Personnel Scheduling Problems Research Articles

Nurse rostering: models and algorithms for theory, practice and integration with other problems

Nurse rostering is a personnel scheduling problem in health care in which shifts are assigned to nurses, subject to a large variety of constraints regarding personal preferences, organisational guidelines, and labour legislation. The present dissertation discusses models and algorithms for nurse rostering, treating three aspects: theory, practice and integration with other problems. This research contributes significantly to scientific, social and industrial aspects in the state of the art of nurse rostering. By studying simplified nurse rostering problems, a basic understanding of the problem’s complexity is established. These new insights identify a boundary between easy and hard problems, which strongly influences computational search approaches to the problem. Furthermore, issues regarding consistent constraint evaluation for long term rostering are exposed, and policies to address these issues are proposed. Computational experiments illustrate the importance of a consistent evaluation procedure and are employed to evaluate the presented policies. Despite the many academic contributions, few results find their way into practice. The present dissertation therefore attempts to bridge this gap by offering two contributions that aim at facilitating the implementation of academic results. First, a general model for nurse rostering problems is introduced, which is capable of representing a large variety of personal, organisational and legislative constraints. Second, an approach is introduced to automatically order constraints according to their priority extracted from historical data. For practitioners, this is a complex and unintuitive task, which nevertheless strongly influences the outcome of any algorithm for nurse rostering. These two contributions have been implemented in a commercial software package for personnel rostering, and are currently used in hospitals and other organisations in Europe. Finally, the scope of decision making is extended to include characteristics of

Duty and workstation rostering considering preferences and fairness: a case study at a department of anaesthesiology

This research addresses a personnel scheduling problem at hospitals. We present two mixed integer linear programming models – a duty-roster model and a workstation-roster model. The duty-roster model determines the assignment of physicians to 24-h and late duties whereas the workstation-roster model assigns physicians to actual workstations as operating rooms. The former serves as an input for the latter. In both models, we maximise the number of assignments subject to labour regulations and internal department-specific scheduling rules. Furthermore, we consider experience levels and qualifications in our models. To promote for job satisfaction, we take into account fairness aspects as well as individual physician preferences. Using real-world data from our cooperating department of anaesthesiology with 120 physicians, we set up a case study. Computational results indicate the superior quality compared to manual scheduling which is currently in use at our cooperation hospital. Furthermore, we develop an extensive computational study with 5800 instances to test the models. We show that the computational burden is negligible and we derive managerial insight for the scheduling process.

Polynomially solvable personnel rostering problems

Personnel rostering is a personnel scheduling problem in which shifts are assigned to employees, subject to complex organisational and contractual time-related constraints. Academic advances in this domain mainly focus on solving specific variants of this problem using intricate exact or (meta)heuristic algorithms, while little attention has been devoted to studying the underlying structure of the problems. The general assumption is that these problems, even in their most simplified form, are NP-hard. However, such claims are rarely supported with a proof for the problem under study. The present paper refutes this assumption by presenting minimum cost network flow formulations for several personnel rostering problems. Additionally, these problems are situated among the existing academic literature to obtain insights into what makes personnel rostering hard.

A Compact Formulation of “Scheduling Security Personnel for the Vancouver 2010 Winter Olympic Games”

This note provides a compact integer linear programming formulation of the personnel scheduling problem presented in the article by B. L. Kaluzny and A. Hill, INFOR, Vol. 49, No. 3, August 2011, pp. 221–231. This formulation is easily solved to optimality by available solvers and results in less total unmet demand (overtime).

CONSTRAINT SOVLING ENGINE BASED NURSE ROSTERING WITH INTELLIGENT BACKTRACKING

Efficient utilization of time and effort is essenti al in Personnel scheduling problems to evenly balan ce the workload among the people and attempt to satisfy th e personnel preferences. In Constraint Satisfaction Problem based scheduling problems, when a branch of the search fails the backtracking search algorithm back up to the preceding variable and try a differe nt value for it. So here the most recent decision p oint is revisited. Its run-time complexity for most nontriv ial problems is still exponential. A solution is in telligent backtracking scheme in which backtracking is done directly to the variable that caused the failure. Th is study proposes Constraint Satisfaction Problem base d Nurse Rostering using Intelligent Backtracking approach. The proposed Minimal Critical Set based I ntelligent Backtracking (MCS-IBT) algorithm incorporates Critical Set detection which is follow ed by Minimal Critical Set reduction in order to re duce the search space for nurse rostering. MCS_IBT overcomes missing good MCSs by visiting optimal number of sets. This study finds its applications in sched uling, temporal reasoning, graph problems, floor pl an design, the planning of genetic experiments and the satisfiability problems. The implemented system is tested on the real life data from the hospital and the results shown remarkable performance.

