Applications of Mathematical Programming in Personnel Scheduling

In the few decades of its existence, mathematical programming has evolved into an important branch of operations research and management science. This thesis consists of four papers in which we apply mathematical programming to real-life personnel scheduling and project management problems. We develop exact mathematical programming formulations. Furthermore, we propose effective heuristic strategies to decompose the original problems into subproblems that can be solved effciently with tailored mathematical programming formulations. We opt for solution methods that are based on mathematical programming, because their advantages in practice are a) the exibility to easily accommodate changes in the problem setting, b) the possibility to evaluate the quality of the solutions obtained, and c) the possibility to use general-purpose solvers, which are often the only software available in practice

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

Manpower planning optimization in three different real world areas: container terminals, hospitals and retail stores

Problems related to the optimization of human resources in working areas have been extensively studied in the literature with the major goal of guaranteeing the greatest benefits from the efforts of workers, while taking into account their personal skills and requirements. In particular, in this thesis we focus on short-term and long-term manpower planning problems. The main goal consists in appropriately assigning shifts to workers in a given time horizon, taking into account their own requirements, their contractual rules, and the quality and efficiency of the work environment. In this thesis the manpower planning problem is studied in three different working areas, namely container terminals, hospitals and retail stores. Different solutions are proposed based on mathematical models that allow to describe in linear algebraic terms the set of feasible solutions. An optimal scheduling is then computed using linear integer programming. The proposed policies have been validated on three different real case studies in Cagliari, Italy

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

Taxonomic classification of planning decisions in health care: a review of the state of the art in OR/MS

We provide a structured overview of the typical decisions to be made in resource capacity planning and control in health care, and a review of relevant OR/MS articles for each planning decision. The contribution of this paper is twofold. First, to position the planning decisions, a taxonomy is presented. This taxonomy provides health care managers and OR/MS researchers with a method to identify, break down and classify planning and control decisions. Second, following the taxonomy, for six health care services, we provide an exhaustive specification of planning and control decisions in resource capacity planning and control. For each planning and control decision, we structurally review the key OR/MS articles and the OR/MS methods and techniques that are applied in the literature to support decision making

A survey of workforce scheduling and routing

In the context of workforce scheduling, there are many scenarios in which personnel must carry out tasks at different locations hence requiring some form of transportation. Examples of these type of scenarios include nurses visiting patients at home, technicians carrying out repairs at customers' locations, security guards performing rounds at different premises, etc. We refer to these scenarios as Workforce Scheduling and Routing Problems (WSRP) as they usually involve the scheduling of personnel combined with some form of routing in order to ensure that employees arrive on time to the locations where tasks need to be performed. This kind of problems have been tackled in the literature for a number of years. This paper presents a survey which attempts to identify the common attributes of WSRP scenarios and the solution methods applied when tackling these problems. Our longer term aim is to achieve an in-depth understanding of how to model and solve workforce scheduling and routing problems and this survey represents the first step in this quest

A survey of workforce scheduling and routing

In the context of workforce scheduling, there are many scenarios in which personnel must carry out tasks at different locations hence requiring some form of transportation. Examples of these type of scenarios include nurses visiting patients at home, technicians carrying out repairs at customers' locations, security guards performing rounds at different premises, etc. We refer to these scenarios as Workforce Scheduling and Routing Problems (WSRP) as they usually involve the scheduling of personnel combined with some form of routing in order to ensure that employees arrive on time to the locations where tasks need to be performed. This kind of problems have been tackled in the literature for a number of years. This paper presents a survey which attempts to identify the common attributes of WSRP scenarios and the solution methods applied when tackling these problems. Our longer term aim is to achieve an in-depth understanding of how to model and solve workforce scheduling and routing problems and this survey represents the first step in this quest

Service supply chain management : a hierarchical decision modeling approach

A Service Supply Chain (SSC) may be described as a network of service provider facilities (in-house or outsourced), each of which is able to process one or more service tasks on an as needed basis. Two key characteristics of a SSC are (i) the business service is decomposable into several sequential tasks that can be processed by different service providers, and (ii) the primary capacity resource is skilled labor. SSCs are increasingly being developed by companies that experience a high variability of demand for their services (e.g., loan processing, analytical consulting services, emergency repair crews, claims processing, etc.). Typically, the customer wait time penalty is very high, to the extent that if the service is not provided within a certain time, the customer service request will abort. As a result, the service provider needs to maintain sufficient processing capacity to meet peak levels of demand. The primary advantage of a SSC, relative to a traditional dedicated facility, is that the processing capacity (labor) can be economically adjusted (lower hiring and firing costs) to match changes in the current demand level. In this dissertation, a hierarchical framework for modeling the decision structure in SSCs is developed. This framework introduces and defines the key SSC entities: service products, service jobs, service providers, and the parameters for characterizing the demand behavior. As part of the framework two problems are formulated and solved. First, given that Service Supply Chains are intended to be dynamic delivery networks that efficiently respond to demand variations, a strategic problem is which candidate service providers are selected to form the SSC network, and how the service tasks are assigned within the provider network. The problem is formulated and solved as a binary program. Second, a consequent tactical problem is how the workforce level at each service provider is dynamically adjusted (hiring and firing) as the real time demand data comes in the problem is formulated and solved as a linear program that bounds a mixed integer program (MIP). The strategic model takes the demand parameters, the competing providers’ information, and the service and tasks parameters, to select the providers that are going to become part of the SSC and assign tasks to them. A method to quantify cumulative demand variation per seasonal cycle is presented to derive aggregate demand parameters from the forecast. The design objective of the strategic model is to minimize set up cost and projected operational cost. The objective is achieved by simultaneously minimizing capital cost, hiring cost, firing cost, service delay cost, excess capacity cost, labor cost, and quality cost while fulfilling the capacity, tasks assignment, facility installation, and task capability constraints. The tactical model is constrained by the providers and task assignment resulting from the strategic model. It uses a more accurate demand forecast, and minimizes actual operational costs represented by hiring cost, firing cost, backlog cost and labor cost, while fulfilling the production balance, routing, capacity, workforce balance and demand constraints. It is solved in two phases. A relaxed model is solved as an LP and its solution is used for bounding a MIP problem. Finally, the behavior of the two models is studied by performing numerical experiments changing key supply chain parameters such as hiring and firing cost, demand variability, labor cost, and backlog cost