An Algorithmic approach to shift structure optimization

Workforce scheduling in organizations often consists of three major phases: workload prediction, shift generation, and staff rostering. Workload prediction involves using historical behaviour of e.g. customers to predict future demand for work. Shift generation is the process of transforming the determined workload into shifts as accurately as possible. In staff rostering, the generated shifts are assigned to employees. In general the problem and even its subproblems are NP-hard, which makes them highly challenging for organizations to solve. Heuristic optimization methods can be used to solve practical instances within reasonable running times, which in turn can result in e.g. improved revenue, improved service, or more satisfied employees for the organizations. This thesis presents some specific subproblems along with practical solution methods--- Työvoiman aikataulutusprosessi koostuu kolmesta päävaiheesta: työtarpeen ennustaminen, työvuorojen muodostus ja työvuorojen miehitys. Tulevaa työtarvetta ennustetaan pääasiassa menneisyyden asiakaskäytöksen perusteella käyttäen esimerkiksi tilastollisia malleja tai koneoppimiseen perustuvia menetelmiä. Työvuorojen muodostuksessa tehdään työvuororakenne, joka noudattaa ennustettua ja ennalta tiedettyä työtarvetta mahdollisimman tarkasti. Työvuorojen miehityksessä määritetään työvuoroille tekijät. Jokainen vaihe itsessään on haasteellinen ratkaistava. Erityisesti työvuorojen miehitys on yleensä NP-kova ongelma. On kuitenkin mahdollista tuottaa käytännöllisiä ratkaisuja järkevässä ajassa käyttäen heuristisia optimointimenetelmiä. Näin on saavutettavissa mitattavia hyötyjä mm. tuottoon, asiakkaiden palvelutasoon sekä työntekijöiden työtyyväisyyteen. Tässä väitöskirjassa esitellään eräitä työvoiman aikataulutuksen aliongelmia sekä niihin sopivia ratkaisumenetelmiä

Development and implementation of a computer-aided method for planning resident shifts in a hospital

Ce mémoire propose une formulation pour le problème de confection d'horaire pour résidents, un problème peu étudiée dans la litérature. Les services hospitaliers mentionnés dans ce mémoire sont le service de pédiatrie du CHUL (Centre Hospitalier de l'Université Laval) et le service des urgences de l'Hôpital Enfant-Jésus à Québec. La contribution principale de ce mémoîre est la proposition d'un cadre d'analyse pour l’analyse de techniques manuelles utilisées dans des problèmes de confection d'horaires, souvent décrits comme des problèmes d'optimisation très complexes. Nous montrons qu'il est possible d'utiliser des techniques manuelles pour établir un ensemble réduit de contraintes sur lequel la recherche d’optimisation va se focaliser. Les techniques utilisées peuvent varier d’un horaire à l’autre et vont déterminer la qualité finale de l’horaire. La qualité d’un horaire est influencée par les choix qu’un planificateur fait dans l’utilisation de techniques spécifiques; cette technique reflète alors la perception du planificateur de la notion qualité de l’horaire. Le cadre d’analyse montre qu'un planificateur est capable de sélectionner un ensemble réduit de contraintes, lui permettant d’obtenir des horaires de très bonne qualité. Le fait que l'approche du planificateur est efficace devient clair lorsque ses horaires sont comparés aux solutions heuristiques. Pour ce faire, nous avons transposées les techniques manuelles en un algorithme afin de comparer les résultats avec les solutions manuelles. Mots clés: Confection d’horaires, Confection d’horaires pour résidents, Creation manuelle d’horaires, Heuristiques de confection d’horaires, Méthodes de recherche localeThis thesis provides a problem formulation for the resident scheduling problem, a problem on which very little research has been done. The hospital departments mentioned in this thesis are the paediatrics department of the CHUL (Centre Hospitalier de l’Université Laval) and the emergency department of the Hôpital Enfant-Jésus in Québec City. The main contribution of this thesis is the proposal of a framework for the analysis of manual techniques used in scheduling problems, often described as highly constrained optimisation problems. We show that it is possible to use manual scheduling techniques to establish a reduced set of constraints to focus the search on. The techniques used can differ from one schedule type to another and will determine the quality of the final solution. Since a scheduler manually makes the schedule, the techniques used reflect the scheduler’s notion of schedule quality. The framework shows that a scheduler is capable of selecting a reduced set of constraints, producing manual schedules that often are of very high quality. The fact that a scheduler’s approach is efficient becomes clear when his schedules are compared to heuristics solutions. We therefore translated the manual techniques into an algorithm so that the scheduler’s notion of schedule quality was used for the local search and show the results that were obtained. Key words: Timetable scheduling, Resident scheduling, Manual scheduling, Heuristic schedule generation, Local search method