A stochastic optimization model for shift scheduling in emergency departments

Excessive waiting time in Emergency Departments (ED) can be both a cause of frustration and more importantly, a health concern for patients. Waiting time arises when the demand for work goes beyond the facility's service capacity. ED service capacity mainly depends on human resources and on beds available for patients. In this paper, we focus on human resources organization in an ED and seek to best balance between service quality and working conditions. More specifically, we address the personnel scheduling problem in order to optimize the shift distribution among employees and minimize the total expected patients' waiting time. The problem is also characterized by a multi-stage re-entrant service process. With an appropriate approximation of patients' waiting times, we first propose a stochastic mixed-integer programming model that is solved by a sample average approximation (SAA) approach. The resulting personnel schedules are then evaluated using a discrete-event simulation model. Numerical experiments are then performed with data from a French hospital to compare different personnel scheduling strategies.

An assessment of a days off decomposition approach to personnel shift scheduling

This paper studies a two-phase decomposition approach to solving 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 into 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 the first 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, but the quality, though often good, depends strongly on the instance at hand. Our analysis identifies which aspects in the instance can jeopardize the quality.

A multistage approach for an employee timetabling problem with a high diversity of shifts as a solution for a strongly varying workforce demand

This work deals with the employee rostering problem at the airport. Such problems, related to the time varying demand of the transport services, use many (e.g., about a hundred) diverse shifts to cover the workforce demand during the day. Together with the strict constraints, given by the collective agreement, the problem becomes difficult to solve. Algorithms commonly used for solving the usual employee rostering problems produce poor quality rosters, which are unusable in practice. This paper suggests a three stage approach allowing one to solve the employee rostering problems where a huge set of different shifts is used to satisfy the coverage requirements. The solution is based on the problem transformation to a simpler problem, thereupon, an evolutionary algorithm is used to determine a rough position of the shifts in the roster. Afterwards, the maximal weighted matching in the bipartite graph is applied as the inverse transformation of the problem and the final roster is obtained by the optimization based on a Tabu Search algorithm. This multistage approach is compared to other approaches. Furthermore, an evaluation methodology was proposed in order to make a complex and fair comparison. Its objective is to verify the contribution of the particular stages used in the different approaches applied on the different personnel scheduling problems.

Monthly clinic assignments for internal medicine housestaff

This article presents a new model for constructing monthly clinic schedules for interns and residents (i.e., housestaff) training in Internal Medicine. Clinical experiences during the three years of residency occur in inpatient and outpatient settings, and on generalist and specialist clinical services. These experiences include spending time in a primary care setting caring for an assigned group of patients over time. Housestaff rotate through different clinical experiences monthly, with their primary care clinic time overlaid longitudinally on these other clinical services. The exact amount of primary care time spent varies between clinical rotations. In fact, it is the variable clinic hour requirements that drive the scheduling process, and is what distinguishes our problem from most personnel scheduling problems. Typically, staff schedules are driven by shift or hourly demand and are designed to minimize some measure of cost. The objective in our work is to both maximize clinic utilization and minimize the number of violations of a prioritized set of goals while ensuring that certain clinic-level and individual constraints are satisfied. The corresponding problem is formulated as an integer goal program in which several of the hard constraints are temporarily allowed to be violated to avoid infeasibility. To find solutions, a three-phase methodology is proposed. In the first phase (pre-processing step), clinic assignments for a subset of the housestaff are either fixed or excluded each month in light of restrictions imposed by their current rotation. In the second phase, tentative solutions are obtained with a commercial solver. In the final phase (post-processing step), all violations of the relaxed hard constraints are removed and an attempt is made to lexicographically reduce violations of the major goals. The effectiveness of the methodology is demonstrated by analyzing eight monthly rosters provided by the Internal Medicine Residency Program at the University of Texas Health Science Center in San Antonio. On average, we found that up to 7.62% more clinic sessions could be assigned each month using our methodology, and that the corresponding rosters admitted an average of 37% fewer violations for 9 out of the 11 soft constraints than did the actual schedules worked.

