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 timedependent activities constraints. These constraints refer to time-wise dependencies between activities. The decomposition method investigated here is called repeated decomposition with con ict repair (RDCR) and it consists of repeatedly applying a phase of problem decomposition and sub-problem solving, followed by a phase dedicated to con ict 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 diffcult 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 accected 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

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

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

Heuristic decomposition and mathematical programming for workforce scheduling and routing problems

This thesis presents a PhD research project using a mathematical programming approach to solve a home healthcare problem (HHC) as well as general workforce scheduling and routing problems (WSRPs). In general, the workforce scheduling and routing problem consists of producing a schedule for mobile workers to make visits at different locations in order to perform some tasks. In some cases, visits may have time-wise dependencies in which a visit must be made within a time period depending on the other visit. A home healthcare problem is a variant of workforce scheduling and routing problems, which consists in producing a daily schedule for nurses or care workers to visit patients at their home. The scheduler must select qualified workers to make visits and route them throughout the time horizon. We implement a mixed integer programming model to solve the HHC. The model is an adaptation of the WSRP from the literature. However, the MIP solver cannot solve a large-scale real-world problem defined in this model form because the problem requires large amounts of memory and computational time. To tackle the problem, we propose heuristic decomposition approaches which split a main problem into sub-problems heuristically and each sub-problem is solved to optimality by the MIP solver. The first decomposition approach is a geographical decomposition with conflict avoidance (GDCA). The algorithm avoids conflicting assignments by solving sub-problems in a sequence in which worker's availabilities are updated after a sub-problem is solved. The approach can find a feasible solution for every HHC problem instance tackled in this thesis. The second approach is a decomposition with conflict repair and we propose two variants: geographical decomposition with conflict repair (GDCR) and repeated decomposition and conflict repair (RDCR). The GDCR works in the same way as GDCA but instead of solving sub-problems in a given sequence, they are solved with no specific order and conflicting assignments are allowed. Later on, the conflicting assignments are resolved by a conflicting assignments repair process. The remaining unassigned visits are allocated by a heuristic assignment algorithm. The second variant, RDCR, tackles the unassigned visits by repeating the decomposition and conflict repair until no further improvement has been found. We also conduct an experiment to use different decomposition rules for RDCR. Based on computational experiments conducted in this thesis, the RDCR is found to be the best of the heuristic decomposition approaches. Therefore, the RDCR is extended to solve a WSRP with time-dependent activities constraints. The approach requires modification to accommodate the time-dependent activities constraints which means that two visits may have time-wise requirements such as synchronisation, time overlapped, etc. In addition, we propose a reformulated MIP model to solve the HHC problem. The new model is considered to be a compact model because it has significantly fewer constraints. The aim of the reformulation is to reduce the solver requirements for memory and computational time. The MIP solver can solve all the HHC instances formulated in a compact model. Most of solutions obtained with this approach are the best known solutions so far except for those the instances for which the optimal solution can be found using the full MIP model. Typically, this approach requires computational time below one hour per instance. This problem reformulation is so far the best approach to solve the HHC instances considered in this thesis. The heuristic decomposition and model reformulation proposed in this thesis can find solutions to the real-world home healthcare problem. The main achievement is the reduction of computational memory and computational time which are required by the optimisation solver. Our studies show the best way to control the use of solver memory is the heuristic decomposition approach, particularly the RDCR method. The RDCR method can find a solution for every instance used throughout this thesis and keep the memory usage within personal computer memory ranges. Also, the computational time required to solve an instance being less than 8 minutes, for which the solution gap to the optimal solution is on average 12%. In contrast, the strong point of the model reformulation approach over the heuristic decomposition is that the model reformulation provides higher quality solutions. The relative gaps of solutions between the solution for solving the reformulated model and the solution from solving the full model is less than 1% whilst its the computational time could be up to one hour and its computational memory could require up to 100 GB. Therefore, the heuristic decomposition approach is a method for finding a solution using restricted resources while the model reformulation is an approach for when a high solution quality is required. Hence, two mathematical programming based heuristic approaches are each more suitable in different circumstances in which both find high quality solutions within an acceptable time limit

Heuristic decomposition and mathematical programming for workforce scheduling and routing problems

