Rostering Problem Research Articles

Multi-agent deep Q-network-based metaheuristic algorithm for Nurse Rostering Problem

The Nurse Rostering Problem (NRP) aims to create an efficient and fair work schedule that balances both the needs of employees and the requirements of hospital operations. Traditional local search-based metaheuristic algorithms, such as adaptive neighborhood search (ANS) and variable neighborhood descent (VND), mainly focus on optimizing the current solution without considering potential long-term consequences, which may easily get stuck in local optima and limit the overall performance. Thus, we propose a multi-agent deep Q-network-based metaheuristic algorithm (MDQN-MA) for NRP to harness the strengths of various metaheuristics. Each agent encapsulates a metaheuristic algorithm, where its available actions represent different perspectives of the problem environment. By combining their strengths and various perspectives, these agents can work collaboratively to navigate and search for a broader range of potential solutions effectively. Furthermore, to improve the performance of an individual agent, we model its neighborhood search as a Markov Decision Process model and integrate a deep Q-network to consider long-term impacts for its neighborhood sequential decision-making. The experimental results clearly show that an individual agent in MDQN-MA can outperform ANS and VND, and multiple agents in MDQN-MA even perform better, achieving the best results among metaheuristic algorithms on the Second International Nurse Rostering Competition dataset.

A branch-and-price algorithm for integrating urban rail crew scheduling and rostering problems

Crew planning, involving how to best schedule crew members during a given period, is a significant problem for urban rail transit companies. This paper proposes a new integer linear programming (ILP) model that can simultaneously optimize urban rail crew scheduling and rostering problems. The proposed ILP model is a set partitioning-based model with only one type of important duty selection variable that connects the two-level problem and circumvents the drawbacks of conventional approaches that usually formulate the crew scheduling and rostering problems separately and couple these two problems through linking constraints. This study demonstrates that the structure of the underlying network used to model the problem enables the development of an effective, heuristic branch-and-price procedure. The study compares the proposed approach with two other decomposition methods, namely Lagrangian relaxation and alternating direction method of multipliers (ADMM), on problems of different sizes and shows that the method provides lower bounds that are on average 16.4% better than Lagrangian relaxation and 5.03% better than ADMM, respectively. Furthermore, the study shows that, with an average optimality gap of 3.28%, the proposed approach obtains high-quality integer solutions to the integrated problem.

Ethical decision-making in human-automation collaboration: a case study of the nurse rostering problem

AbstractAs artificial intelligence (AI) is increasingly present in different aspects of society and its harmful impacts are more visible, concrete methods to help design ethical AI systems and limit currently encountered risks must be developed. Taking the example of a well-known Operations Research problem, the Nurse Rostering Problem (NRP), this paper presents a way to help close the gap between abstract principles and on-the-ground applications with two different steps. We first propose a normative step that uses dedicated scientific knowledge to provide new rules for an NRP model, with the aim of improving nurses’ well-being. However, this step alone may be insufficient to comprehensively deal with all key ethical issues, particularly autonomy and explicability. Therefore, as a complementary second step, we introduce an interactive process that integrates a human decision-maker in the loop and allows practical ethics to be applied. Using input from stakeholders to enrich a mathematical model may help compensate for flaws in automated tools.

AN APPLICATION OF GRAPH COLORING: NURSE SCHEDULING PROBLEM

The Nurse Rostering Problem (NRP), also known as the Nurse Scheduling Problem (NSP), represents a challenging scheduling issue that significantly impacts hospital staff worldwide on a daily basis. Nursing staff scheduling is one of the most important but complex problem for the hospital management. NSP is a critical subclass of scheduling problems known for their complexity. This paper introduces an efficient approach to solving the Nurse Scheduling Problem (NSP), aiming to meet the needs of nurses, patients, and hospital management. It requires critical thinking and good decision-making skills to develop a roster that effectively balances patient care, employee and other needs in the organization. To reduce the problem's complexity, graph coloring techniques have been utilized.

