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A review of technician and task scheduling problems, datasets and solution approaches
... Khalfay et al. [18] focus on five problems which compose the WSRP family: the Technician Task Scheduling Problem (TTSP), the Technician Routing and Scheduling Problem (TRSP), the Service Technician Routing and Scheduling problem (STRSP), the Multi-period Field Service Routing Problem (MFSRP), and the Multi-period Technician Routing and Scheduling Problem (MTRSP). According to their observation, to make an impact in the industry, future research should focus on multi-period variants, technician unavailability, strategies to build teams, and precedence constraints. ...
... Their problem is concerned with the assignment of workers to time slots along the week, and not the particular visitation of tasks. The problem being studied here fits under the umbrella of WSRPs defined by Castillo-Salazar et al. [9] and Khalfay et al. [18]. These works describe a list of characteristics that combined will define specific WSRPs. ...
... methods) Algethami et al. [4] Genetic Algorithm Anoshkina and Meisel [5] Bi-level decomposition Bostel et al. [7] Hybrid Castillo-Salazar et al. [9] Survey (WSRP features and sol. methods) Chen et al. [10] Hybrid Chen et al. [11] Dynamic programming, experience-based service times and stochastic customers Cordeau et al. [12] ALNS Dohn et al. [13] Branch-and-Price Estellon et al. [15] Heuristics Fırat and Hurkens [16] Hybrid Khalfay et al. [18] Survey (WSRP features and sol. methods) Kovacs et al. [19] ALNS Mathlouthi et al. [22] Tabu Search Mosquera et al. [23] Hybrid metaheuristic Pillac et al. [24] ALNS Pillac et al. [25] Hybrid Rasmussen et al. [26] Branch-and-Price Solomon [27] Heuristics Tang et al. [28] Tabu Search Tricoire et al. [29] Branch-and-Price Zamorano and Stolletz [30] Branch-and-Price Zamorano et al. [31] Branch-and-Price MWSRPDT MIP model and ACO The next constraint states that a task can only be executed if the tasks on which it depends have already been executed: ...
In this paper, we study a new Workforce Scheduling and Routing Problem, denoted Multiperiod Workforce Scheduling and Routing Problem with Dependent Tasks. In this problem, customers request services from a company. Each service is composed of dependent tasks, which are executed by teams of varying skills along one or more days. Tasks belonging to a service may be executed by different teams, and customers may be visited more than once a day, as long as precedences are not violated. The objective is to schedule and route teams so that the makespan is minimized, i.e., all services are completed in the minimum number of days. In order to solve this problem, we propose a Mixed-Integer Programming model, a constructive algorithm and heuristic algorithms based on the Ant Colony Optimization (ACO) metaheuristic. The presence of precedence constraints makes it difficult to develop efficient local search algorithms. This motivates the choice of the ACO metaheuristic, which is effective in guiding the construction process towards good solutions. Computational results show that the model is capable of consistently solving problems with up to about 20 customers and 60 tasks. In most cases, the best performing ACO algorithm was able to match the best solution provided by the model in a fraction of its computational time.
... Workforce scheduling is a relevant research topic in transportation and logistics, since it can be applied in many fields [6], such as technician routing and scheduling, manpower allocation, security personnel routing and rostering and home care services. Interest in this research area is also driven by the importance of ensuring an efficient and satisfying client service policy after a product delivery, which substantially contributes to the maintain of the market share [15]. The workforce scheduling problem focuses on the elaboration of models and solution methods for planning in-field personnel activities, including their mobilization between different locations. ...
... The values for each parameter are listed in Table (1). [10,15,20] Twelve instances were arbitrarily selected for this purpose, and each instance was executed 10 times for each combination of parameter values, that is, 144 * 10 runs for each instance. Figures 2,3 and 4 show the aggregated overall gaps for each combination of the three parameters, whereas figures 5,6 and 7 show the overall computational times variations according to the values of the same parameters. ...
Most public facilities in the European countries, including France, Germany, and the UK, were built during the reconstruction projects between 1950 and 1980. Owing to the deteriorating state of such vital infrastructure has become relatively expensive in the recent decades. A significant part of the maintenance operation costs is spent on the technical staff. Therefore, the optimal use of the available workforce is essential to optimize the operation costs. This includes planning technical interventions, workload balancing, productivity improvement, etc. In this paper, we focus on the routing of technicians and scheduling of their tasks. We address for this purpose a variant of the workforce scheduling problem called the technician routing and scheduling problem (TRSP). This problem has applications in different fields, such as transportation infrastructure (rail and road networks), telecommunications, and sewage facilities. To solve the TRSP, we propose an enhanced iterated local search (eILS) approach. The enhancement of the ILS firstly includes an intensification procedure that incorporates a set of local search operators and removal-repair heuristics crafted for the TRSP. Next, four different mechanisms are used in the perturbation phase. Finally, an elite set of solutions is used to extensively explore the neighborhood of local optima as well as to enhance diversification during search space exploration. To measure the performance of the proposed method, experiments were conducted based on benchmark instances from the literature, and the results obtained were compared with those of an existing method. Our method achieved very good results, since it reached the best overall gap, which is three times lower than that of the literature. Furthermore, eILS improved the best-known solution for 34 instances among a total of 56 while maintaining reasonable computational times.
