Shift rostering using decomposition: assign weekend shifts first

This paper introduces a shift rostering problem that surprisingly has not been studied in literature: the weekend shift rostering problem. It is motivated by our experience that employees’ shift preferences predominantly focus on the weekends, since many social activities happen during weekends. The Weekend Rostering Problem (WRP) addresses the rostering of weekend shifts, for which we design a problem specific heuristic. We consider the WRP as the first phase of the shift rostering problem. To complete the shift roster, the second phase assigns the weekday shifts using an existing algorithm. We discuss effects of this two-phase approach both on the weekend shift roster and on the roster as a whole. We demonstrate that our first-phase heuristic is effective both on generated instances and real-life instances. For situations where the weekend shift roster is one of the key determinants of the quality of the complete roster, our two-phase approach shows to be effective when incorporated in a commercially implemented algorithm

Optimal staffing under an annualized hours regime using Cross-Entropy optimization

This paper discusses staffing under annualized hours. Staffing is the selection of the most cost-efficient workforce to cover workforce demand. Annualized hours measure working time per year instead of per week, relaxing the restriction for employees to work the same number of hours every week. To solve the underlying combinatorial optimization problem this paper develops a Cross-Entropy optimization implementation that includes a penalty function and a repair function to guarantee feasible solutions. Our experimental results show Cross-Entropy optimization is efficient across a broad range of instances, where real-life sized instances are solved in seconds, which significantly outperforms an MILP formulation solved with CPLEX. In addition, the solution quality of Cross-Entropy closely approaches the optimal solutions obtained by CPLEX. Our Cross-Entropy implementation offers an outstanding method for real-time decision making, for example in response to unexpected staff illnesses, and scenario analysis

An assessment of a days off decomposition approach to personnel scheduling

This paper studies a two-phase decomposition approach to solve the personnel scheduling problem. The first phase creates a days off schedule, indicating working days and days off for each employee. The second phase assigns shifts to the working days in the days off schedule. This decomposition is motivated by the fact that personnel scheduling constraints are often divided in two categories: one specifies constraints on working days and days off, while the other specifies constraints on shift assignments. To assess the consequences of the decomposition approach, we apply it to public benchmark instances, and compare this to solving the personnel scheduling problem directly. In all steps we use mathematical programming. We also study the extension that includes night shifts in thefirst phase of the decomposition. We present a detailed results analysis, and analyze the effect of various instance parameters on the decompositions' results. In general, we observe that the decompositions significantly reduce the computation time, and that they produce good solutions for most instances

A Two-Stage Dynamic Programming Model for Nurse Rostering Problem Under Uncertainty

No abstract provided.Master of Science in EngineeringIndustrial and Manufacturing Systems Engineering, College of Engineering and Computer ScienceUniversity of Michigan-Dearbornhttps://deepblue.lib.umich.edu/bitstream/2027.42/140733/1/WENJIE WANG_Thesis_Embedded.pdfDescription of WENJIE WANG_Thesis_Embedded.pdf : Thesi

A stochastic integer programming approach to reserve staff scheduling with preferences

Nowadays, reaching a high level of employee satisfaction in efficient schedules is an important and difficult task faced by companies. We tackle a new variant of the personnel scheduling problem under unknown demand by considering employee satisfaction via endogenous uncertainty depending on the combination of their preferred and received schedules. We address this problem in the context of reserve staff scheduling, an unstudied operational problem from the transit industry. To handle the challenges brought by the two uncertainty sources, regular employee and reserve employee absences, we formulate this problem as a two-stage stochastic integer program with mixed-integer recourse. The first-stage decisions consist in finding the days off of the reserve employees. After the unknown regular employee absences are revealed, the second-stage decisions are to schedule the reserve staff duties. We incorporate reserve employees' days-off preferences into the model to examine how employee satisfaction may affect their own absence rates.Comment: 25 pages, 4 figures, submitted to International Transactions in Operational Researc

A stochastic integer programming approach to reserve staff scheduling with preferences