Solving Nurse Rostering Optimization Problem using Reinforcement Learning - Simulated Annealing with Reheating Hyper-heuristics Algorithm

Nurse rostering is the process of scheduling hospital nurses for a certain period of time. This is a complex and interesting task that involves multiple perspectives, including those of the hospital, nurses, and patients. In addition, nurse scheduling must consider existing constraints to obtain a schedule that is close to optimal. Common constraints include the number of available nurses, their abilities, labor regulations, and hospital policies. The numerous constraints in nurse scheduling lead to a problem known as the Nurse Rostering Problem (NRP), which is difficult to solve conventionally and is considered an NP-hard problem. Many researchers have attempted to solve NRP computationally, as this approach reduces the time required to create nurse schedules. The less time needed to create nurse schedules, the more time can be allocated to improving medical services, which ultimately impacts the quality of healthcare in the hospital's surrounding area. Several approaches have been used to solve NRP, including hyper-heuristic methods, which are search methods used to solve optimization problems. The aim of this study is to employ a hyper-heuristic approach using Reinforcement Learning - Simulated Annealing with Reheating algorithm to solve the nurse scheduling problem in hospitals in Norway. The results show that the Reinforcement Learning - Simulated Annealing with Reheating algorithm can produce schedules with an 82% improvement in solutions. This algorithm also outperforms the comparison algorithms, with a 3% to 47% improvement over the Simple Random - Hill Climbing algorithm, a 2% to 12% improvement over the Reinforcement Learning - Hill Climbing algorithm, and a 0.7% to 7% improvement over the Reinforcement Learning - Simulated Annealing algorithm.

Integrated task scheduling and personnel rostering of airports ground staff: A case study

In dealing with personnel management in companies, two fundamental planning issues have to be handled: staff rostering and activities assignment. These two problems have historically been treated separately, in a sequential way; however, it is evident how strongly they are tied to each other and that solution quality inevitably drops if this connection is not taken into proper account. For this reason, also taking advantage of the massive recent advances in software and hardware technologies, the integrated task scheduling and personnel rostering problem (TSPR) has been formalized along with suitable algorithmic approaches to tackle both planning stages altogether. In this paper, we describe how the peculiar and complex case of airport ground staff was handled in a scenario defined by real-world data from a large airport in Italy. Specifically, we show that the problem can be cast into a mixed integer linear programming model. We then show that, to make the problem computationally tractable, the introduction within the model of a set of suitable valid inequalities is crucial. Indeed, as opposed to the base model from the literature, the novel, improved formulation allowed to effectively obtain near-optimal solutions in reasonable time even for the considered large-scale and real-world scenario.

Solving a new mathematical model for the integrated cockpit crew pairing and rostering problem by meta-heuristic algorithms under the COVID-19 pandemic

This study examines the problem of crew pairing and rostering under COVID-19 conditions. To keep the cockpit crew members safe against COVID-19, the problem is investigated in such a way that each cockpit crew member spends less daily sit time period in the airports and returns to his/her home base at the end of the day to take a rest. This study aims to introduce a Mixed-Integer Linear Programming (MILP) formulation for the problem. In order to solve the problem, three meta-heuristic algorithms including Genetic Algorithm (GA), Firefly Algorithm (FA), and Particle Swarm Optimization (PSO) are applied based on a new chromosome representation. The proposed algorithms could obtain solutions with the least possible number of cockpit crew members to cover the existing flights by considering some rules and regulation related to employing cockpits. Moreover, the findings indicate that the algorithms can provide solutions near the optimal solutions (1.94%, 2.49%, and 2.43% gaps for the GA, FA, and PSO on average, respectively) for the small-scale instances extracted from the data sets. Additionally, the proposed GA can find lower-cost solutions in comparison to the FA and PSO in approximately similar CPU time for problem instances with different sizes.

On the complexity of Nurse Rostering problems

In Nurse Rostering problems the goal is to assign nurses to shifts, subject to a number of constraints. In this paper we consider the computational complexity of such problems. We review the major complexity results obtained so far and show that a problem with coverage constraints, day off requests, and forbidden sequences of shifts of length 2 is NP-hard in the strong sense, even if there are only three work shifts and a day off shift involved.