... Companies that deal with technician planning should consider maintaining and improving their current status in a competitive global market. Also, companies challenge the goods provided and the quality level of customer service and aftercare provided by authors (Khalfay et al. 2017). ...
... The occurrence of routing is performed in a way in which proficient technician group starts and fulfills their tasks in the central depot on the allowed days. The travel times between nodes are calculated as Euclidean distance (Khalfay et al. 2017;Pekel and Kara 2019). ...
This paper proposes an improved genetic algorithm (IGA) to provide feasible solutions to the technician routing and scheduling problem (TRSP). The TRSP covers the feasible team generation, the assignment of feasible teams to suitable tasks, the proficiency level of workers, routings considering the allowed days, and the skill desire of the task. The paper deals with a five-day multi-period planning horizon, and a task is performed in any one of 5 days. The IGA consists of crossover, mutation, and three neighborhood structures. Mutation and crossover largely try to avoid getting caught in the local solution trap. Three neighborhood structures improve genetic algorithm (GA) by searching for better solutions. Further, the performance of the proposed algorithm is experimentally compared with GA and improved particle swarm optimization (IPSO) algorithm by providing the TRSP solutions on the generated benchmark instances. The numerical results indicate that IGA offers fast and better solutions considering GA and IPSO algorithms.
... The technician scheduling problems are significant as a way for industries to maintain market share and ensure repeat business (Haugen and Hill 1999). In a competitive market, specialist organizations compete for not only the product they provide but also the quality of client service supplied by them and the after-care service (Khalfay et al. 2017). ...
... The occurrence of routing means that there is a central depot, from which proficient personnel depart and return to the central depot at the end of the day. The travel times between locations and the depot are regularly calculated as Euclidean distance (Khalfay et al. 2017). Nevertheless, there are important distinctions such as talent requirements to complete different types of tasks and relatively large service times when compared to travel times. ...
In this paper, an improved particle swarm optimization (IPSO) algorithm is proposed to solve the technician routing and scheduling problem (TRSP). The TRSP consists of the assignment of technicians into teams, the assignment of teams to tasks, the construction of routes, and the selection of the day on which a service is provided by considering the proficiency level of workers and the proficiency requirement of the task. The paper considers the planning horizon as a multi-period covering 5 days, which further increases the complexity of the problem. Then a task can be fulfilled in any one of 5 days. The IPSO algorithm includes a particle swarm optimization (PSO) algorithm and one neighborhood operator. One neighborhood operator is used to avoid the local solution trap since the global best solution found by PSO is falling into a local solution trap. Further, the proposed algorithm’s performance is experimentally compared with the branch-and-cut algorithm for the solution of the TRSP, on the benchmark instances generated from the literature. The computational results show that IPSO provides better solutions considering the branch-and-cut algorithm within reasonable computing time.
... So, why not simply assign expert technicians to advanced tasks and regular technicians to everyday issues to avoid rework? One reason is that technicians, as all employees, call in sick regularly (Khalfay et al. 2017). In Germany, employees working in the maintenance and repair sector called in sick for almost five weeks in 2022 (IWD 2024). ...
Home repair and installation services require technicians to visit customers and resolve tasks of different complexity. Technicians often have heterogeneous skills and working experiences. The geographical spread of customers makes achieving only perfect matches between technician skills and task requirements impractical. Additionally, technicians are regularly absent due to sickness. With non-perfect assignments regarding task requirement and technician skill, some tasks may remain unresolved and require a revisit and rework. Companies seek to minimize customer inconvenience due to delay. We model the problem as a sequential decision process where, over a number of service days, customers request service while heterogeneously skilled technicians are routed to serve customers in the system. Each day, our policy iteratively builds tours by adding "important" customers. The importance bases on analytical considerations and is measured by respecting routing efficiency, urgency of service, and risk of rework in an integrated fashion. We propose a state-dependent balance of these factors via reinforcement learning. A comprehensive study shows that taking a few non-perfect assignments can be quite beneficial for the overall service quality. We further demonstrate the value provided by a state-dependent parametrization.
... Routing is carried out so that the expert technician group leaves and returns to the central warehouse at the end of the day. Travelling times between each node are computed as Euclidean distance (Khalfay et al., 2017). ...
This paper proposes a hybrid algorithm including the Adam algorithm and body change operator (BCO). Feasible solutions to technician routing and scheduling problems (TRSP) are investigated by performing deep learning based on the Adam algorithm and the hybridization of Adam-BCO. TRSP is a problem where all tasks are routed, and technicians are scheduled. In the deep learning method based on the Adam algorithm and Adam-BCO algorithm, the weights of the network are updated, and these weights are evaluated as Greedy approach, and routing and scheduling are performed. The performance of the Adam-BCO algorithm is experimentally compared with the Adam and BCO algorithm by solving the TRSP on the instances developed from the literature. The numerical results evidence that Adam-BCO offers faster and better solutions considering Adam and BCO algorithm. The average solution time increases from 0.14 minutes to 4.03 minutes, but in return, Gap decreases from 9.99% to 5.71%. The hybridization of both algorithms through deep learning provides an effective and feasible solution, as evidenced by the results.
