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

Optimisation models and algorithms for workforce scheduling and routing

This thesis investigates the problem of scheduling and routing employees that are required to perform activities at clients’ locations. Clients request the activities to be performed during a time period. Employees are required to have the skills and qualifications necessary to perform their designated activities. The working time of employees must be respected. Activities could require more than one employee. Additionally, an activity might have time-dependent constraints with other activities. Time-dependent activities constraints include: synchronisation, when two activities need to start at the same time; overlap, if at any time two activities are being performed simultaneously; and with a time difference between the start of the two activities. Such time difference can be given as a minimum time difference, maximum time difference, or a combination of both (min-max). The applicability of such workforce scheduling and routing problem (WSRP) is found in many industries e.g. home health care provision, midwives visiting future mothers, technicians performing installations and repairs, estate agents showing residences for sale, security guards patrolling different locations, etc. Such diversity makes the WSRP an important combinatorial optimisation problem to study. Five data sets, obtained from the literature, were normalised and used to investigate the problem. A total of 375 instances were derived from these data sets. Two mathematical models, an integer and a mixed integer, are used. The integer model does not consider the case when the number of employees is not enough to perform all activities. The mixed integer model can leave activities unassigned. A mathematical solver is used to obtain feasible solutions for the instances. The solver provides optimal solutions for small instances, but it cannot provide feasible solutions for medium and large instances. This thesis presents the gradual development of a greedy heuristic that is designed to tackle medium and large instances. Five versions of the greedy heuristic are presented, each of them obtains better results than the previous one. All versions are compared to the results obtained by the mathematical solver when using the mixed integer model. The greedy heuristic exploits domain information to speed the search and discard infeasible solutions. It uses tailored functions to deal with each of the time-dependent activity constraints. These constraints make more difficult the solution process. Further improvements are obtained by using tabu search. It provides moves based on the tailored functions of the greedy heuristic. Overall, the greedy heuristic and the tabu search, maintain feasible solutions at all times. The main contributions of this thesis are: the definition of WSRP; the introduction of 375 instances based on five data sets; the adaptation of two mathematical models; the introduction of a greedy heuristic capable of obtaining better results than the solver; and, the implementation of a tabu search to further improve the results

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

Optimisation models and algorithms for workforce scheduling and routing

This thesis investigates the problem of scheduling and routing employees that are required to perform activities at clients’ locations. Clients request the activities to be performed during a time period. Employees are required to have the skills and qualifications necessary to perform their designated activities. The working time of employees must be respected. Activities could require more than one employee. Additionally, an activity might have time-dependent constraints with other activities. Time-dependent activities constraints include: synchronisation, when two activities need to start at the same time; overlap, if at any time two activities are being performed simultaneously; and with a time difference between the start of the two activities. Such time difference can be given as a minimum time difference, maximum time difference, or a combination of both (min-max). The applicability of such workforce scheduling and routing problem (WSRP) is found in many industries e.g. home health care provision, midwives visiting future mothers, technicians performing installations and repairs, estate agents showing residences for sale, security guards patrolling different locations, etc. Such diversity makes the WSRP an important combinatorial optimisation problem to study. Five data sets, obtained from the literature, were normalised and used to investigate the problem. A total of 375 instances were derived from these data sets. Two mathematical models, an integer and a mixed integer, are used. The integer model does not consider the case when the number of employees is not enough to perform all activities. The mixed integer model can leave activities unassigned. A mathematical solver is used to obtain feasible solutions for the instances. The solver provides optimal solutions for small instances, but it cannot provide feasible solutions for medium and large instances. This thesis presents the gradual development of a greedy heuristic that is designed to tackle medium and large instances. Five versions of the greedy heuristic are presented, each of them obtains better results than the previous one. All versions are compared to the results obtained by the mathematical solver when using the mixed integer model. The greedy heuristic exploits domain information to speed the search and discard infeasible solutions. It uses tailored functions to deal with each of the time-dependent activity constraints. These constraints make more difficult the solution process. Further improvements are obtained by using tabu search. It provides moves based on the tailored functions of the greedy heuristic. Overall, the greedy heuristic and the tabu search, maintain feasible solutions at all times. The main contributions of this thesis are: the definition of WSRP; the introduction of 375 instances based on five data sets; the adaptation of two mathematical models; the introduction of a greedy heuristic capable of obtaining better results than the solver; and, the implementation of a tabu search to further improve the results

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

Identificación de sitios potenciales para la disposición final de residuos sólidos en los municipios Atlacomulco, Ixtlahuaca y Jocotitlán, Estado de México

Contiene fotografías, mapas y cuadrosEn México la disposición final de residuos sólidos urbanos ha estado orientada al depósito incontrolado en lugares inadecuados, elegidos arbitrariamente, como barrancos, lagos y lagunas, zonas pantanosas, minas abandonadas, etc. Durante décadas, esto no supuso mayor problema, pues las características de composición de los residuos permitían su reintegración a la naturaleza sin daños aparentes. Al cambiar los hábitos de consumo, las cantidades de residuos generadas y la composición de éstos, esta actividad se convirtió en un problema serio. En este documento se analizan los sitios donde los residuos terminan, asi como lugares potenciales para la disposición de residuos sólidos en los municipios de Atlacomulco, Ixtlahuaca y Jocotitlán

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