A computational study and heuristic algorithms for the home healthcare scheduling and routing problem - Pinheiro, Rodrigo Lankaites (2017)
The workforce scheduling and routing problem (WSRP) arises in many scenarios in which skilled workers need to deliver services at different locations. Examples of these scenarios include nurses visiting patients at home, technicians carrying out repairs at customers’ locations, security guards performing rounds at different premises, etc. Hence, finding a solution to this type of problem involves tackling both the scheduling of tasks to be carried out and the routing of workers to visit the locations of tasks. The focus of this thesis is a challenging real-world problem in the planning and scheduling of healthcare delivery, denoted by home healthcare (HHC) problem. The first intended contribution of this PhD research is to provide to the research community six benchmark datasets for a real-world workforce scheduling and routing problem arising in healthcare delivery as well as benchmark results obtained with heuristic methods. The next contribution is an algorithm to obtain lower bound values for the HHC problem that is capable of providing results when mathematical techniques are not applicable. The lower bounds are obtained by splitting and relaxing the problem into a scheduling and a routing subproblems, and calculating individual lower bounds for each subproblem. In order to further understand the HHC problem, its multiobjective characteristics were assessed. Understanding the relationships between objectives in a multiobjective optimisation problem is important for developing tailored and efficient solving techniques. In particular, when tackling combinatorial optimisation problems with many objectives that arise in real-world scenarios, better support for the decision maker can be achieved through better understanding of the often complex fitness landscape. This thesis makes a contribution in this direction by presenting a technique that allows a visualisation and analysis of the local and global relationships between objectives in optimisation problems with many objectives. The proposed technique uses four steps: first the global pairwise relationships are analysed using the Kendall correlation method; then the ranges of the values found on the given Pareto front are estimated and assessed; next these ranges are used to plot a map using Gray code, similar to Karnaugh maps, that has the ability to highlight the trade-offs between multiple objectives; and finally local relationships are identified using scatter-plots. Results show that each dataset has different characteristics, and the relationships between objectives and their importance vary across datasets; also, instances of the same dataset share similar fitness landscapes. A Variable Neighbourhood Search (VNS) metaheuristic algorithm is proposed to tackle the HHC problem, incorporating three heuristics tailored to the problem-domain. The first heuristic restricts the search space using a priority list of candidate workers; the second heuristic seeks to reduce the violation of worker availabilities soft constraints; the third heuristic estimate the objective costs of all possible individual assignments and uses the estimated costs instead of the objective function, hence substantially increasing the speed of the search. Two greedy constructive heuristics are presented to give the VNS a good starting point. It is shown that the proposed VNS obtains substantial improvements in the quality of solutions regardless of the datasets unique features. The proposed VNS provides the current benchmark results for the set of real-world HHC scenarios considered. The last contribution of this thesis is a multiobjective solving methodology that exploits the fact that instances of the same dataset share similar fitness landscapes. The methodology consists of obtaining an approximation set of a single instance and using that approximation set, goal programming and the proposed VNS to reach target solutions in the remaining instances. Results show that the methodology is accurate enough to reach the target solution and is able to provide quick results when multiobjective algorithms take long computational times.