A three-stage approach for aircraft line maintenance personnel rostering using MIP, discrete event simulation and DEA

Personnel scheduling problems need to cope with personnel preferences, coverage constraints, legal restrictions, and many other constraints. We present a three-stage methodology that can be used to select personnel rosters. In the first stage we generate multiple personnel rosters with a mathematical programming model. In the second stage, the performance of the rosters regarding a number of service criteria is evaluated through discrete event simulation. In the third stage, a ranking is made using data envelopment analysis. The methodology is tested on a personnel scheduling problem for aircraft line maintenance.

Personnel scheduling: A literature review

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.

Network flow models for intraday personnel scheduling problems

Personnel scheduling problems can be decomposed into two stages. In the first stage for each employee the working days have to be fixed. In the second stage for each day of the planning period an intraday scheduling problem has to be solved. It consists of the assignment of shifts to the employees who have to work on the day and for each working period of an employee a task assignment such that the demand of all tasks for personnel is covered. In Robinson et al. (Burke and Trick (Eds.), Proceedings of the 5th International Conference on the Practice and Theory of Automated Timetabling, 18th August–20th August 2004, Pittsburgh, PA, USA, pp. 561–566, 2005), the intraday problem has been formulated as a maximum flow problem. The assumptions are that, employees are qualified for all tasks, their shifts are given, and they are allowed to change tasks during the day. In this work, we extend the network flow model to cover the case where not all employees are qualified to perform all tasks. The model is further extended to be able to calculate shifts of employees for the given day, assuming that an earliest starting time, a latest finishing time, and a minimal working time are given. Labour cost can be also taken into account by solving a minimum cost network flow problem.

An Evolutionary Squeaky Wheel Optimisation Approach to Personnel Scheduling

The quest for robust heuristics that are able to solve more than one problem is ongoing. In this paper, we present, discuss and analyse a technique called Evolutionary Squeaky Wheel Optimisation and apply it to two different personnel scheduling problems. Evolutionary Squeaky Wheel Optimisation improves the original Squeaky Wheel Optimisation's effectiveness and execution speed by incorporating two extra steps (Selection and Mutation) for added evolution. In the Evolutionary Squeaky Wheel Optimisation, a cycle of Analysis-Selection-Mutation-Prioritization-Construction continues until stopping conditions are reached. The aim of the Analysis step is to identify below average solution components by calculating a fitness value for all components. The Selection step then chooses amongst these underperformers and discards some probabilistically based on fitness. The Mutation step further discards a few components at random. Solutions can become incomplete and thus repairs may be required. The repairs are carried out by using the Prioritization to first produce priorities that determine an order by which the following Construction step then schedules the remaining components. Therefore, improvement in the Evolutionary Squeaky Wheel Optimisation is achieved by selective solution disruption mixed with interative improvement and constructive repair. Strong experimental results are reported on two different domains of personnel scheduling: bus and rail driver scheduling and hospital nurse scheduling.

A multi-agent-based approach for personnel scheduling in assembly centers

This paper presents a multi-agent-based approach for personnel scheduling problems in the context of a paced multi-product assembly center. Our purpose is to elaborate daily assignment of employees to workstations in order to minimize simultaneously the operational costs and personnel dissatisfactions. The proposed approach considers the individual competencies, mobility and preferences of each employee, as well as the personnel and competency requirements associated with each assembly activity given both the current master assembly schedule and the line balancing for each product. To benchmark the performance of the multi-agent approach, we use optimal solutions obtained through a linear programming model resolution using a commercial solver. Experimental results show that our multi-agent approach can produce high-quality and efficient solutions in a short computational time.

An Evolutionary Squeaky Wheel Optimization Approach to Personnel Scheduling

The quest for robust heuristics that are able to solve more than one problem is ongoing. In this paper, we present, discuss and analyze a technique called Evolutionary Squeaky Wheel Optimization and apply it to two different personnel scheduling problems. Evolutionary Squeaky Wheel Optimization improves the original squeaky wheel optimization's effectiveness and execution speed by incorporating two additional steps (selection and mutation) for added evolution. In the evolutionary squeaky wheel optimization, a cycle of analysis-selection-mutation-prioritization-construction continues until stopping conditions are reached. The aim of the analysis step is to identify below average solution components by calculating a fitness value for all components. The selection step then chooses amongst these underperformers and discards some probabilistically based on fitness. The mutation step further discards a few components at random. Solutions can become incomplete and thus repairs may be required. The repair is carried out by using the prioritization step to first produce priorities that determine an order by which the following construction step then schedules the remaining components. Therefore, improvements in the evolutionary squeaky wheel optimization is achieved by selective solution disruption mixed with iterative improvement and constructive repair. Strong experimental results are reported on two different domains of personnel scheduling: bus and rail driver scheduling and hospital nurse scheduling.