... Despite the fact that the TRSPTW is categorized as a vehicle routing problem (VRP) (Laporte and Osman, 1995), which means that its applications are not limited to specific industries, there are few studies in this field. Most TRSPTW models that are adopted from VRPs are based on a single-day scheduling horizon (Khalfay et al., 2017), while those based on multiday scheduling horizons provide technician routing and scheduling planners with the ability to plan for several days. Table 1 summarizes the relevant studies in the TRSPTW field based on the several characteristics: technician skills, time windows considered, scheduling horizon, and terms included in the optimization model objective function. ...
This paper proposes two models for the Technician Routing and Scheduling Problem (TRSP), which are motivated by a telecom provider based in Saskatchewan, Canada. The proposed TRSP models are distinguished from existing models by their ability to address two key issues: overnight and lunch break scheduling. The models aim to scheduling a set of technicians with homogeneous skill levels and different working hours for the purpose of providing services with different service times and time windows to a diverse set of widely spread communities. As the large-sized experiments of this problem categorized into NP-hard problems, a metaheuristic-based technique, Invasive Weed Optimization, is developed to solve them. A comparative analysis is performed to choose the optimum TRSP model based on two factors which are distance of communities to the main depot and balanced service times during planning horizon. The performance of the models is evaluated through the real-world data obtained from the telecom provider. The results prove that the overnight TRSP model is capable of substantially decreasing travel costs and the number of technicians that are required to perform the same set of services.
... Consequently, a Pareto set of optimal solutions exists. Considering the papers already examined and two additional review articles [26,27], it can be established that no such an approach exists. ...
This research considers the single-vehicle routing problem (VRP) with multi-shift and fuzzy uncertainty. In such a problem, a company constantly uses one vehicle to fulfill demand over a scheduling period of several work shifts. In our case, a crew executes maintenance jobs in different sites. The working team runs during different work shifts, but recurrently returns to the depot by the end of the shift (overtime avoidance). The goal consists in minimizing the number of work shifts (makespan). We observe the impact of uncertainty in travel and maintenance processing time on the overtime avoidance constraint. We realize an Artificial Immune Heuristic to get optimal solutions considering both makespan and overtime avoidance. First, we present a Pareto-based framework to evaluate the uncertainty influence. Then, we show a numerical real case study to survey the problem. In particular, a case study scenario has been created on the basis of the environmental changes in travel and processing times observed in Italy during the Covid-19 lockdown period (started on March 9, 2020). Results present important improvements are obtained with the proposed approach.
This study aims to conduct a bibliometric analysis inherent to assessing competitive intelligence and business intelligence concepts using the Scopus database and the Bibliometrix R software. The study’s articles were found using precise criteria in the Scopus database. The 42 publications were then examined with Bibliometrix software, which included extensive parameterization for each component under evaluation. The results of this study consisted of establishing the number of existing publications on the topic under analysis between 2017 and 2021 – in this sense, it was possible to identify that the publications are experiencing an annual decrease rate of 22.69%; the trends in terms of publications and collaborations between countries; the most relevant journals in the area; and the interconnections between authors, keywords, and publications. This study has as an added value the possibility to evaluate the relevance attributed by academics to ascertain the most important contributions in terms of authors, articles, and journals. One major limitation in this study could be addressed in future research. The study focused on a limited study field in the context of business, management, and accounting, so it would be very pertinent to understand how this topic has evolved, particularly in the area of computer science.Keywords
Bibliometric analysis
Business intelligence
Competitive intelligence
Scientometrics
The problem of routing and scheduling of technicians is a problem that technical assistance and maintenance companies face nowadays, market competitiveness requires quick response, service diversification, and customer satisfaction. The relationship between competitiveness and profitability of companies involves the effective management of their resources. The work developed addresses a real problem of a major Portuguese company providing technical assistance to the home, a varied set of services (need for specific skills and execution times) must be scheduled for a set of technicians with heterogeneous skills and geographical locations (start and end of the route) based on their different places of residence. The results show a considerable increase in the efficiency levels of the solution obtained when compared to the company’s current solution and reveals that the lack of homogeneity of skills among technicians and the variation in service flows are factors that should be considered in the operational management of resources and the contracting of work, and that the increase in working hours can also contribute to improving the efficiency of the process.
In this paper, we study a new Workforce Scheduling and Routing Problem, denoted Multiperiod Workforce Scheduling and Routing Problem with Dependent Tasks. In this problem, customers request services from a company. Each service is composed of dependent tasks, which are executed by teams of varying skills along one or more days. Tasks belonging to a service may be executed by different teams, and customers may be visited more than once a day, as long as precedences are not violated. The objective is to schedule and route teams so that the makespan is minimized, i.e., all services are completed in the minimum number of days. In order to solve this problem, we propose a Mixed-Integer Programming model, a constructive algorithm and heuristic algorithms based on the Ant Colony Optimization (ACO) metaheuristic. The presence of precedence constraints makes it difficult to develop efficient local search algorithms. This motivates the choice of the ACO metaheuristic, which is effective in guiding the construction process towards good solutions. Computational results show that the model is capable of consistently solving problems with up to about 20 customers and 60 tasks. In most cases, the best performing ACO algorithm was able to match the best solution provided by the model in a fraction of its computational time.
