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

Computational study for workforce scheduling and routing problems

We present a computational study on 112 instances of the Workforce Scheduling and Routing Problem (WSRP). This problem has applications in many service provider industries where employees visit customers to perform activities. Given their similarity, we adapt a mathematical programming model from the literature on vehicle routing problem with time windows (VRPTW) to conduct this computational study on the WSRP. We generate a set of WSRP instances from a well-known VRPTW data set. This work has three objectives. First, to investigate feasibility and optimality on a range of medium size WSRP instances with different distribution of visiting locations and including teaming and connected activities constraints. Second, to compare the generated WSRP instances to their counterpart VRPTW instances with respect to their difficulty. Third, to determine the computation time required by a mathematical programming solver to find feasible solutions for the generated WSRP instances. It is observed that although the solver can achieve feasible solutions for some instances, the current solver capabilities are still limited. Another observation is the WSRP instances present an increased degree of difficulty because of the additional constraints. The key contribution of this paper is to present some test instances and corresponding benchmark study for the WSRP

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

Computational study for workforce scheduling and routing problems

We present a computational study on 112 instances of the Workforce Scheduling and Routing Problem (WSRP). This problem has applications in many service provider industries where employees visit customers to perform activities. Given their similarity, we adapt a mathematical programming model from the literature on vehicle routing problem with time windows (VRPTW) to conduct this computational study on the WSRP. We generate a set of WSRP instances from a well-known VRPTW data set. This work has three objectives. First, to investigate feasibility and optimality on a range of medium size WSRP instances with different distribution of visiting locations and including teaming and connected activities constraints. Second, to compare the generated WSRP instances to their counterpart VRPTW instances with respect to their difficulty. Third, to determine the computation time required by a mathematical programming solver to find feasible solutions for the generated WSRP instances. It is observed that although the solver can achieve feasible solutions for some instances, the current solver capabilities are still limited. Another observation is the WSRP instances present an increased degree of difficulty because of the additional constraints. The key contribution of this paper is to present some test instances and corresponding benchmark study for the WSRP

Mixed integer programming with decomposition for workforce scheduling and routing with time-dependent activities constraints

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 time dependent 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

An investigation of heuristic decomposition to tackle workforce scheduling and routing with time-dependent activities constraints

This paper presents an investigation into the application of heuristic decomposition and mixed-integer programming to tackle workforce scheduling and routing problems (WSRP) that involve time dependent activities constraints. These constraints refer to time-wise dependencies between activities. The decomposition method investigated here 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. In order to deal with the time-dependent activities constraints, the problem decomposition puts all activities associated to the same location and their dependent activities in the same sub-problem. This is to guarantee the satisfaction of time-dependent activities constraints as each sub-problem is solved exactly with an exact solver. Once the assignments are made, the time windows of dependent activities are fixed even if those activities are subject to the repair phase. The paper presents an experimental study to assess the performance of the decomposition method when compared 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. Also, an analysis is conducted in order to understand how the performance of the different solution methods (the decomposition, the tailored heuristic and the MIP solver) is affected by the size of the problem instances and other features of the problem. The paper concludes by making some recommendations on the type of method that could be more suitable for different problem sizes

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

Workforce scheduling and routing problems: literature survey and computational study

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 and 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 at the locations where tasks need to be performed. The first part of this paper presents a survey which attempts to identify the common features of WSRP scenarios and the solution methods applied when tackling these problems. The second part of the paper presents a study on the computational difficulty of solving these type of problems. For this, five data sets are gathered from the literature and some adaptations are made in order to incorporate the key features that our survey identifies as commonly arising in WSRP scenarios. The computational study provides an insight into the structure of the adapted test instances, an insight into the effect that problem features have when solving the instances using mathematical programming, and some benchmark computation times using the Gurobi solver running on a standard personal computer

Particle swarm optimization for the Steiner tree in graph and delay-constrained multicast routing problems

This paper presents the first investigation on applying a particle swarm optimization (PSO) algorithm to both the Steiner tree problem and the delay constrained multicast routing problem. Steiner tree problems, being the underlining models of many applications, have received significant research attention within the meta-heuristics community. The literature on the application of meta-heuristics to multicast routing problems is less extensive but includes several promising approaches. Many interesting research issues still remain to be investigated, for example, the inclusion of different constraints, such as delay bounds, when finding multicast trees with minimum cost. In this paper, we develop a novel PSO algorithm based on the jumping PSO (JPSO) algorithm recently developed by Moreno-Perez et al. (Proc. of the 7th Metaheuristics International Conference, 2007), and also propose two novel local search heuristics within our JPSO framework. A path replacement operator has been used in particle moves to improve the positions of the particle with regard to the structure of the tree. We test the performance of our JPSO algorithm, and the effect of the integrated local search heuristics by an extensive set of experiments on multicast routing benchmark problems and Steiner tree problems from the OR library. The experimental results show the superior performance of the proposed JPSO algorithm over a number of other state-of-the-art approaches

An investigation of heuristic decomposition to tackle workforce scheduling and routing with time-dependent activities constraints

This paper presents an investigation into the application of heuristic decomposition and mixed-integer programming to tackle workforce scheduling and routing problems (WSRP) that involve time dependent activities constraints. These constraints refer to time-wise dependencies between activities. The decomposition method investigated here 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. In order to deal with the time-dependent activities constraints, the problem decomposition puts all activities associated to the same location and their dependent activities in the same sub-problem. This is to guarantee the satisfaction of time-dependent activities constraints as each sub-problem is solved exactly with an exact solver. Once the assignments are made, the time windows of dependent activities are fixed even if those activities are subject to the repair phase. The paper presents an experimental study to assess the performance of the decomposition method when compared 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. Also, an analysis is conducted in order to understand how the performance of the different solution methods (the decomposition, the tailored heuristic and the MIP solver) is affected by the size of the problem instances and other features of the problem. The paper concludes by making some recommendations on the type of method that could be more suitable for different problem sizes