Scheduling healthcare services in a home healthcare system

We consider a scheduling problem in a home healthcare system in which nurses visit patients regularly for relatively minor healthcare services. Intervals between the visits may differ for different patients. On each day in the planning horizon, a nurse must visit the patients assigned to her/him on that day, and then return to the hospital. For the problem of determining the visiting schedule with the objective of minimizing total travel time of the nurse over the planning horizon, we develop a two-phase heuristic algorithm. To evaluate performance of the proposed algorithm, a series of computational tests is performed on a number of randomly generated problem instances and a real instance. Results of the tests show that the heuristic algorithm gives near optimal solutions for problems of practical sizes in a reasonable time.     

Modelling the requirement for supplementary nurses in an intensive care unit

The intensive care unit (ICU) of a hospital is an essential yet costly resource. Consequently, intensive care modelling has become increasingly prevalent in recent years in attempts to increase efficiency and reduce costs. Previous models have usually assumed that the numbers of beds available are restricted; when all beds are occupied, any additional patients are referred elsewhere or elective surgeries are cancelled. In this study, activities at the ICU at a large teaching hospital were modelled using data relating to all admissions to the ICU during the year 2000—a total of 1084 admissions. The unit is unusual in that the majority of patients referred for intensive care therapy are admitted. Bed numbers are increased when necessary to cope with demand. However, nurses are a restricted resource. In order to maintain the required nurse:patient ratio of at least one:one, supplementary nurses are employed during busy periods. Supplementary nurse costs are substantial and so nurse utilization must be closely monitored. The development of a model that calculates the required number of supplementary nurses per shift, and also encapsulates the time-dependent nature of elective surgery admissions and complex duration-of-stay profiles, is presented in this paper. In particular, the model is used to determine the number of rostered nurses that are required to minimize overall nursing staff costs.     

A patient assignment algorithm for home care services

We consider the problem of assigning patients to nurses for home care services. The aim is to balance the workload of the nurses while avoiding long travels to visit the patients. We analyse the case of the CSSS Côte-des-Neiges, Métro and Parc Extension for which a previous analysis has shown that demand fluctuations may create work overload for the nursing staff. We propose a mixed integer programming model with some non-linear constraints and a non-linear objective which we solve using a Tabu Search algorithm. A simplification of the workload measure leads to a linear mixed integer program which we optimize using CPLEX.     

A shift sequence based approach for nurse scheduling and a new benchmark dataset

This paper investigates an adaptive constructive method for solving nurse rostering problems. The constraints considered in the problems are categorised into three classes: those that are sequence related, those that are nurse schedule related and those that are roster related. We propose a decomposition approach (to construct solutions) that consists of two stages: (1) to construct high quality sequences for nurses by only considering the sequence constraints, and (2) to iteratively construct schedules for nurses and the overall rosters, based on the sequences built and considering the schedule and roster constraints. In the second stage of the schedule construction, nurses are ordered and selected adaptively according to the quality of the schedules they were assigned to in the last iteration. Greedy local search is carried out during and after the roster construction, in order to improve the (partial) rosters built. We show that the local search heuristic during the roster construction can further improve the constructed solutions for the benchmark problems tested.     

A Pareto-based search methodology for multi-objective nurse scheduling

In this paper, we propose a search technique for nurse scheduling, which deals with it as a multi-objective problem. For each nurse, we first randomly generate a set of legal shift patterns which satisfy all shift-related hard constraints. We then employ an adaptive heuristic to quickly find a solution with the least number of violations on the coverage-related hard constraint by assigning one of the available shift patterns of each nurse. Next, we apply a coverage repairing procedure to make the resulting solution feasible, by adding/removing any under-covered/over-covered shifts. Finally, to satisfy the soft constraints (or preferences), we present a simulated annealing based search method with the following two options: one with a weighted-sum evaluation function which encourages moves towards users?? predefined preferences, and another one with a domination-based evaluation function which encourages moves towards a more diversified approximated Pareto set. Computational results demonstrate that the proposed technique is applicable to modern hospital environments.     

Workforce staffing and scheduling: Hospital nursing specific models

Decisions relating to hospital nurse staffing and scheduling are among the most important decisions made in hospitals today. Staffing and scheduling choices must be made which will result in timely and high-quality care to patients. These choices are complicated by the requirement for round-the-clock staffing in many hospital nursing units, a severe nursing shortage, and an outcry from many quarters to cut costs of health care. In general, patients today are kept in hospitals only if they are in need of highly skilled nursing care. In this paper we present a review of some of the issues in health care currently influencing the hospital nurse staffing and scheduling environment. In addition, we review the literature that illustrates nurse manager's concerns, and approaches taken in the past by operations researchers to address those concerns. We present some data from a recent study of nurse managers in 31 hospitals that illustrates the complexity of the issues. We conclude with a discussion of future research directions in hospital nurse staffing and scheduling.     

