 activities or more required considerable computational time. Hence, a greedy heuristic tailored for such scenarios with connected activities was proposed in [9] and an MIP with decomposition method was proposed in [10]. That decomposition method splits each problem into subproblems and solves each sub-problem with an MIP solver.…”

A constraint-programming based decomposition method for the Generalised Workforce Scheduling and Routing Problem (GWSRP)

“…Nevertheless, the boundary between these two categories is not always clearly defined and, for example, some studies addressing HHC problems do not consider coordination constraints (Bertels and Fahle, 2006), (Maenhout and Vanhoucke, 2009), (Chahed et al, 2009) while other articles take coordination constraints into account (Blais et al, 2003), (Eveborn et al, 2006), (Bachouch et al, 2011). Similar remarks hold for the WSRP without coordination constraints in (Castillo et al, 2009), (Goel and Meisel, 2013), (Laesanklang et al, 2015), , (Laesanklang and Landa-Silva, 2017) and (Algethami et al, 2018) and with coordination constraints in (Laesanklang et al, 2016). Let us note that Vehicle Routing Problems (VRP) or VRP with Time-Windows (VRPTW) are commonly studied without coordination constraints, but recent studies include theses considerations, (Drexl, 2012) presents a survey of VRP with theses constraints and their applications.…”

“…A clustering based approach referred to as Geographical Decomposition with Conflict Avoidance (GDCA) that splits the problem into sub-problems which consider geographical considerations and workers not performing a trip is proposed by (Laesanklang et al, 2015). The approach is extended by (Laesanklang et al, 2016) to Repeated Decomposition with Conflict Repair (RDCR) where all workers are available during the resolution of each sub-problem and may create conflicts (a worker is assigned to several trips) which are iteratively addressed. GDCA and RDCR are sub-problem resolution order dependent.…”

Nurse-patient relationship for multi-period home health care routing and scheduling problem

“…For a single-period model, the problem focuses on finding an integrated routing and scheduling plan. The plan must respect constraints related to patient visiting time window, minimum worker requirements, worker skill qualifications, and patient visit time window [4,5]. The objective function for a single-period model includes operation costs, travel distances, worker active times, preferences, etc.…”