De nos jours, atteindre un niveau élevé de satisfaction des employés à l’intérieur d’horaires efficients est une tâche importante et ardue à laquelle les compagnies font face. Dans ce travail, nous abordons une nouvelle variante du problème de création d’horaire de personnel face à une demande inconnue, en tenant compte de la satisfaction des employés via l’incertitude endogène qui découle de la combinaison des préférences des employés envers les horaires, et de ceux qu’ils reçoivent. Nous abordons ce problème dans le contexte de la création d’horaire d’employés remplaçants, un problème opérationnel de l’industrie du transport en commun qui n’a pas encore été étudié, bien qu’assez présent dans les compagnies nord-américaines. Pour faire face aux défis qu’amènent les deux sources d’incertitude, les absences des employés réguliers et des employés remplaçants, nous modélisons ce problème en un programme stochastique en nombres entiers à deux étapes avec recours mixte en nombres entiers. Les décisions de première étape consistent à trouver les journées de congé des employés remplaçants. Une fois que les absences inconnues des employés réguliers sont révélées, les décisions de deuxième étape consistent à planifier les tâches des employés remplaçants. Nous incorporons les préférences des employés remplaçants envers les journées de congé dans notre modèle pour observer à quel point la satisfaction de ces employés peut affecter leurs propres taux d’absence. Nous validons notre approche sur un an de données de la ville de Los Angeles. Notre travail est présentement en cours d’implémentation chez un fournisseur mondial de solutions logicielles pour les opérations de transport en commun.Nowadays, reaching a high level of employee satisfaction in efficient schedules is an important and difficult task faced by companies. In this work, we tackle a new variant of the personnel scheduling problem under unknown demand by considering employee satisfaction via endogenous uncertainty depending on the combination of their preferred and received schedules. We address this problem in the context of reserve staff scheduling, an operational problem from the transit industry that has not yet been studied, although rather present in North American transit companies. To handle the challenges brought by the two uncertainty sources, regular employee and reserve employee absences, we formulate this problem as a two-stage stochastic integer program with mixed-integer recourse. The first-stage decisions consist in finding the days off of the reserve employees. After the unknown regular employee absences are revealed, the second-stage decisions are to schedule the reserve staff duties. We incorporate reserve employees’ preferences for days off into the model to examine how employee satisfaction may affect their own absence rates. We validate our approach on one year of data from the city of Los Angeles. Our work is currently being implemented in a world-leader software solutions provider for public transit operations