This thesis presents a PhD research project using a mathematical programming approach to solve a home healthcare problem (HHC) as well as general workforce scheduling and routing problems (WSRPs). In general, the workforce scheduling and routing problem consists of producing a schedule for mobile workers to make visits at different locations in order to perform some tasks. In some cases, visits may have time-wise dependencies in which a visit must be made within a time period depending on the other visit. A home healthcare problem is a variant of workforce scheduling and routing problems, which consists in producing a daily schedule for nurses or care workers to visit patients at their home. The scheduler must select qualified workers to make visits and route them throughout the time horizon. We implement a mixed integer programming model to solve the HHC. The model is an adaptation of the WSRP from the literature. However, the MIP solver cannot solve a large-scale real-world problem defined in this model form because the problem requires large amounts of memory and computational time. To tackle the problem, we propose heuristic decomposition approaches which split a main problem into sub-problems heuristically and each sub-problem is solved to optimality by the MIP solver. The first decomposition approach is a geographical decomposition with conflict avoidance (GDCA). The algorithm avoids conflicting assignments by solving sub-problems in a sequence in which worker's availabilities are updated after a sub-problem is solved. The approach can find a feasible solution for every HHC problem instance tackled in this thesis. The second approach is a decomposition with conflict repair and we propose two variants: geographical decomposition with conflict repair (GDCR) and repeated decomposition and conflict repair (RDCR). The GDCR works in the same way as GDCA but instead of solving sub-problems in a given sequence, they are solved with no specific order and conflicting assignments are allowed. Later on, the conflicting assignments are resolved by a conflicting assignments repair process. The remaining unassigned visits are allocated by a heuristic assignment algorithm. The second variant, RDCR, tackles the unassigned visits by repeating the decomposition and conflict repair until no further improvement has been found. We also conduct an experiment to use different decomposition rules for RDCR. Based on computational experiments conducted in this thesis, the RDCR is found to be the best of the heuristic decomposition approaches. Therefore, the RDCR is extended to solve a WSRP with time-dependent activities constraints. The approach requires modification to accommodate the time-dependent activities constraints which means that two visits may have time-wise requirements such as synchronisation, time overlapped, etc. In addition, we propose a reformulated MIP model to solve the HHC problem. The new model is considered to be a compact model because it has significantly fewer constraints. The aim of the reformulation is to reduce the solver requirements for memory and computational time. The MIP solver can solve all the HHC instances formulated in a compact model. Most of solutions obtained with this approach are the best known solutions so far except for those the instances for which the optimal solution can be found using the full MIP model. Typically, this approach requires computational time below one hour per instance. This problem reformulation is so far the best approach to solve the HHC instances considered in this thesis. The heuristic decomposition and model reformulation proposed in this thesis can find solutions to the real-world home healthcare problem. The main achievement is the reduction of computational memory and computational time which are required by the optimisation solver. Our studies show the best way to control the use of solver memory is the heuristic decomposition approach, particularly the RDCR method. The RDCR method can find a solution for every instance used throughout this thesis and keep the memory usage within personal computer memory ranges. Also, the computational time required to solve an instance being less than 8 minutes, for which the solution gap to the optimal solution is on average 12%. In contrast, the strong point of the model reformulation approach over the heuristic decomposition is that the model reformulation provides higher quality solutions. The relative gaps of solutions between the solution for solving the reformulated model and the solution from solving the full model is less than 1% whilst its the computational time could be up to one hour and its computational memory could require up to 100 GB. Therefore, the heuristic decomposition approach is a method for finding a solution using restricted resources while the model reformulation is an approach for when a high solution quality is required. Hence, two mathematical programming based heuristic approaches are each more suitable in different circumstances in which both find high quality solutions within an acceptable time limit

Metaheuristics For Solving Real World Employee Rostering and Shift Scheduling Problems

Optimising resources and making considerate decisions are central concerns in any responsible organisation aiming to succeed in efficiently achieving their goals. Careful use of resources can have positive outcomes in the form of fiscal savings, improved service levels, better quality products, improved awareness of diminishing returns and general output efficiency, regardless of field. Operational research techniques are advanced analytical tools used to improve managerial decision-making. There have been a variety of case studies where operational research techniques have been successfully applied to save millions of pounds. Operational research techniques have been successfully applied to a multitude of fields, including agriculture, policing, defence, conservation, air traffic control, and many more. In particular, management of resources in the form of employees is a challenging problem --- but one with the potential for huge improvements in efficiency. The problem this thesis tackles can be divided into two sub-problems; the personalised shift scheduling & employee rostering problem, and the roster pattern problem. The personalised shift scheduling & employee rostering problem involves the direct scheduling of employees to hours and days of week. This allows the creation of schedules which are tailored to individuals and allows a fine level over control over the results, but with at the cost of a large and challenging search space. The roster pattern problem instead takes existing patterns employees currently work, and uses these as a pool of potential schedules to be used. This reduces the search space but minimises the number of changes to existing employee schedules, which is preferable for personnel satisfaction. Existing research has shown that a variety of algorithms suit different problems and hybrid methods are found to typically outperform standalone ones in real-world contexts. Several algorithmic approaches for solving variations of the employee scheduling problem are considered in this thesis. Initially a VNS approach was used with a Metropolis-Hastings acceptance criterion. The second approach utilises ER&SR controlled by the EMCAC, which has only been used in the field of exam timetabling, and has not before been used within the domain of employee scheduling and rostering. ER&SR was then hybridised with our initial approach, producing ER&SR with VNS. Finally, ER&SR was hybridised into a matheuristic with Integer Programming and compared to the hybrid's individual components. A contribution of this thesis is evidence that the algorithm ER&SR has merit outside of the original sub-field of exam scheduling, and can be applied to shift scheduling and employee rostering. Further, ER&SR was hybridised and schedules produced by the hybridisations were found to be of higher quality than the standalone algorithm. In the literature review it was found that hybrid algorithms have become more popular in real-world problems in recent years, and this body of work has explored and continued this trend. Problem formulations in this thesis provide insight into creating constraints which satisfy the need for minimising employee dissatisfaction, particularly in regards to abrupt change. The research presented in this thesis has positively impacted a multinational and multibillion dollar field service operations company. This has been achieved by implementing a variety of techniques, including metaheuristics and a matheuristic, to schedule shifts and roster employees over a period of several months. This thesis showcases the research outputs by this project, and highlights the real-world impact of this research

