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

Extended decomposition for mixed integer programming 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. 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. We decompose the problem based on geographical areas. 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. We also use a procedure to have additional workforce from neighbouring regions and this helps to improve results in some instances. We also developed a genetic algorithm to compare the results produced by the decomposition methods. Our experimental results show that although the decomposition method does not always outperform the genetic algorithm, it finds high quality solutions in practical computational times using an exact optimization method

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

Stochastic multi-period multi-product multi-objective Aggregate Production Planning model in multi-echelon supply chain

In this paper a multi-period multi-product multi-objective aggregate production planning (APP) model is proposed for an uncertain multi-echelon supply chain considering financial risk, customer satisfaction, and human resource training. Three conflictive objective functions and several sets of real constraints are considered concurrently in the proposed APP model. Some parameters of the proposed model are assumed to be uncertain and handled through a two-stage stochastic programming (TSSP) approach. The proposed TSSP is solved using three multi-objective solution procedures, i.e., the goal attainment technique, the modified ε-constraint method, and STEM method. The whole procedure is applied in an automotive resin and oil supply chain as a real case study wherein the efficacy and applicability of the proposed approaches are illustrated in comparison with existing experimental production planning method

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

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

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