A hyper-heuristic with two guidance indicators for bi-objective mixed-shift vehicle routing problem with time windows

In this paper, a Mixed-Shift Vehicle Routing Problem is proposed based on a real-life container transportation problem. In a long planning horizon of multiple shifts, transport tasks are completed satisfying the time constraints. Due to the different travel distances and time of tasks, there are two types of shifts (long shift and short shift) in this problem. The unit driver cost for long shifts is higher than that of short shifts. A mathematical model of this Mixed-Shift Vehicle Routing Problem with Time Windows (MS-VRPTW) is established in this paper, with two objectives of minimizing the total driver payment and the total travel distance. Due to the large scale and nonlinear constraints, the exact search showed is not suitable to MS-VRPTW. An initial solution construction heuristic (EBIH) and a selective perturbation Hyper-Heuristic (GIHH) are thus developed. In GIHH, five heuristics with different extents of perturbation at the low level are adaptively selected by a high level selection scheme with the Hill Climbing acceptance criterion. Two guidance indicators are devised at the high level to adaptively adjust the selection of the low level heuristics for this bi-objective problem. The two indicators estimate the objective value improvement and the improvement direction over the Pareto Front, respectively. To evaluate the generality of the proposed algorithms, a set of benchmark instances with various features is extracted from real-life historical datasets. The experiment results show that GIHH significantly improves the quality of the final Pareto Solution Set, outperforming the state-of-the-art algorithms for similar problems. Its application on VRPTW also obtains promising results

An exact optimization approach for personnel scheduling problems in the call center industry

Dissertação de mestrado em Engenharia de SistemasNowadays, the importance of the call center industry is increasing because they are a major mean of communication between organizations and their costumers. So, ensuring good and optimized personnel schedules in call centers is crucial and has several advantages: reduction of total labor costs, reducing overstaffing, employees’ satisfaction, meeting their preferences, and costumers’ satisfaction, presenting acceptable waiting times. The considered problem concerns personnel scheduling in a 24/7 call center where the scheduling process is done manually. So, the main goal is to explore exact solution approaches in order to obtain solutions whose quality is preferable to the manually achieved ones and to reduce the processing time. The proposed optimization model is an Integer Programming model. The purpose of this model is to assign shifts to workers, while minimizing the total penalization that are associated to employees’ time preferences. The model is implemented on ILOG CPLEX Optimization Studio 12.7.0.0, using OPL, and tested with various instances, including randomly generated and real-world data instances. In order to analyze the quality of the model, a computational study of its linear relaxation was carried out, concluding that the model presents null integrality gaps in all the tested instances. So, the proposed model has a strong formulation, that is, a good quality model. Additionally, to evaluate the performance of the model when running large instances, several randomly generated instances were tested using ILOG CPLEX Optimization Studio 12.10.0.0, achieving good computational results.Hoje em dia, a importância da indústria dos call centers tem vindo a aumentar, uma vez que estes são um grande meio de comunicação entre as empresas e os respetivos clientes. Nesse sentido, garantir um bom e otimizado escalonamento de pessoal é crucial e traz consigo bastantes vantagens: redução dos custos totais de trabalho, reduzindo excesso de trabalhadores, aumento da satisfação dos empregados, atendendo às suas preferências, e ainda aumento da satisfação dos clientes, apresentando tempos de espera aceitáveis. O problema considerado envolve escalonamento de pessoal num call center que opera 24 horas por dia, 7 dias por semana. Atualmente, o processo de escalonamento é feito manualmente. Assim, o principal objetivo é explorar abordagens de resolução exata para obter soluções que apresentam qualidade preferível às das soluções obtidas até ao momento e para reduzir o tempo gasto em todo o processo. O modelo de otimização proposto é um modelo de Programação Inteira, cujo objectivo é associar turnos de trabalho aos trabalhadores, minimizando o total das penalizações associadas às preferências horárias dos mesmos. O modelo é implementado no ILOG CPLEX Optimization Studio 12.7.0.0, utilizando linguagem OPL, e testado com várias instâncias, incluindo instâncias geradas aleatoriamente e instâncias com dados reais. A análise da qualidade do modelo passou pelo estudo computacional da sua relaxação linear, podendo concluir-se que o modelo apresenta um intervalo de integralidade nulo em todas as instâncias testadas. Assim, o modelo proposto é um modelo forte, isto é, um modelo de boa qualidade. De forma a avaliar o desempenho do modelo a resolver instâncias grandes, várias instâncias geradas aletoriamente são testadas utilizando o software ILOG CPLEX Optimization Studio 12.10.0.0., apresentando bons resultados computacionais

