Decomposition techniques with mixed integer programming and heuristics for home healthcare planning

We tackle home healthcare planning scenarios in the UK using decomposition methods that incorporate mixed integer programming solvers and heuristics. Home healthcare planning is a difficult problem that integrates aspects from scheduling and routing. Solving real-world size instances of these problems still presents a significant challenge to modern exact optimization solvers. Nevertheless, we propose decomposition techniques to harness the power of such solvers while still offering a practical approach to produce high-quality solutions to real-world problem instances. We first decompose the problem into several smaller sub-problems. Next, mixed integer programming and/or heuristics are used to tackle the sub-problems. Finally, the sub-problem solutions are combined into a single valid solution for the whole problem. The different decomposition methods differ in the way in which subproblems are generated and the way in which conflicting assignments are tackled (i.e. avoided or repaired). We present the results obtained by the proposed decomposition methods and compare them to solutions obtained with other methods. In addition, we conduct a study that reveals how the different steps in the proposed method contribute to those results. The main contribution of this paper is a better understanding of effective ways to combine mixed integer programming within effective decomposition methods to solve real-world instances of home healthcare planning problems in practical computation time

A permutation flowshop model with time-lags and waiting time preferences of the patients

The permutation flowshop is a widely applied scheduling model. In many real-world applications of this model, a minimum and maximum time-lag must be considered between consecutive operations. We can apply this model to healthcare systems in which the minimum time-lag could be the transfer times, while the maximum time-lag could refer to the number of hours patients must wait. We have modeled a MILP and a constraint programming model and solved them using CPLEX to find exact solutions. Solution times for both methods are presented. We proposed two metaheuristic algorithms based on genetic algorithm and solved and compared them with each other. A sensitivity of analysis of how a change in minimum and maximum time-lags can impact waiting time and Cmax of the patients is performed. Results suggest that constraint programming is a more efficient method to find exact solutions and changes in the values of minimum and maximum time-lags can impact waiting times of the patients and Cmax significantly

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes

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

Energy and Route Optimization of Moving Devices

This thesis highlights our efforts in energy and route optimization of moving devices. We have focused on three categories of such devices; industrial robots in a multi-robot environment, generic vehicles in a vehicle routing problem (VRP) context, automatedguided vehicles (AGVs) in a large-scale flexible manufacturing system (FMS). In the first category, the aim is to develop a non-intrusive energy optimization technique, based on a given set of paths and sequences of operations, such that the original cycle time is not exceeded. We develop an optimization procedure based on a mathematical programming model that aims to minimize the energy consumption and peak power. Our technique has several advantages. It is non-intrusive, i.e. it requires limited changes in the robot program and can be implemented easily. Moreover,it is model-free, in the sense that no particular, and perhaps secret, parameter or dynamic model is required. Furthermore, the optimization can be done offline, within seconds using a generic solver. Through careful experiments, we have shown that it is possible to reduce energy and peak-power up to about 30% and 50% respectively. The second category of moving devices comprises of generic vehicles in a VRP context. We have developed a hybrid optimization approach that integrates a distributed algorithm based on a gossip protocol with a column generation (CG) algorithm, which manages to solve the tested problems faster than the CG algorithm alone. The algorithm is developed for a VRP variation including time windows (VRPTW), which is meant to model the task of scheduling and routing of caregivers in the context of home healthcare routing and scheduling problems (HHRSPs). Moreover,the developed algorithm can easily be parallelized to further increase its efficiency. The last category deals with AGVs. The choice of AGVs was not arbitrary; by design, we decided to transfer our knowledge of energy optimization and routing algorithms to a class of moving devices in which both techniques are of interest. Initially, we improve an existing method of conflict-free AGV scheduling and routing, such that the new algorithm can manage larger problems. A heuristic version of the algorithm manages to solve the problem instances in a reasonable amount of time. Later, we develop strategies to reduce the energy consumption. The study is carried out using an AGV system installed at Volvo Cars. The results are promising; (1)the algorithm reduces performance measures such as makespan up to 50%, while reducing the total travelled distance of the vehicles about 14%, leading to an energy saving of roughly 14%, compared to the results obtained from the original traffic controller. (2) It is possible to reduce the cruise velocities such that more energy is saved, up to 20%, while the new makespan remains better than the original one

Mind the gap: a review of optimisation in mental healthcare service delivery

Well-planned care arrangements with effective distribution of available resources have the potential to address inefficiencies in mental health services. We begin by exploring the complexities associated with mental health and describe how these influence service delivery. We then conduct a scoping literature review of studies employing optimisation techniques that address service delivery issues in mental healthcare. Studies are classified based on criteria such as the type of planning decision addressed, the purpose of the study and care setting. We analyse the modelling methodologies used, objectives, constraints and model solutions. We find that the application of optimisation to mental healthcare is in its early stages compared to the rest of healthcare. Commonalities between mental healthcare service provision and other services are discussed, and the future research agenda is outlined. We find that the existing application of optimisation in specific healthcare settings can be transferred to mental healthcare. Also highlighted are opportunities for addressing specific issues faced by mental healthcare services

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

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order

Using goal programming on estimated Pareto fronts to solve multiobjective problems

Modern multiobjective algorithms can be computationally inefficient in producing good approximation sets for highly constrained many-objective problems. Such problems are common in real-world applications where decision-makers need to assess multiple conflicting objectives. Also, different instances of real-world problems often share similar fitness landscapes because key parts of the data are the same across these instances. We we propose a novel methodology that consists of solving one instance of a given problem scenario using computationally expensive multiobjective algorithms to obtain a good approximation set and then using Goal Programming with efficient single-objective algorithms to solve other instances of the same problem scenario. We propose three goal-based objective functions and show that on a real-world home healthcare planning problem the methodology can produce improved results in a shorter computation time