This paper discusses the occurrence of dependency relationships within NP hard personnel scheduling problems. These dependencies, commonly referred to as precedence constraints, arise in a number of industries including but not limited to: maintenance scheduling, home health care, and unmanned aerial vehicle scheduling. Precedence relationships, as demonstrated in this research, can significantly impact the quality of solution that can be obtained. In such a competitive market it is imperative that new and innovative ways of finding high quality solutions in short computational times are discovered. This paper presents novel datasets, containing 100–1000 jobs to allocate, that are used to benchmark two heuristic algorithms; an intelligent decision heuristic and a greedy heuristic. Each heuristic is coupled with a multi start metaheuristic to provide a set of benchmark results.
In this paper, we consider a multi-attribute technician routing and scheduling problem motivated from an application for the repair of electronic transaction equipment. This problem consists in routing technicians to serve requests for service, while taking into account many attributes like technician skills, task priorities, multiple time windows, parts inventory, breaks and overtime. A mixed integer programming model is proposed to address this problem, which is then solved with a commercial solver. The computational results explore the difficulty of the problem along various dimensions and underline its inherent complexity.
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.
The Technician Routing and Scheduling Problem (TRSP) consists in routing staff to serve requests for service, taking into account time windows, skills, tools, and spare parts. Typical applications include maintenance operations and staff routing in telecoms, public utilities, and in the health care industry. In this paper we tackle the Dynamic TRSP (D-TRSP) in which new requests appear over time. We propose a fast reoptimization approach based on a parallel Adaptive Large Neighborhood Search (pALNS) and a Multiple Plan Approach (MPA). Finally, we present computational experiments on randomly generated instances.
The Technician Routing and Scheduling Problem (TRSP) consists in routing staff to serve requests for service, taking into account time windows, skills, tools, and spare parts. Typical applications include maintenance operations and staff routing in telecoms, public utilities, and in the health care industry. In this paper, we present a formal definition of the TRSP, discuss its relation with the Vehicle Routing Problem with Time Windows (VRPTW), and review related research. From a methodological perspective, we describe a matheuristic composed of a constructive heuristic, a parallel Adaptive Large Neighborhood Search, and a mathematical programming based post-optimization procedure that successfully tackles the TRSP. We validate the matheuristic on the Solomon VRPTW instances, where we achieve an average gap of
, and matched 44 out of 55 optimal solutions. Finally, we illustrate how the matheuristic successfully solves a set of TRSP instances extended from the Solomon benchmark.
Due to its complexity, its challenging features, and its practical relevance,
personnel scheduling has been heavily investigated in the last few decades. However,
there is a relatively low level of study on models and complexity in these important
problems. In this paper, we present mathematical models which cover specificc aspects
in the personnel scheduling literature. Furthermore, we address complexity issues by
identifying polynomial solvable and NP-hard special cases.
We present a general framework for solving a real-world multimodal home-healthcare scheduling (MHS) problem from a major Austrian home-healthcare provider. The goal of MHS is to assign home-care staff to customers and determine efficient multimodal tours while considering staff and customer satisfaction. Our approach is designed to be as problem-independent as possible, such that the resulting methods can be easily adapted to MHS setups of other home-healthcare providers. We chose a two-stage approach: in the first stage, we generate initial solutions either via constraint programming techniques or by a random procedure. During the second stage, the initial solutions are (iteratively) improved by applying one of four metaheuristics: variable neighborhood search, a memetic algorithm, scatter search and a simulated annealing hyper-heuristic. An extensive computational comparison shows that the approach is capable of solving real-world instances in reasonable time and produces valid solutions within only a few seconds.
The key idea underlying iterated local search is to focus the search not on the full space of all candidate solutions but on the solutions that are returned by some underlying algorithm, typically a local search heuristic. The resulting search behavior can be characterized as iteratively building a chain of solutions of this embedded algorithm. The result is also a conceptually simple metaheuristic that nevertheless has led to state-of-the-art algorithms for many computationally hard problems. In fact, very good performance is often already obtained by rather straightforward implementations of the metaheuristic. In addition, the modular architecture of iterated local search makes it very suitable for an algorithm engineering approach where, progressively, the algorithms' performance can be further optimized. Our purpose here is to give an accessible description of the underlying principles of iterated local search and a discussion of the main aspects that need to be taken into account for a successful application of it. In addition, we review the most important applications of this method and discuss its relationship to other metaheuristics.
This paper deals with scheduling complex tasks with an inhomogeneous set of resources. The problem is to assign technicians to tasks with multi-level skill requirements. Here, the requirements are merely the presence of a set of technicians that possess the necessary capabilities. An additional complication is that a set of combined technicians stays together for the duration of a work day. This typically applies to scheduling of maintenance and installation operations. We build schedules by repeated application of a flexible matching model that selects tasks to be processed and forms groups of technicians assigned to combinations of tasks. The underlying mixed integer programming (MIP) model is capable of revising technician-task allocations and performs very well, especially in the case of rare skills.
Heuristic search procedures that aspire to find globally optimal solutions to hard combinatorial optimization problems usually
require some type of diversification to overcome local optimality. One way to achieve diversification is to re-start the procedure
from a new solution once a region has been explored. In this chapter we describe the best known multi-start methods for solving
optimization problems. We propose classifying these methods in terms of their use of randomization, memory, and degree of
rebuild. We also present a computational comparison of these methods on solving the maximum diversity problem in terms of
solution quality and diversification power.