Service scheduling and vehicle routing problem to minimise the risk of missing appointments

This research studies a workforce scheduling and vehicle routing problem where technicians drive a vehicle to customer locations to perform service tasks. The service times and travel times are subject to stochastic events. There is an agreed time window for starting each service task. The risk of missing the time window for a task is defined as the probability that the technician assigned to the task arrives at the customer site later than the time window. The problem is to generate a schedule that minimises the maximum of risks and the sum of risks of all the tasks considering the effect of skill levels and task priorities. A new approach is taken to build schedules that minimise the risks of missing appointments as well as the risks of technicians not being able to complete their daily tours on time.We first analyse the probability distribution of the arrival time to any customer location considering the distributions of activities prior to this arrival. Based on the analysis, an efficient estimation method for calculating the risks is proposed, which is highly accurate and this is verified by comparing the results of the estimation method with a numerical integral method.We then develop three new workforce scheduling and vehicle routing models that minimise the risks with different considerations such as an identical standard deviation of the duration for all uncertain tasks in the linear risk minimisation model, and task priorities in the priority task risk minimisation model. A simulated annealing algorithm is implemented for solving the models at the start of the day and for re-optimisation during the day. Computational experiments are carried out to compare the results of the risk minimisation models with those of the traditional travel cost model. The performance is measured using risks and robustness. Simulation is used to compare the numbers of missed appointments and test the effect of re-optimisation.The results of the experiments demonstrate that the new models significantly reduce the risks and generate schedules with more contingency time allowances. Simulation results also show that re-optimisation reduces the number of missed appointments significantly. The risk calculation methods and risk minimisation algorithm are applied to a real-world problem in the telecommunication sector.</div

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

Personaneinsatz- und Tourenplanung für Mitarbeiter mit Mehrfachqualifikationen

In workforce routing and scheduling there are many applications in which differently skilled workers must perform jobs that occur at different locations, where each job requires a particular combination of skills. In many such applications, a group of workers must be sent out to provide all skills required by a job. Examples are found in maintenance operations, the construction sector, health care operations, or consultancies. In this thesis, we analyze the combined problem of composing worker groups (teams) and routing these teams under goals expressing service-, fairness-, and cost-objectives. We develop mathematical optimization models and heuristic solution methods for an integrated solution and a sequential solution of the teaming- and routing-subproblems . Computational experiments are conducted to identify the tradeoff of better solution quality and computational effort

Operational Research IO2017, Valença, Portugal, June 28-30

This proceedings book presents selected contributions from the XVIII Congress of APDIO (the Portuguese Association of Operational Research) held in Valença on June 28–30, 2017. Prepared by leading Portuguese and international researchers in the field of operations research, it covers a wide range of complex real-world applications of operations research methods using recent theoretical techniques, in order to narrow the gap between academic research and practical applications. Of particular interest are the applications of, nonlinear and mixed-integer programming, data envelopment analysis, clustering techniques, hybrid heuristics, supply chain management, and lot sizing and job scheduling problems. In most chapters, the problems, methods and methodologies described are complemented by supporting figures, tables and algorithms. The XVIII Congress of APDIO marked the 18th installment of the regular biannual meetings of APDIO – the Portuguese Association of Operational Research. The meetings bring together researchers, scholars and practitioners, as well as MSc and PhD students, working in the field of operations research to present and discuss their latest works. The main theme of the latest meeting was Operational Research Pro Bono. Given the breadth of topics covered, the book offers a valuable resource for all researchers, students and practitioners interested in the latest trends in this field.info:eu-repo/semantics/publishedVersio