Meta-Heuristic Solver with Parallel Genetic Algorithm Framework in Airline Crew Scheduling

Airline crew scheduling is a very important part of the operational planning of commercial airlines, but it is a linear integer programming problem with multi-constraints. Traditionally, the airline crew scheduling problem is determined by solving the crew pairing problem (CPP) and the crew rostering problem (CRP), sequentially. In this paper, we propose a new heuristic solver based on the parallel genetic algorithm and an innovative crew scheduling algorithm, which improves traditional crew scheduling by integrating CPP and CRP into a single problem. The innovative scheduling method includes a global heuristic search and an adjustment for flights and crew so as to realize crew scheduling. The parallel genetic algorithm is used to divide the population into multiple threads for parallel calculation and to optimize the randomly generated flight sequence to maximize the number of flights that meet the crew configuration. Compared with the genetic algorithm, CPLEX and Gurobi, it shows high optimization efficiency, with a time reduction of 16.57–85.82%. The experiment shows that our crew utilization ratio is higher than that for traditional solvers, achieving almost 44 flights per month, with good scalability and stability in both 206 and 13,954 flight datasets, and can better manage airline crew scheduling in times of crew scarcity.

Flexibility and Consistency in Long-Term Care Rostering

Problem definition: We consider the rostering decisions—that is, the assignment of workers scheduled for a shift to units—of a long-term care facility. The facility’s objective is to minimize the monthly inconsistency level, a widely promoted quality metric representing the number of different caregivers working in each unit over one month. Methodology/results: We introduce simple rostering heuristics that prioritize either part-time or full-time workers and present a stochastic model of the repeated rostering problem to compare the performance of different strategies analytically. Our analysis shows that in order to minimize the inconsistency level, part-time workers should receive higher priority than full-time workers for assignment to their home units. We also establish an analytical upper bound for a threshold on the time horizon above which a policy giving assignment priority to part-time workers is guaranteed to outperform one giving priority to full-time workers. Using data from more than 15,000 shifts worked by nursing assistants at three nursing homes, we compare the actual rosters to the hindsight optimal consistency-maximizing schedules, demonstrating a significant opportunity for improvement. We then compare the performance of our rostering heuristics via trace-based simulation of the historical schedules. This reinforces the superiority of prioritizing part-time workers, yielding reductions in the inconsistency level between 20% and 30% compared with the historical rosters. Managerial implications: Contrary to popular guidance, our results show that managers should focus on part-time workers and assign them as consistently as possible. Even if some full-time workers are always assigned to their home units (because of preferences or work rules), assignment flexibility among the remaining full-time workers still enables significant improvements in the consistency of care. This flexibility among full-time workers helps because their higher work frequency tends to make a reassignment away from their home unit contribute less to inconsistency, because they are able to work multiple shifts in these nonhome units. Supplemental Material: The e-companion is available at https://doi.org/10.1287/msom.2022.1174 .

Nurse rostering with fatigue modelling

We use a real Nurse Rostering Problem and a validated model of human sleep to formulate the Nurse Rostering Problem with Fatigue. The fatigue modelling includes individual biologies, thus enabling personalised schedules for every nurse. We create an approximation of the sleep model in the form of a look-up table, enabling its incorporation into nurse rostering. The problem is solved using an algorithm that combines Mixed-Integer Programming and Constraint Programming with a Large Neighbourhood Search. A post-processing algorithm deals with errors, to produce feasible rosters minimising global fatigue. The results demonstrate the realism of protecting nurses from highly fatiguing schedules and ensuring the alertness of staff. We further demonstrate how minimally increased staffing levels enable lower fatigue, and find evidence to suggest biological complementarity among staff can be used to reduce fatigue. We also demonstrate how tailoring shifts to nurses’ biology reduces the overall fatigue of the team, which means managers must grapple with the issue of fairness in rostering.

