Mixed integer programming with decomposition to solve a workforce scheduling and routing problem

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 survey of workforce scheduling and routing

In the context of workforce scheduling, there are many scenarios in which personnel must carry out tasks at different locations hence requiring some form of transportation. Examples of these type of scenarios include nurses visiting patients at home, technicians carrying out repairs at customers' locations, security guards performing rounds at different premises, etc. We refer to these scenarios as Workforce Scheduling and Routing Problems (WSRP) as they usually involve the scheduling of personnel combined with some form of routing in order to ensure that employees arrive on time to the locations where tasks need to be performed. This kind of problems have been tackled in the literature for a number of years. This paper presents a survey which attempts to identify the common attributes of WSRP scenarios and the solution methods applied when tackling these problems. Our longer term aim is to achieve an in-depth understanding of how to model and solve workforce scheduling and routing problems and this survey represents the first step in this quest

A survey of workforce scheduling and routing

In the context of workforce scheduling, there are many scenarios in which personnel must carry out tasks at different locations hence requiring some form of transportation. Examples of these type of scenarios include nurses visiting patients at home, technicians carrying out repairs at customers' locations, security guards performing rounds at different premises, etc. We refer to these scenarios as Workforce Scheduling and Routing Problems (WSRP) as they usually involve the scheduling of personnel combined with some form of routing in order to ensure that employees arrive on time to the locations where tasks need to be performed. This kind of problems have been tackled in the literature for a number of years. This paper presents a survey which attempts to identify the common attributes of WSRP scenarios and the solution methods applied when tackling these problems. Our longer term aim is to achieve an in-depth understanding of how to model and solve workforce scheduling and routing problems and this survey represents the first step in this quest

Resource constrained routing and scheduling: Review and research prospects

In the service industry, it is crucial to efficiently allocate scarce resources to perform tasks and meet particular service requirements. What considerably complicates matters is when these resources, for example skilled technicians, nurses, and home carers have to visit different customer locations. This paper provides a comprehensive survey on resource constrained routing and scheduling that unveils the problem characteristics with respect to resource qualifications, service requirements and problem objectives. It also identifies the most effective exact and heuristic algorithms for this class of problems. The paper closes with several research prospects

A greedy heuristic for workforce scheduling and routing with time-dependent activities constraints

We present a greedy heuristic (GHI) designed to tackle five time-dependent activities constraints (synchronisation, overlap, minimum difference, maximum difference and minimum-maximum difference) on workforce scheduling and routing problems. These types of constraints are important because they allow the modelling of situations in which activities relate to each other time-wise, e.g. synchronising two technicians to complete a job. These constraints often make the scheduling and routing of employees more difficult. GHI is tested on set of benchmark instances from different workforce scheduling and routing problems (WSRPs). We compare the results obtained by GHI against the results from a mathematical programming solver. The comparison seeks to determine which solution method achieves more best solutions across all instances. Two parameters of GHI are discussed, the sorting of employees and the sorting of visits. We conclude that using the solver is adequate for instances with less than 100 visits but for larger instances GHI obtains better results in less time

Selecting genetic operators to maximise preference satisfaction in a workforce scheduling and routing problem

The Workforce Scheduling and Routing Problem (WSRP) is a combinatorial optimisation problem that involves scheduling and routing of workforce. Tackling this type of problem often requires handling a considerable number of requirements, including customers and workers preferences while minimising both operational costs and travelling distance. This study seeks to determine effective combinations of genetic operators combined with heuristics that help to find good solutions for this constrained combinatorial optimisation problem. In particular, it aims to identify the best set of operators that help to maximise customers and workers preferences satisfaction. This paper advances the understanding of how to effectively employ different operators within two variants of genetic algorithms to tackle WSRPs. To tackle infeasibility, an initialisation heuristic is used to generate a conflict-free initial plan and a repair heuristic is used to ensure the satisfaction of constraints. Experiments are conducted using three sets of real-world Home Health Care (HHC) planning problem instances

Modelling the Home Health Care Nurse Scheduling Problem for Patients with Long-Term Conditions in the UK

In this work, using a Behavioural Operational Research (BOR) perspective, we develop a model for the Home Health Care Nurse Scheduling Problem (HHCNSP) with application to renal patients taking Peritoneal Dialysis (PD) at their own homes as treatment for their Chronic Kidney Disease (CKD) in the UK. The modelling framework presented in this paper can be extended to much wider spectra of scheduling problems concerning patients with different long-term conditions in future work

Homecare staff scheduling with three-step algorithm

This paper introduces a three-step algorithm, an efficient framework for solving a homecare staff scheduling problem (HSSP) service schedule, a multi-objective problem requiring a combination of the VRP and the staff scheduling problem. The proposed scheduling technique takes account of the design of optimal daily service routes and the dispatch of caregivers to visit patients under time and capacity constraints. The framework consists of three major stages: Step 1) Route scheduling creates effective routes for homecare caregivers to service patients at different task locations with the shortest path. Step 2) Resource selection seeks to match qualified staff to each route with the minimum cost and preferences under possible time, qualification requirement constraints, and modes of transportation. Step 3) Local improvement enhances the output solution generated by the resource selection by swapping tasks based on the cost function. Our empirical study reveals that the proposed scheduling technique can explore the improved service plan for an adapted case study with the minimum service cost and highest efficiency for arranging service tasks compared to the manual procedure

A Genetic Algorithm for a Workforce Scheduling and Routing Problem

The Workforce Scheduling and Routing Problem refers to the assignment of personnel to visits across various geographical locations. Solving this problem demands tackling scheduling and routing constraints while aiming to minimise the total operational cost. This paper presents a Genetic Algorithm (GA) tailored to tackle a set of real-world instances of this problem. The proposed GA uses a customised chromosome representation to maintain the feasibility of solutions. The performance of several genetic operators is investigated in relation to the tailored chromosome representation. This paper also presents a study of parameter settings for the proposed GA in relation to the various problem instances considered. Results show that the proposed GA, which incorporates tailored components, performs very well and is an effective baseline evolutionary algorithm for this difficult problem