Nurse Scheduling Problem (NSP) is the assignment of a number of nurses to a number of shifts in order to satisfy hospital’s demand. The objectives of NSP are the minimization of the overall hospital cost, and the maximization of nurses’ preferences while taking into consideration the governmental rules and hospital standards. In this article, a proposed mathematical model for the NSP is presented, which is based on the idea of multi-commodity network flow model. The proposed model was verified using hypothetical instances as well as benchmark instances, then, it is applied to a real case study in an Egyptian hospital. The results demonstrate the advantage of using the proposed model in generating schedule required to solve the problem. Furthermore, it proves the superiority of the obtained schedule to those generated manually by the supervisor head nurse as it improves the level of nurses’ satisfaction by creating fair schedule system take care about nurses’ preferences as well as decreases the overall overtime cost by 36%.

A new formulation and solution for the nurse scheduling problem: A case study in Egypt

To make a fair and satisfactory nurse shift schedule, this paper proposes a novel preference satisfaction function, in which numbers of the preferred work shifts and days-off of the nursing staff are balanced, and ranks for preferences and number of the preference ranks satisfied so far are also considered. Such a preference function is capable of equivalently and fairly planning the nurse preference schedule to improve the total satisfaction. Additionally, distributed sensors can be applied to collect the information on hospital beds to provide the schedule planner to determine the lowest required amount of manpower for each work shift, to avoid the working overload of the nursing staff. To solve the nursing schedule problem, we propose a genetic algorithm (GA) with an immigrant scheme, in which utilization of the immigrant scheme is helpful in efficiently reducing amount of infeasible solutions due to practical scheduling constraints, so that the GA can efficiently find better solutions for larger-scale problems. Performance of the proposed GA with and without solution recovery scheme is evaluated by conducting a comprehensive experimental analysis on three different-size instances.

https://journals.sagepub.com/doi/pdf/10.1155/2015/595419

Nurse scheduling with joint normalized shift and day-off preference satisfaction using a genetic algorithm with immigrant scheme

Motivated by the need to make frequent changes in operating suites, this paper presents a highly scalable and efficient solution framework for scheduling nurses in operating suites over the day. This framework consists of two core optimization models that are necessary for scheduling OR nurses in the clinic. The first model addresses the multi-objective optimization problem of assigning nurses to upcoming surgery cases based on their specialties and competency levels. The second model is designed to generate lunch break assignments for the nurses once their caseloads are determined. The latter problem has been largely overlooked by the research community despite its importance. Because the multi-objective model is too large to solve using commercial software, we developed both a column generation algorithm and a two-phase swapping heuristic to find feasible assignments in a fast manner. For both approaches, initial solutions are obtained with a restricted model and lunch breaks are scheduled in a post-processing step. Experiments were conducted to determine the value of the models and the performance of the algorithms using real data provided by MD Anderson Cancer Center in Houston, Texas. The results show that the two approaches can produce implementable daily schedules in a matter of minutes for instances with over 100 nurses, 50 surgery cases and 33 operating rooms.

Nurse scheduling with lunch break assignments in operating suites

Effective local search algorithms for high school timetabling problems

Heuristic decomposition approaches for an integrated task scheduling and personnel rostering problem

This paper tackles a Nurse Scheduling Problem which consists of generating work schedules for a set of nurses while considering their shift preferences and other requirements. The objective is to maximize the satisfaction of nurses? preferences and minimize the violation of soft constraints. This paper presents a new deterministic heuristic algorithm, called MAPA (multi-assignment problem-based algorithm), which is based on successive resolutions of the assignment problem. The algorithm has two phases: a constructive phase and an improvement phase. The constructive phase builds a full schedule by solving successive assignment problems, one for each day in the planning period. The improvement phase uses a couple of procedures that re-solve assignment problems to produce a better schedule. Given the deterministic nature of this algorithm, the same schedule is obtained each time that the algorithm is applied to the same problem instance. The performance of MAPA is benchmarked against published results for almost 250,000 instances from the NSPLib dataset. In most cases, particularly on large instances of the problem, the results produced by MAPA are better when compared to best-known solutions from the literature. The experiments reported here also show that the MAPA algorithm finds more feasible solutions compared with other algorithms in the literature, which suggest that this proposed approach is effective and robust.

/pdf/a-heuristic-algorithm-based-on-multi-assignment-procedures-25u7qpqagc.pdf

Douglas Baroni Rizzato

Papers

A heuristic algorithm based on multi-assignment procedures for nurse scheduling