The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important metaheuristics from a conceptual point of view. We outline the different components and concepts that are used in the different metaheuristics in order to analyze their similarities and differences. Two very important concepts in metaheuristics are intensification and diversification. These are the two forces that largely determine the behaviour of a metaheuristic. They are in some way contrary but also complementary to each other. We introduce a framework, that we call the I&D frame, in order to put different intensification and diversification components into relation with each other. Outlining the advantages and disadvantages of different metaheuristic approaches we conclude by pointing out the importance of hybridization of metaheuristics as well as the integration of metaheuristics and other methods for optimization.
In this paper, a real-life problem of task scheduling with human resource allocation is addressed. This problem was approached by the authors in the context of the ROADEF 2007 Challenge, which is an international competition organized by the French Operations Research Society. The subject of the contest, proposed by the telecommunications company France Télé
com, consists in planning maintenance interventions and teams of technicians needed for their achievements. The addressed combinatorial optimization problem is very hard: it contains several NP-hard subproblems and its scale (hundreds of interventions and technicians) induces a huge combinatorics. An effective and efficient local-search heuristic is described to solve this problem. This algorithm was ranked 2nd of the competition (over the 35 teams who have submitted a solution). Moreover, a methodology is revealed to design and engineer high-performance local-search heuristics for solving practically discrete optimization problems.
The best exact algorithms for the capacitated Vehicle Routing Problem (CVRP) have been based on either branch-and-cut or Lagrangean relaxation/column generation. This paper presents an algorithm that combines both approaches: it works over the intersection of two polytopes, one associated with a traditional Lagrangean relaxation over q-routes, the other defined by bound, degree and capacity constraints. This is equivalent to a linear program with exponentially many variables and constraints that can lead to lower bounds that are superior to those given by previous methods. The resulting branch-and-cut-and-price algorithm can solve to optimality almost all instances from the literature with up to 100 vertices, nearly doubling the size of instances that can be consistently solved.
The Technicians and Interventions Scheduling Problem for Telecommunications embeds the scheduling of interventions, the assignment
of teams to interventions and the assignment of technicians to teams. Every intervention is characterized, among other attributes,
by a priority. The objective of this problem is to schedule interventions such that the interventions with the highest priority
are scheduled at the earliest time possible while satisfying a set of constraints like the precedence between some interventions
and the minimum number of technicians needed with the required skill levels for the intervention. We present a Greedy Randomized
Adaptive Search Procedure (GRASP) for solving this problem. In the proposed implementation, we integrate learning to the GRASP
framework in order to generate good-quality solutions using information brought by previous ones. We also compute lower bounds
and present experimental results that validate the effectiveness of this approach.
This paper proposes a construction heuristic and an adaptive large neighborhood search heuristic for the technician and task
scheduling problem arising in a large telecommunications company. This problem was solved within the framework of the 2007
challenge set up by the French Operational Research Society (ROADEF). The paper describes the authors’ entry in the competition
which tied for second place.
There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom
in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given
function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization
of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and
provides an unfamiliar perspective on traditional optimization problems and methods.
this paper is posed in the context of a home health care problem. Despite the fact that in this industry, health care is provided by many qualified individuals such as registered nurses, physical therapists and home health aides, for notational simplicity, we will refer to the employees as simply nurses. The only differentiation that we make is between salaried workers (full-time nurses) and non-salaried workers (part-time nurses). Salaried workers are paid for a full-time shift everyday, whether or not they are scheduled to work the entire time. They are paid overtime if they are required to work for longer than the standard shift length. Part-time nurses are paid by the hour. The differences in the nurses' qualifications are represented by a binary relationship with each patient; a nurse-patient pair is thus, either a feasible match or an infeasible match. Accordingly, the nurse may be scheduled to visit the patient, or he or she may not. Additionally, a company in this industry would like to not only satisfy a customer's need for health care, but also keep the customer happy by providing dependable service (i.e. providing health care when the customer requests it). Thus, most home health care companies allow the customer to specify a time window during which he or she will be at home awaiting the requested care. In summary, the problem is to find an optimal schedule such that each nurse that is scheduled to work leaves from his or her home, visits a set of "feasible" patients within their time windows, takes a lunch break within the nurse's lunch time window, and returns home, all within the nurse's time window (which indicates the times during which the nurse is willing to work) and within the known limit on the length of a shift. The optimal schedule minimizes th...
This paper addresses a technician routing and scheduling problem motivated by the case of an external maintenance provider. Technicians are proficient in different skills and paired into teams to perform maintenance tasks. Tasks are skill constrained and have time windows that may span multiple days. The objective is to determine the daily assignment of technicians into teams, of teams to tasks, and of teams to daily routes such that the operation costs are minimized. We propose a mixed integer program and a branch-and-price algorithm to solve this problem. Exploiting the structure of the problem, alternative formulations are used for the column generation-phase of the algorithm. Using real-world data from an external maintenance provider, we conduct numerical studies to evaluate the performance of our proposed solution approaches.