A subproblem-centric model and approach to the nurse scheduling problem

The number of hospitals in Japan exceeds 10,000, and every month nurses are scheduled to shifts in about 30,000 units in total. There is serious demand for automating this scheduling task. In this paper, we introduce a mathematical programming formulation of the nurse scheduling problem in Japan, and develop a meta-heuristic approach to solve the problem. This scheduling problem is a hard combinatorial problem due to tight constraints involving such factors as the skill level of a team, the need to balance workload among nurses, and the consideration of nurses' preferences, even though the number of the nurses to be scheduled is not large, at between 20 and 40. The performance of our approach is demonstrated by the successful solution of data taken from actual scheduling problems. The proposed model and approach can be adapted for the majority of hospitals in Japan, as well as for some hospitals in other countries, and is likely applicable to many other scheduling problems in the fields of business and logistics. Key words.nurse scheduling – block-angular problem – subproblem – integer programming – relaxation – tabu search – branch-and-boundMathematics Subject Classification (1991):20E28, 20G40, 20C20     

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

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.     

A branch-and-bound based solution approach for the mixed-model assembly line-balancing problem for minimizing stations and task duplication costs

A common assumption in the literature on mixed-model assembly line balancing is that a task that is common to multiple models must be assigned to a single station. In this paper, we relax this restriction, and allow a common task to be assigned to different stations for different models. We seek to minimize the sum of costs of the stations and the task duplication. We develop an optimal solution procedure based on a backtracking branch-and-bound algorithm and evaluate its performance via a large set of experiments. A branch-and-bound based heuristic is then developed for solving large-scale problems. The heuristic solutions are compared with a lower bound and experiments show that the heuristic provides much better solutions than those obtained by traditional approaches.     

Solving the multi-objective nurse scheduling problem with a weighted cost function

The primary objective of the nurse scheduling problem is to ensure there are sufficient nurses on each shift. There are also a number of secondary objectives designed to make the schedule more pleasant. Neighbourhood search implementations use a weighted cost function with the weights dependent on the importance of each objective. Setting the weights on binding constraints so they are satisfied but still allow the search to find good solutions is difficult. This paper compares two methods for overcoming this problem, SAWing and Noising with simulated annealing and demonstrates that Noising produces better schedules.     

Nurses allocation models for maternal and child health services

Maternal and Child Health (MCH) centres in Hong Kong offer, for children aged below six and women of childbearing age, a comprehensive range of health services regularly performed by nurses of different ranks. While each rank has its specific duties, nurses of a higher rank can step down to the work of a more junior rank when necessary. However, cross-regional deployments of nurses occur less frequently. We develop goal programming models of ‘optimal’ MCH nurses allocation. The presence and absence of nurses’ ‘cross-over’ of work functions are explicitly considered. The results show that more equitable manpower levelling can be achieved, with flexibility (in the longer term) on cross-regional deployment of nurses as a possible way of operational improvement when the entire MCH service is taken as a whole.     

A multi-heuristic approach for solving the pre-marshalling problem

Minimizing the number of reshuffling operations at maritime container terminals incorporates the pre-marshalling problem (PMP) as an important problem. Based on an analysis of existing solution approaches we develop new heuristics utilizing specific properties of problem instances of the PMP. We show that the heuristic performance is highly dependent on these properties. We introduce a new method that exploits a greedy heuristic of four stages, where for each of these stages several different heuristics may be applied. Instead of using randomization to improve the performance of the heuristic, we repetitively generate a number of solutions by using a combination of different heuristics for each stage. In doing so, only a small number of solutions is generated for which we intend that they do not have undesirable properties, contrary to the case when simple randomization is used. Our experiments show that such a deterministic algorithm significantly outperforms the original nondeterministic method. The improvement is twofold, both in the quality of found solutions, and in the computational effort.     

Stochastic dynamic nursing service budgeting

We address the nursing service budgeting problem from the department manager’s point of view. The model allocates the budget dynamically to three types of nursing care capacities: 1) permanent nurses, 2) temporary nurses, and 3) overtime. The quarterly tactical decisions are the aggregate weekly shift pattern of permanent nurses and the policy for hiring temporary nurses and using overtime. The decisions are optimized with respect to nursing care shortage and a soft-constraint on the annual budget. For the aggregate weekly shift pattern, permanent nurses require a notification lead-time of one quarter to prepare the personal rosters. Our model offers a solution to the nursing service budgeting problem that extends the existing literature by using a Markovian demand model, resolving the anticipation of the operational decisions, and applying general budget as well as shortage penalty functions.     