Strategic Nurse Allocation Policies Under Dynamic Patient Demand

ABSTRACT STRATEGIC NURSE ALLOCATION POLICIES UNDER DYNAMIC PATIENT DEMAND by Osman T. Aydas The University of Wisconsin-Milwaukee, 2017 Under the Supervision of Professor Anthony D. Ross Several studies have shown a strong association between nurse staffing and patient outcomes. When a nursing unit is chronically short-staffed, nurses must maintain an intense pace to ensure that patients receive timely care. Over time this can result in nurse burnout, as well as dissatisfied patients and even medical errors. Improved accuracy in the allocation of nursing staff can mitigate these operational risks and improve patient outcomes. Nursing care is identified as the single biggest factor in both the cost of hospital care and patient satisfaction. Yet, there is widespread dissatisfaction with the current methods of determining nurse staffing levels, including the most common one of using minimum nurse-to-patient ratios. Nurse shortage implications go beyond healthcare quality, extending to health economics as well. In addition, implementation of mandatory nurse-to-patient ratios in some states creates a risk of under- or over-estimating required nurse resources. With this motivation, this dissertation aims to develop methodologies that generate feasible six-week nurse schedules and efficiently assign nurses from various profiles to these schedules while controlling staffing costs and understaffing ratios in the medical unit. First, we develop and test various medium-term staff allocation approaches using mixed-integer optimization and compare their performance with respect to a hypothetical full information scenario. Second, using stochastic integer programming approach, we develop a short-term staffing level adjustment model under a sizable list of patient admission scenarios. We begin by providing an overview of the organization of the dissertation. Chapter 1 presents the problem context and we provide research questions for this dissertation. Chapter 2 provides a review of the literature on nurse staffing and scheduling specifically from the Operations Management journals. We introduce the challenges of nursing care and nurse scheduling practices. We identify major research areas and solution approaches. This is followed by a discussion of the complexities associated with computing nursing requirements and creating rosters. Staffing requirements are the result of a complex interaction between care-unit sizes, nurse-to-patient ratios, bed census distributions, and quality-of-care requirements. Therefore, we review the literature on nursing workload measurement approaches because workloads depend highly on patient arrivals and lengths of stay, both of which can vary greatly. Thus, predicting these workloads and staffing nurses accordingly are essential to guaranteeing quality of care in a cost-effective manner. For completeness, a brief review of the literature on workforce planning and scheduling that is linked to the nurse staffing and scheduling problem is also provided. Chapter 3 develops a framework for estimating the daily number of nurses required in Intensive Care Units (ICUs). Many patient care units, including ICUs, find it difficult to accurately estimate the number of nurses needed. One factor contributing to this difficulty is not having a decision support tool to understand the distribution of admissions to healthcare facilities. We statistically evaluate the existing staff allocation system of an ICU using clinical operational data, then develop a predictive model for estimating the number of admissions to the unit. We analyze clinical operational data covering 44 months for three wards of a pediatric ICU. The existing staff allocation model does not accurately estimate the required number of nurses required. This is due in part to not understanding the pattern and frequency of admissions, particularly those which are not known 12 hours in advance. We show that these “unknown” admissions actually follow a Poisson distribution. Thus, we can more accurately estimate the number of admissions overall. Analytical predictive methods that complement intuition and experience can help to decrease unplanned requirements for nurses and recommend more efficient nurse allocations. The model developed here can be inferred to estimate admissions for other intensive care units, such as pediatric facilities. Chapter 4 examines an integrated nurse staffing and scheduling model for a Pediatric Intensive Care Unit (PICU). This model is targeted to recommend initial staffing plans and schedules for a six-week horizon given a variety of nurse groups and nursing shift assignment types in the PICU. Nurse rostering is an NP-hard combinatorial problem, which makes it extremely difficult to efficiently solve life-sized problems due to their complexity. Usually, real problem instances have complicated work rules related to safety and quality of service issues, as well as preferences of the personnel. To avoid the size and complexity limitations, we generate feasible nurse schedules for the full-time equivalent (FTE) nurses, using algorithms that will be employed in the mixed-integer programming models we develop. Pre-generated schedules eliminate the increased number of constraints, and reduce the number of decision variables of the integrated nurse staffing and scheduling model. We also include a novel methodology for estimating nurse workloads by considering the patient, and individual patient’s acuity, and activity in the unit. When the nursing administration prepares the medium-term nurse schedules for the next staffing cycle (six weeks in our study), one to two months before the actual patient demand realizations, it typically uses a general average staffing level for the nursing care needs in the medical units. Using our mixed-integer optimization model, we examine fixed vs. dynamic medium-term nurse staffing and scheduling policy options for the medical units. In the fixed staffing option, the medical unit is staffed by a fixed number of nurses throughout the staffing horizon. In the dynamic staffing policy, we propose, historical patient demand data enables us to suggest a non-stationary staffing scheme. We compare the performance of both nurse allocation policy options, in terms of cost savings and understaffing ratios, with the optimal staffing scheme reached by the actual patient data. As a part of our experimental design, we evaluate our optimization model for the three medical units of the PICU in the “as-is” state. In Chapter 5, we conduct two-stage short-term staffing adjustments for the upcoming nursing shift. Our proposed adjustments are first used at the beginning of each nursing shift for the upcoming 4-hour shift. Then, after observing actual patient demand for nursing at the start of the next shift, we make our final staffing adjustments to meet the patient demand for nursing. We model six different adjustment options for the two-stage stochastic programming model (five options available as first-stage decisions and one option available as the second-stage decision). Because the adjustment horizon is less than 12 hours, the current patient census, patient acuity, and the number of scheduled admissions/discharges in the current and upcoming shift are known to the unit nurse manager. We develop a two-stage stochastic integer programming model which will minimize total nurse staffing costs (and the cost of adjustments to the original schedules developed in the medium-term planning phase) while ensuring adequate coverage of nursing demand. Chapter 6 provides conclusions from the study and identify both limitations and future research directions