A hybrid metaheuristic case-based reasoning system for nurse rostering

In this paper we present a novel Case-Based Reasoning (CBR) system called CABAROST (CAsed-BAsed ROSTering) which was developed for personnel scheduling problems. CBR is used to capture and store examples of personnel manager behaviour which are then used to solve future problems. Previous examples of constraint violations in schedules and the repairs that were used to solve the violations are stored as cases. The sequence in which violations are repaired can have a great impact on schedule quality. A novel memetic algorithm is proposed which evolves good quality sequences of repairs generated by CABAROST. The algorithm was tested on instances of the real-world nurse rostering problem at the Queens Medical Centre NHS Trust in Nottingham.

Competency and preference based personnel scheduling in large assembly lines

This paper introduces a formal description and mathematical modelling of the personnel scheduling problem in the context of a paced multi-product assembly centre. The model explicitly takes into consideration the individual competencies; mobility and preferences of each worker, as well as the personnel and competency requirements associated with each assembly activity given both the current master assembly schedule and the line balancing for each product. The paper then validates and analyses the performance of the model through the optimal resolution of a small yet representative case using a commercial solver. For simplicity, we focus on the deterministic case; however the stochastic case will be discussed in the future research.

A (0–1) goal programming model for scheduling the tour of a marketing executive

This paper addresses the problem of scheduling the tour of a marketing executive (ME) of a large electronics manufacturing company in India. In this problem, the ME has to visit a number of customers in a given planning period. The scheduling problem taken up in this study is different from the various personnel scheduling problems addressed in the literature. This type of personnel scheduling problem can be observed in many other situations such as periodical visits of inspection officers, tour of politicians during election campaigns, tour of mobile courts, schedule of mobile stalls in various areas, etc. In this paper the tour scheduling problem of the ME is modeled using (0–1) goal programming (GP). The (0–1) GP model for the data provided by the company for 1 month has 802 constraints and 1167 binary variables. The model is solved using LINDO software package. The model takes less than a minute (on a 1.50 MHz Pentium machine with 128 MB RAM) to get a solution of the non-preemptive version and about 6 days for the preemptive version. The main contribution is in problem definition and development of the mathematical model for scheduling the tour.

Mining the data from a hyperheuristic approach using associative classification

Associative classification is a promising classification approach that utilises association rule mining to construct accurate classification models. In this paper, we investigate the potential of associative classifiers as well as other traditional classifiers such as decision trees and rule inducers in solutions (data sets) produced by a general-purpose optimisation heuristic called the hyperheuristic for a personnel scheduling problem. The hyperheuristic requires us to decide which of several simpler search neighbourhoods to apply at each step while constructing a solutions. After experimenting 16 different solution generated by a hyperheuristic called Peckish using different classification approaches, the results indicated that associative classification approach is the most applicable approach to such kind of problems with reference to accuracy. Particularly, associative classification algorithms such as CBA, MCAR and MMAC were able to predict the selection of low-level heuristics from the data sets more accurately than C4.5, RIPPER and PART algorithms, respectively.

A Neural Network Application in Personnel Scheduling

In this paper, we present and evaluate a neural network model for solving a typical personnel-scheduling problem, i.e. an airport ground staff rostering problem. Personnel scheduling problems are widely found in servicing and manufacturing industries. The inherent complexity of personnel scheduling problems has normally resulted in the development of integer programming-based models and various heuristic solution procedures. The neural network approach has been admitted as a promising alternative to solving a variety of combinatorial optimization problems. While few works relate neural network to applications of personnel scheduling problems, there is great theoretical and practical value in exploring the potential of this area. In this paper, we introduce a neural network model following a relatively new modeling approach to solve a real rostering case. We show how to convert a mixed integer programming formulation to a neural network model. We also provide the experiment results comparing the neural network method with three popular heuristics, i.e. simulated annealing, Tabu search and genetic algorithm. The computational study reveals some potential of neural networks in solving personnel scheduling problems.