A branch-and-price approach for integrating nurse and surgery scheduling

A common problem at hospitals is the extreme variation in daily (even hourly) workload pressure for nurses. The operating room is considered to be the main engine and hence the main generator of variance in the hospital. The purpose of this paper is threefold. First of all, we present a concrete model that integrates both the nurse and the operating room scheduling process. Second, we show how the column generation technique approach, one of the most employed exact methods for solving nurse scheduling problems, can easily cope with this model extension. Third, by means of a large number of computational experiments we provide an idea of the cost saving opportunities and required solution times.     

Flexible flow shop scheduling with uniform parallel machines

We consider the multistage flexible flow shop scheduling problem with uniform parallel machines in each stage and the objective of minimizing makespan. We develop a general class of heuristics for this strongly NP-hard problem that extend several well-known heuristics for the corresponding embedded serial flow shop problem, and obtain absolute performance guarantees for heuristics in this class by building on similar absolute performance guarantees for the corresponding serial flow shop heuristics. Our approach is quite robust, since it can extend any heuristic for the serial flow shop problem (with an absolute performance guarantee) to a similar one for the flexible flow shop problem with uniform parallel machines.     

An efficient computational approach for railway booking problems

This paper deals with the determination of seat allocations for a rail booking system. It is assumed that demand for each trip in the network can be divided into two segments, namely a full fare segment and a discounted fare segment. A constrained nonlinear integer programming model is formulated to deal with this problem. The purpose of this paper is to develop an efficient heuristic approach to develop the booking limits for all ticket types in the railway network. The solutions obtained by the heuristic approach are compared with those found by the Lingo software and the DICOPT solver. Numerical results show that the proposed heuristic approach only require a small number of CPU time to obtain superior solutions.     

A scatter search methodology for the nurse rostering problem

The benefits of automating the nurse scheduling process in hospitals include reducing the planning workload and associated costs and being able to create higher quality and more flexible schedules. This has become more important recently in order to retain nurses and to attract more people into the profession. Better quality rosters also reduce fatigue and stress due to overwork and poor scheduling and help to maximise the use of leisure time by satisfying more requests. A more contented workforce will lead to higher productivity, increased quality of patient service and a better level of healthcare. This paper presents a scatter search approach for the problem of automatically creating nurse rosters. Scatter search is an evolutionary algorithm, which has been successfully applied across a number of problem domains. To adapt and apply scatter search to nurse rostering, it was necessary to develop novel implementations of some of scatter search's subroutines. The algorithm was then tested on publicly available real-world benchmark instances and compared against previously published approaches. The results show the proposed algorithm is a robust and effective method on a wide variety of real-world instances.     

Developing a dynamic portfolio selection model with a self-adjusted rebalancing method

In this paper, we propose a comprehensive investment strategy for not only selecting but also maintaining an investment portfolio that takes into account changing market conditions. First, we implement a dynamic portfolio selection model (DPSM) that uses a time-varying investment target according to market forecasts. We then develop a self-adjusted rebalancing (SAR) method to assess the portfolio’s relevance to current market conditions, and further identify the appropriate timing for rebalancing the portfolio. We then integrate the DPSM and SAR into a comprehensive investment strategy, and develop an adaptive learning heuristic for determining the parameter of the proposed investment strategy. We further evaluate the performance of the proposed investment strategy by simulating investments with historical stock return data from different markets around the world, across a period of 10 years. The SAR Portfolio, maintained according to the proposed investment strategy, showed superior performance compared with benchmarks in each of the target markets.     

The travelling salesperson problem with hotel selection

In this paper, we present the travelling salesperson problem with hotel selection (TSPHS), an extension of the TSP with a number of interesting applications. We present a mathematical formulation, explain the difference with related optimization problems and indicate what makes this problem inherently more difficult. We develop a simple but efficient heuristic that uses two constructive initialization procedures and an improvement procedure consisting of several neighbourhood search operators designed specifically for this problem, as well as some typical neighbourhoods from the literature. We generate several benchmark instances of varying sizes and compare the performance of our heuristic with CPLEX (10.0). We also generate some problems with known optimal solutions and use these to further demonstrate that our heuristic achieves good results in very limited computation times.     

A production scheduling heuristic for an electronics manufacturer with sequence-dependent setup costs

In this paper, we develop a three-step heuristic to address a production scheduling problem at a high volume assemble-to-order electronics manufacturer. The heuristic provides a solution for scheduling multiple product families on parallel, identical production lines so as to minimize setup costs. The heuristic involves assignment, sequencing, and time scheduling steps, with an optimization approach developed for each step. For the most complex step, the sequencing step, we develop a greedy randomized adaptive search procedure (GRASP). We compare the setup costs resulting from the use of our scheduling heuristic against a heuristic previously developed and implemented at the electronics manufacturer that assumes approximately equal, sequence-independent, setup costs. By explicitly considering the sequence-dependent setup costs and applying GRASP, our empirical results show a reduction in setups costs for an entire factory of 14–21% with a range of single production line reductions from 0% to 49%.