A Fuzzy Crew Rostering Model Based on Crew Preferences and Seniorities considering Training Courses: A Robust Optimization Approach

Crew scheduling problem is divided into crew pairing problem (CPP) and crew rostering problem (CRP). In this paper, a rostering model is presented to assign crew to pairings in such a way that total weighted preference is maximized. Crew members declare which parings they wish to be assigned and which ones are undesirable for them. A score is calculated in the objective function if a crew member is assigned to his/her preferred pairing, and a penalty is considered if he/she is assigned to an undesirable pairing. Moreover, crew seniorities are considered in calculating total preference. In addition, the model considers standard rules and regulations as well as crew attendance at the required training courses. The model is formulated in such a way that inconsistent crew members are not assigned to a flight. Due to the uncertainty in determining of the seniority weight, this parameter is considered as fuzzy. At the end, the robust counterpart of the nominal model is developed due to the uncertainty of time away from the base (TAFB). In this research, the issue of inconsistent crew in rostering problem is considered for the first time. Moreover, a new scoring mechanism is introduced to calculate desirable and undesirable assignments in the objective function. The proposed CRP is solved using the genetic algorithm (GA), and its performance is verified in comparison with GAMS in some test problems. On average, the optimality gap in GA is only 0.5 percent. Finally, the proposed model is examined with real-world data from Air India Airline. In comparison with the previous research studies, the suggested model (scoring mechanism) reduced the number of undesirable rosters by 61.59%.

Metro crew planning with day-off pattern, duty type, and rostering scheme considerations

The metro crew planning must consider various complex factors in real scenarios, such as day-off requirements, duty types, and rostering rules. The metro crew planning problem is often divided into crew scheduling and rostering problems, which are modeled separately and solved sequentially. However, the solution determined in a sequential planning process may not guarantee the optimality of the entire crew planning problem. This study is a first attempt at including rostering pattern consideration in the metro crew planning problem, where a rostering pattern is defined as the combination of a day-off pattern, a set of duty types and a rostering scheme. To solve this complicated problem, we first generate a multiple-layer time–space network where duty time windows with specific duty types are represented by different layers. We then model the considered crew planning problem using a path-based integer program on the time–space network and develop two column generation-based heuristics to solve the problem, where dual prices are particularly used in generating train paths. A computational study is conducted with real-life data derived from Hefei Metro to examine the effectiveness of the modeling and solution methods as well as observe the benefits of roster pattern designs.

Coordinating aircraft maintenance routing and integrated maintenance staffing and rostering: a Stackelberg game theoretical model

There is an interdependence between operational-based flight delay aircraft maintenance routing problem (AMRPD) and maintenance staffing problem (MSP). Furthermore, MSP and maintenance rostering problem (MRP) are interdependent. In the literature, most of the studies only consider a single interdependence and neglect the other one. This results in difficulties in implementing the optimal plan constructed by each problem, leading finally to an increase in the operational cost of airlines and maintenance providers. Therefore, the main objective of this study is to investigate these interdependences simultaneously. This is accomplished by developing a Stackelberg game model (LFSGM), in which leader and follower are the airlines and maintenance providers, respectively. This LFSGM is modelled as a bi-level mixed integer linear programming (MILP) model. The upper-level is represented by the AMRPD, while the integrated maintenance staffing and rostering (IMSR) functions as the lower-level. The solution of the LFSGM is obtained from an iterative algorithm. The viability and superiority of the LFSGM are demonstrated by presenting a case study of a leading airline in the Middle East serviced by four maintenance providers. The results reveal a significant cost saving for airline and maintenance providers.