Resource constrained routing and scheduling: Review and research prospects

In the service industry, it is crucial to efficiently allocate scarce resources to perform tasks and meet particular service requirements. What considerably complicates matters is when these resources, for example skilled technicians, nurses, and home carers have to visit different customer locations. This paper provides a comprehensive survey on resource constrained routing and scheduling that unveils the problem characteristics with respect to resource qualifications, service requirements and problem objectives. It also identifies the most effective exact and heuristic algorithms for this class of problems. The paper closes with several research prospects

Optimization Model for Base-Level Delivery Routes and Crew Scheduling

In the U.S. Air Force, a Logistic Readiness Squadron (LRS) provides material management, distribution, and oversight of contingency operations. Dispatchers in the LRS must quickly prepare schedules that meet the needs of their customers while dealing with real-world constraints, such as time windows, delivery priorities, and intermittent recurring missions. Currently, LRS vehicle operation elements are faced with a shortage of manpower and lack an efficient scheduling algorithm and tool. The purpose of this research is to enhance the dispatchers\u27 capability to handle flexible situations and produce good schedules within current manpower restrictions. In this research, a new scheduling model and algorithm are provided as an approach to crew scheduling for a base-level delivery system with a single depot. A Microsoft Excel application, the Daily Squadron Scheduler (DSS), was built to implement the algorithm. DSS combines generated duties with the concept of a set covering problem. It utilizes a Linear Programming pricing algorithm and Excel Solver as the primary engine to solve the problem. Reduced costs and shadow prices from subproblems are used to generate a set of feasible duties from which an optimal solution to the LP relaxation can be found. From these candidate duties the best IP solution is then found. The culmination of this effort was the development of both a scheduling tool and an analysis tool to guide the LRS dispatcher toward efficient current and future schedules

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

Approximate Algorithms for the Combined arrival-Departure Aircraft Sequencing and Reactive Scheduling Problems on Multiple Runways

The problem addressed in this dissertation is the Aircraft Sequencing Problem (ASP) in which a schedule must be developed to determine the assignment of each aircraft to a runway, the appropriate sequence of aircraft on each runway, and their departing or landing times. The dissertation examines the ASP over multiple runways, under mixed mode operations with the objective of minimizing the total weighted tardiness of aircraft landings and departures simultaneously. To prevent the dangers associated with wake-vortex effects, separation times enforced by Aviation Administrations (e.g., FAA) are considered, adding another level of complexity given that such times are sequence-dependent. Due to the problem being NP-hard, it is computationally difficult to solve large scale instances in a reasonable amount of time. Therefore, three greedy algorithms, namely the Adapted Apparent Tardiness Cost with Separation and Ready Times (AATCSR), the Earliest Ready Time (ERT) and the Fast Priority Index (FPI) are proposed. Moreover, metaheuristics including Simulated Annealing (SA) and the Metaheuristic for Randomized Priority Search (Meta-RaPS) are introduced to improve solutions initially constructed by the proposed greedy algorithms. The performance (solution quality and computational time) of the various algorithms is compared to the optimal solutions and to each other. The dissertation also addresses the Aircraft Reactive Scheduling Problem (ARSP) as air traffic systems frequently encounter various disruptions due to unexpected events such as inclement weather, aircraft failures or personnel shortages rendering the initial plan suboptimal or even obsolete in some cases. This research considers disruptions including the arrival of new aircraft, flight cancellations and aircraft delays. ARSP is formulated as a multi-objective optimization problem in which both the schedule\u27s quality and stability are of interest. The objectives consist of the total weighted start times (solution quality), total weighted start time deviation, and total weighted runway deviation (instability measures). Repair and complete regeneration approximate algorithms are developed for each type of disruptive events. The algorithms are tested against difficult benchmark problems and the solutions are compared to optimal solutions in terms of solution quality, schedule stability and computational time

Nurse Rostering Problems: A Bibliographic Survey

10.1016/S0377-2217(03)00021-3European Journal of Operational Research1513447-460EJOR