In recent years there has been an increased demand in use of multiple unmanned aerial vehicles (UAVs) for surveillance and material handling tasks in indoor environments. However, only a limited number of studies have been reported on UAV scheduling in an indoor 3D environment. This paper presents the indoor UAV scheduling problem and models it as a constraint satisfaction problem (CSP) to find a feasible solution in less computation time. A numerical example of the problem is presented to illustrate the proposed methodology.
This paper proposes a new approach, an intelligent decision (ID) heuristic, to solve a technician and task scheduling problem (TTSP) defined by the ROADEF 2007 challenge. The ID heuristic is unlike other approaches because at each stage the heuristic considers multiple scenarios of team configurations and job assignments. Within the ID heuristic, novel operators have been designed which focus on flexibility in team configurations. Furthermore, outsourcing is a sub-problem of the ROADEF 2007 challenge, so computational experiments have been performed to evaluate various strategies of outsourcing to utilize the ID heuristic. Results obtained using the ID heuristic have been compared against other researchers who have tackled this problem.
While home services is a fast growing industry, little attention has been given to the management of its workforce. In particular, the productivity of home-service technicians depends not only on efficiently routing from customer-to-customer, but also the management of their skillsets. This paper introduces a model of technician routing that explicitly models individualized, experience-based learning. The results demonstrate that explicit modeling and the resulting ability to capture changes in productivity over time due to learning lead to significantly better and different solutions than those found when learning and workforce heterogeneity is ignored. We show that these differences result from the levels of specialization that occur in the workforce.
We consider a real problem faced by a large company providing repair services of office machines in Santiago, Chile. In a typical day about twenty technicians visit seventy customers in a predefined service area in Santiago. We design optimal routes for technicians by considering travel times, soft time windows for technician arrival times at client locations, and fixed repair times. A branch-and-price algorithm was developed, using a constraint branching strategy proposed by Ryan and Foster along with constraint programming in the column generation phase. The column generation takes advantage of the fact that each technician can satisfy no more than five to six service requests per day. Different instances of the problem were solved to optimality in a reasonable computational time, and the results obtained compare favorably with the current practice.
In this paper we propose a new strategy for solving the Capacitated Vehicle Routing Problem using a quantum annealing algorithm. The Capacitated Vehicle Routing Problem is a variant of the Vehicle Routing Problem being characterized by capacitated vehicles which contain goods up to a certain maximum capacity. Quantum annealing is a metaheuristic that uses quantum tunneling in the annealing process. We discuss devising a spin encoding scheme for solving the Capacitated Vehicle Routing Problem with a quantum annealing algorithm and an empirical approach for tuning parameters. We study the effectiveness of quantum annealing in comparison with best known solutions for a range of benchmark instances.
The constant need to maintain and develop the infrastructure underlying all the telecommunications services offered by France Telecom is the basis of this challenge proposal. With the strong development of high bandwidth Internet (ADSL) and the related services such as VoIP and television broadcasts over ADSL, the number of interventions is steadily increasing. However, with the end of the telecommunication monopoly France Telecom has to be even more competitive and therefore has to limit the growth of its group of technicians. In order to make the most out of the existing groups, we are considering a new approach to intervention scheduling. Currently, the schedules are created on a day-to-day basis, each group having a supervisor who decides who will work on which interventions. This assignment takes into account a lot of parameters that are difficult to integrate into a modelling system, such as personal affinity between technicians, tutoring, very specific knowledge of the intervention or geographical informations (where the technician lives for example). The aim of this challenge is to provide efficient schedules which will serve as a first sketch to help the supervisor in his duty. These schedules will be produced based on the formal description of the interventions and the capabilities of the technicians. We will describe in section 3 how these informations are provided as input files to the solver. Informally, a local group can be composed of between 20 and 60 technicians. There is a large number of possible interventions requiring different skills. In order to know which technician can be a part of an intervention, the skills are grouped into a small number of domains, and the level of each technician in each domain is rated. For example there can be up to twenty five domains with five levels for each domain. A technician of level 0 in one domain has no knowledge in this specific domain, whereas a technician of level 4 is an expert. To perform an intervention, the supervisor has to send a team to the inter-vention location, with enough qualified technicians to meet all the intervention requirements. For example, an intervention requiring one technician of level 2 in the domain d1 can be done by one technician of level 2, 3 or 4 in domain d1, but cannot be done by two technicians of level 1 in domain d1. * INRIA Sophia Antipolis 1 A strong constraint here is that teams are formed for the day and should not change during one day. This is due to the limited number of available cars, and to the time it would take to get several teams back to a central point to mix the teams. Finally, interventions also have some characteristics such as a duration, a priority (which determines due dates for completing interventions), a fixed cost if an external company is hired to do it and a list of interventions which have to be completed before starting the intervention.
This article deals with a particular class of routing problem, consisting of the planning and routing of technicians in the field. This problem has been identified as a multiperiod, multidepot uncapacitated vehicle routing problem with specific constraints that we call the multiperiod field service routing problem (MPFSRP). We propose a set covering formulation of the problem for the column generation technique and we develop an exact branch and price solution method for small-sized instances. We also propose several heuristic versions for larger instances. We present the results of experiments on realistic data adapted from an industrial application.