Lomien kustannustehokas suunnittelu vaihtelevan kysynnän ja vaihtelevan työvoiman määrän tilanteessa

Vacation planning can be a complicated process as multiple law and contract based rules must be respected, while at the same time the wishes of employees must be taken into account. The problem is especially difficult in transit industry, where demand and available manpower can vary and the products of transit industry have no shelf life. Also, temporary workers cannot be recruited as long training is needed. In this thesis, a constraint programming formulation for solving vacation planning problems is developed. Constraint programming allows modeling each vacation as a single interval variable. This makes the approach more effective than modeling the problem as MILP, which would require a large amount of additional constraints and variables to model the problem, especially the consecutiveness of vacations. The objective of vacation planning is to find a solution, which has as large as possible minimum reserve of employees after all vacations are assigned. An additional objective of minimizing maximum reserve is introduced to even out the distribution of reserve. The problem is solved to optimality with a commercial optimization solver with running times varying from a few seconds to three minutes. The results of two real world cases of a transportation company show that the model provides improvement in solution quality and the planning time needed is reduced considerably. The issue of planning vacations has received little attention in literature. In many cases the vacations are planned by mutual agreement or a named employee assigns vacations by hand. This can result in a lot of manual labor after which the solution quality might still be poor. This thesis presents the first constraint programming based approach for planning employees’ vacations. It allows the modeling of multiple constraints that are used to improve solution quality, and takes into account the preferences of the employees, the planning personnel and the company.Lomien suunnittelu voi olla hankala prosessi, koska lain ja työehtosopimuksen asettamia rajoitteita pitää kunnioittaa ja samalla työntekijöiden toiveet pitää ottaa huomioon. Ongelma on erityisen hankala kuljetusalalla, koska kysyntä ja työvoiman määrä voivat vaihdella, ja kuljetuksia ei voi laittaa varastoon. Lisäksi väliaikaisia työntekijöitä ei voida palkata vaadittavan pitkän koulutuksen vuoksi. Tässä työssä kehitetään rajoiteohjelmointimalli (engl. constraint programming), jota käytetään lomien suunnitteluongelman ratkaisemiseen. Rajoiteohjelmointi mahdollistaa yksittäisen loman mallintamisen yhtenä intervallimuuttujana. Tämä tekee lähestymistavasta paljon tehokkaamman kuin ongelman mallintaminen MILP-tehtävänä, mikä vaatii monia lisärajoitteita ja –muuttujia, erityisesti lomien yhdenjaksoisuuden mallintamiseksi. Lomien suunnittelussa on tavoitteena tuottaa ratkaisu, jossa on mahdollisimman suuri minimityöntekijäreservi lomien kiinnittämisen jälkeen. Lisätavoitteena otetaan käyttöön suurimman reservin minimointi, mikä tasoittaa reservin ajallista jakautumista. Ongelma ratkaistaan optimiin kaupallisella optimointiohjelmistolla ja ratkaisuajat vaihtelevat muutamista sekunneista kolmeen minuuttiin. Kaksi oikeaan dataan perustuvaa esimerkkitapausta näyttävät, että kehitetty malli parantaa tulosten laatua ja vähentää huomattavasti lomien suunnitteluun tarvittavia työtunteja. Lomien suunnittelu on saanut vain vähän huomiota kirjallisuudessa. Monissa tapauksissa lomat suunnitellaan yhteisellä sopimisella tai yksi työntekijä suunnittelee käsin kaikkien lomien ajankohdat. Tämä voi vaatia paljon manuaalista työtä ja silti tulosten laatu voi olla huono. Tässä tutkielmassa esitetään ensimmäinen rajoiteohjelmointiin perustuva lähestymistapa työntekijöiden lomien suunnitteluun, mikä mahdollistaa useiden ratkaisujen laatua parantavien rajoitteiden mallintamisen, ottaen huomioon työntekijöiden, henkilöstösuunnittelijoiden ja työnantajan preferenssit