A mat-heuristic based solution approach for an extended nurse rostering problem with skills and units

The Nurse Rostering Problem (NRP) is a combinatorial optimization problem that deals with assignment of nurses to shifts based on a set of constraints. The real-life NRP applications are difficult to solve because of the fact that the problem is NP-hard. In this paper, we focus on two main aspects of the problem, model and solution methodology. Firstly, we propose a novel model that also considers unit assignments. Majority of the studies in the literature accounts for nurse, day, and shift assignments. Due to skill and experience levels, not every nurse can be assigned to every unit. Therefore, accounting for unit assignments helps the model to be more accurate in terms of real-life scenarios. Lastly, we propose a new mathematical based heuristic that combines Integer Programming (IP) and Discrete Particle Swarm Optimization (PSO). IP is used to generate initial schedules and PSO further improves the schedule. Any infeasibility is corrected by IP along the process. IP and PSO coordinate until final stopping criterion. Computational experiments on test data show that the proposed algorithm generates near optimal solutions.

Scheduling of Physicians with Time‐Varying Productivity Levels in Emergency Departments

Emergency department (ED) overcrowding and long patient wait times have become a worldwide problem. We propose a novel approach to assigning physicians to shifts such that ED wait times are reduced without adding new physicians. In particular, we extend the physician rostering problem (PRP) by including heterogeneity among emergency physicians in terms of their productivity (measured by the number of new patients seen in 1 hour) and by considering the stochastic nature of patient arrivals and physician productivity. We formulate the PRP as a two‐stage stochastic program and solve it with a sample average approximation and the L‐shaped method. To formulate the problem, we perform a data analysis to investigate the major drivers of physician productivity using patient visit data from our partner ED, and we find that the individual physician, shift hour, and shift type (e.g., day or night) are the determining factors of ED productivity. A simulation study calibrated using real data shows that the new scheduling method can reduce patient wait times by as much as 13% compared to the current scheduling system at our study ED. We also demonstrate how to incorporate physician preference in scheduling through physician clustering based on productivity. Our simulation results show that EDs can receive almost the full benefit of the new scheduling method even when the number of clusters is small.

Solving an integrated mathematical model for crew pairing and rostering problems by an ant colony optimisation algorithm

Solving an integrated mathematical model for crew pairing and rostering problems by an ant colony optimisation algorithm

A 2-Stage Approach for the Nurse Rostering Problem

In this paper, we are addressing the NP-hard nurse rostering problem utilizing a 2-stage approach. In stage one, Monte Carlo Tree Search (MCTS) and Hill Climbing (HC) are hybridized in finding a feasible solution (satisfying all the hard constraints). We propose a new constant <i>C</i> value (which balances search diversification and intensification of MCTS) and tree policy/node selection function in the selection procedure of MCTS. In stage two, the feasible solution is further improved using Iterated Local Search (ILS) with Variable Neighbourhood Descent as the local search component. We introduce several unique neighbourhood structures for the ILS. In addition, we propose a novel perturbation strategy to allow the search to escape from local optimum. The proposed methodology is tested on the Shift Scheduling dataset (24 benchmark instances). New best results are reported for seven and two instances for the 10 and 60 minutes run respectively. An in-depth discussion on the attributes of the proposed methodology that lead to its good performance is provided.

An integrated model of aircraft routing and crew rostering problems to develop fair schedule for the crew under COVID-19 condition

An integrated model of aircraft routing and crew rostering problems to develop fair schedule for the crew under COVID-19 condition

An integrated model of aircraft routing and crew rostering problems to develop fair schedule for the crew under COVID-19 condition

This paper focuses on aircraft routing and crew rostering problems simultaneously considering the risk of COVID-19 infection. As airports are among high-risk places in COVID-19 pandemic, the crew prefer to spend less sit time in airports and come back to their home base at the end of each duty day. In this research, an integrated model is developed to assign crew and aircraft to flights in order to achieve a fair schedule for the crew. The objective function is minimisation of the difference between crew sit times. Moreover in this model, a framework including flight hours, number of days and number of take-offs is considered for maintenance requirements. Particle swarm optimisation (PSO) is used as the solution approach. To validate the solution approach, 20 test problems were solved using GAMS and PSO. The results show that PSO improved CPU time significantly (98.279% in average) in turn of 1.902% gap with GAMS in optimum solution.