This paper presents a review of the literature on personnel scheduling problems. Firstly, we discuss the classification methods in former review papers. Secondly, we evaluate the literature in the many fields that are related to either the problem setting or the technical features. Each perspective is presented as a table in which the classification is displayed. This method facilitates the identification of manuscripts related to the reader’s specific interests. Throughout the literature review, we identify trends in research on personnel staffing and scheduling, and we indicate which areas should be subject to future research.
In the Home Care Crew Scheduling Problem a staff of home carers has to be assigned a number of visits to patients’ homes, such that the overall service level is maximised. The problem is a generalisation of the vehicle routing problem with time windows. Required travel time between visits and time windows of the visits must be respected. The challenge when assigning visits to home carers lies in the existence of soft preference constraints and in temporal dependencies between the start times of visits.We model the problem as a set partitioning problem with side constraints and develop an exact branch-and-price solution algorithm, as this method has previously given solid results for classical vehicle routing problems. Temporal dependencies are modelled as generalised precedence constraints and enforced through the branching. We introduce a novel visit clustering approach based on the soft preference constraints. The algorithm is tested both on real-life problem instances and on generated test instances inspired by realistic settings. The use of the specialised branching scheme on real-life problems is novel. The visit clustering decreases run times significantly, and only gives a loss of quality for few instances. Furthermore, the visit clustering allows us to find solutions to larger problem instances, which cannot be solved to optimality.
This research addresses the problem of scheduling technicians to travel from customer site to customer site to perform emergency maintenance on office machines, computers, robots, telecommunications equipment, medical equipment, heating/cooling equipment, household appliances, and other equipment. We call this the Traveling Technician Problem (TTP). In its simplest form, the TTP is a multiserver, sequence-dependent, tardiness minimization problem. This research frames the TTP as a service quality maximization problem in which service quality is defined in terms of mean tardiness, mean technician phone response time, mean promise time, and mean response time. Tardiness is defined with respect to contractually guaranteed response times. Industry practice is to use dispatching rules to assign service calls to technicians. This research proposes scheduling procedures to maximize field service quality in a dynamic environment. A simulation experiment was used to compare three dispatching rules and three scheduling procedures for the TTP. The scheduling procedures dominated the dispatching rules on all four service quality measures. The proposed scheduling procedures hold promise for improving service quality in a wide variety of field service organizations and in other scheduling environments as well.
Motivated by the problem situation faced by infrastructure service and maintenance providers, we define the service technician
routing and scheduling problem with and without team building: a given number of technicians have to complete a given number
of service tasks. Each technician disposes of a number of skills at different levels and each task demands technicians that
provide the appropriate skills of at least the demanded levels. Time windows at the different service sites have to be respected.
In the case where a given task cannot be serviced by any of the technicians, outsourcing costs occur. In addition, in some
companies technicians have to be grouped into teams at the beginning of the day since most of the tasks cannot be completed
by a single technician. The objective is to minimize the sum of the total routing and outsourcing costs. We solve both problem
versions by means of an adaptive large neighborhood search algorithm. It is tested on both artificial and real-world instances;
high quality solutions are obtained within short computation times.
KeywordsLarge neighborhood search–Service technician routing and scheduling–Vehicle routing–Metaheuristics
Home health care, i.e. visiting and nursing patients in their homes, is a growing sector in the medical service business. From a staff rostering point of view, the problem is to find a feasible working plan for all nurses that has to respect a variety of hard and soft constraints, and preferences. Additionally, home health care problems contain a routing component: a nurse must be able to visit her patients in a given roster using a car or public transport. It is desired to design rosters that consider both, the staff rostering and vehicle routing components while minimizing transportation costs and maximizing satisfaction of patients and nurses.In this paper we present the core optimization components of the PARPAP software. In the optimization kernel, a combination of linear programming, constraint programming, and (meta-)heuristics for the home health care problem is used, and we show how to apply these different heuristics efficiently to solve home health care problems. The overall concept is able to adapt to various changes in the constraint structure, thus providing the flexibility needed in a generic tool for real-world settings.
This paper reports a fast local search (FLS) algorithm which helps to improve the efficiency of hill climbing and a guided local search (GLS) algorithm which was developed to help local search to escape local optima and distribute search effort. To illustrate how these algorithms work, this paper describes their application to British Telecom's workforce scheduling problem, which is a hard real life problem. The effectiveness of FLS and GLS are demonstrated by the fact that they both outperform all the methods applied to this problem so far, which include simulated annealing, genetic algorithms and constraint logic programming.
This study considers the application of a genetic algorithm (GA) to the basic vehicle routing problem (VRP), in which customers of known demand are supplied from a single depot. Vehicles are subject to a weight limit and, in some cases, to a limit on the distance travelled. Only one vehicle is allowed to supply each customer. The best known results for benchmark VRPs have been obtained using tabu search or simulated annealing. GAs have seen widespread application to various combinatorial optimisation problems, including certain types of vehicle routing problem, especially where time windows are included. However, they do not appear to have made a great impact so far on the VRP as described here. In this paper, computational results are given for the pure GA which is put forward. Further results are given using a hybrid of this GA with neighbourhood search methods, showing that this approach is competitive with tabu search and simulated annealing in terms of solution time and quality.
This paper considers the design and analysis of algorithms for vehicle routing and scheduling problems with time window constraints. Given the intrinsic difficulty of this problem class, approximation methods seem to offer the most promise for practical size problems. After describing a variety of heuristics, we conduct an extensive computational study of their performance. The problem set includes routing and scheduling environments that differ in terms of the type of data used to generate the problems, the percentage of customers with time windows, their tightness and positioning, and the scheduling horizon. We found that several heuristics performed well in different problem environments; in particular an insertion-type heuristic consistently gave very good results.
This paper addresses a field technician scheduling problem faced by many service providers in telecommunication industry. The problem is to assign a set of jobs, at different locations with time windows, to a group of field technicians with different job skills. Such a problem can be viewed as a generalization of the well-known vehicle routing problem with time windows since technician skills need to be matched with job types. We designed and tested several heuristic procedures for solving the problem, namely a greedy heuristic, a local search algorithm, and a greedy randomized adaptive search procedure (GRASP). Our computational results indicate that GRASP is the most effective among them but requires more CPU time. However, the unique structure of GRASP allows us to exploit parallelism to achieve linear speed-up with respect to the number of machines used.
Linear programming techniques can be used in constructing schedules but their application is not trivial. This in particular holds true if a trade-off has to be made between computation time and solution quality. However, it turns out that – when handled with care – mixed integer linear programs may provide effective tools. This is demonstrated in the successful approach to the benchmark constructed for the 2007 ROADEF computation challenge on scheduling problems furnished by France Telecom. L'application de techniques programmation linéaire pour la résolution de problème d'ordonnancement n'est pas trivial, particulièrement lorsque qu'un compromis entre qualité de la solution fournie et temps de calcul est recherché. Dans ce cas des heuristiques peuvent être couplées pour améliorer les performances des modèles de programmation linéaire. La combinaison de telles méthodes a montré son efficacité dans le cadre de la résolution du Challenge ROADEF 2007.
In this paper we introduce the Personnel Task Scheduling Problem (FTSP) and provide solution algorithms for a variant of this problem known as the Shift Minimisation Personnel Task Scheduling Problem (SMPTSP). The PTSP is a problem in which a set of tasks with fixed start and finish times have to be allocated to a heterogenous workforce. Personnel work in shifts with fixed start and end times and have skills that enable them to perform some, but not all tasks. In other words, some personnel are qualified to only perform a subset of all tasks. The objective is to minimise the overall cost of personnel required to perform the given set of tasks. In this paper we introduce a special case in which the only cost incurred is due to the number of personnel (shifts) that are used. This variant of the PTSP is referred to as the Shift Minimisation Personnel Task Scheduling Problem (SMPTSP). While our motivation is a real-life Personnel Task Scheduling Problem, the formulation may also be applied to machine shop scheduling. We review the existing literature, provide mathematical formulations, and develop a heuristic approach for the SMPTSP.
This paper presents a review of staff scheduling and rostering, an area that has become increasingly important as business becomes more service oriented and cost conscious in a global environment.Optimised staff schedules can provide enormous benefits, but require carefully implemented decision support systems if an organisation is to meet customer demands in a cost effective manner while satisfying requirements such as flexible workplace agreements, shift equity, staff preferences, and part-time work. In addition, each industry sector has its own set of issues and must be viewed in its own right. There are many computer software packages for staff scheduling, ranging from spreadsheet implementations of manual processes through to mathematical models using efficient optimal or heuristic algorithms. We do not review software packages in this paper. Rather, we review rostering problems in specific application areas, and the models and algorithms that have been reported in the literature for their solution. We also survey commonly used methods for solving rostering problems.
We propose a tabu search heuristic capable of solving three well-known routing problems: the periodic vehicle routing problem, the periodic traveling salesman problem, and the multi-depot vehicle routing problem. Computational experiments carried out on instances taken from the literature indicate that the proposed method outperforms existing heuristics for all three problems. © 1997 John Wiley & Sons, Inc. Networks 30: 105–119, 1997
The paper is concerned with the optimum routing of a fleet of gasoline delivery trucks between a bulk terminal and a large number of service stations supplied by the terminal. The shortest routes between any two points in the system are given and a demand for one or several products is specified for a number of stations within the distribution system. It is desired to find a way to assign stations to trucks in such a manner that station demands are satisfied and total mileage covered by the fleet is a minimum A procedure based on a linear programming formulation is given for obtaining a near optimal solution. The calculations may be readily performed by hand or by an automatic digital computing machine. No practical applications of the method have been made as yet. A number of trial problems have been calculated, however.
We use a local search method we term Large Neighbourhood Search (LNS) for solving vehicle routing problems. LNS meshes well with constraint programming technology and is analogous to the shuffling technique of job-shop scheduling. The technique explores a large neighbourhood of the current solution by selecting a number of customer visits to remove from the routing plan, and re-inserting these visits using a constraint-based tree search. We analyse the performance of LNS on a number of vehicle routing benchmark problems. Unlike related methods, we use Limited Discrepancy Search during the tree search to re-insert visits. We also maintain diversity during search by dynamically altering the number of visits to be removed, and by using a randomised choice method for selecting visits to remove. We analyse the performance of our method for various parameter settings controlling the discrepancy limit, the dynamicity of the size of the removal set, and the randomness of the choice. We demonst...
When to hire the a-team
- P Korteweg
What is the roadef 2007 challenge
- F O R Society