Scheduling an operating theatre under human resource constraints

In the present economic context, the operating theatre is considered as a critical activity in health care management. By virtue of its huge consumption of human and material resources, the operating theatre is one of the most important sources of expenses of the hospitals. A less costly organization of the operating rooms calls for a more rational use of the resources and a more refined planning of the surgical units. In addition to these considerations, we are concerned about the well-being of the medical staff. We integrate this human factor into the optimization procedure by stressing the human resources’ availabilities in the design of the schedules. This planning process is typically decomposed in two sequential phases: a planning stage followed by a scheduling stage. Due to this decomposition the resulting solutions may turn out to be sub-optimal. In this paper, we propose a formulation that includes both the planning and scheduling of the surgical operations. We also propose a heuristic solution procedure based on genetic algorithms to counter the large running times inherent in tackling this kind of hard optimization problem.     

Operating room management under uncertainty

The operating room management problems are legion. This paper tackles the scheduling of surgical procedures in an operating theatre containing up to two operating rooms and two surgeons. We first solve a deterministic version that uses the constraint programming paradigm and then a stochastic version which embeds the former in a sample average approximation scheme. The latter produces more robust schedules that cope better with the surgeries’ time variability     

A new heuristic algorithm for the operating room scheduling problem

Due to the great importance of operating rooms in hospitals, this paper studies an operating room scheduling problem with open scheduling strategy. According to this strategy, no time slot is reserved for a particular surgeon. The surgeons can use all available time slots. Based on Fei et al.’s model which is considered to be close to reality, we develop a heuristic algorithm to solve it. The idea of this heuristic algorithm is from dynamic programming by aggregating states to avoid the explosion of the number of states. The objective of this paper is to design an operating program to maximize the operating rooms’ use efficiency and minimize the overtime cost. Computational results show that our algorithm is efficient, especially for large size instances where our algorithm always finds feasible solutions while the algorithm of Fei et al. does not.     

A two level metaheuristic for the operating room scheduling and assignment problem

Given a surgery department comprising several specialties that share a fixed number of operating rooms and post-surgery beds, we study the joint operating room (OR) planning and advanced scheduling problem. More specifically, we consider the problem of determining, over a one week planning horizon, the allocation of OR time blocks to specialties together with the subsets of patients to be scheduled within each time block. The aim of this paper is to extend and generalize existing approaches for the joint OR planning and scheduling problem. First, by allowing schedules that include patients requiring weekend stay beds which was not the case previously. Second, by tackling simultaneously both the OR planning and patient scheduling decision levels, instead of taking them into account in successive phases. To achieve this, we exploit the inherent hierarchy between the two decision levels, i.e., the fact that the assignment decisions of OR time blocks to surgical specialties directly affect those regarding the scheduling of patients, but not the reverse. The objective function used in this study is an extension of an existing one. It seeks to optimize both patient utility (by reducing waiting time costs) and hospital utility (by reducing production costs measured in terms of the number of weekend stay beds required by the surgery planning). 0–1 linear programming formulations exploiting the stated hierarchy are proposed and used to derive a formal proof that the problem is NP-hard. A two level metaheuristic is then developed for solving the problem and its effectiveness is demonstrated through extensive numerical experiments carried out on a large set of instances based on real data.     

Operating room scheduling with Generalized Disjunctive Programming

This paper addresses the short-term scheduling problem involved in the selection of a subset of elective surgeries from a large waiting list. In order to overcome the combinatorial complexity, a decomposition algorithm is proposed that relies on two continuous-time Generalized Disjunctive Programming (GDP) models. More specifically, there is an upper-level planning model to select surgical assignments to operating rooms and a lower-level constrained scheduling model to synchronize surgeons operating in different rooms on a given day. The GDP models are reformulated using standard convex hull and big-M techniques so as to generate the most efficient set of integer or mixed-integer linear programming constraints. Through the solution of a set of real-life instances from the literature, we show that the new algorithm outperforms a full-space discrete-time formulation and a genetic algorithm, improving the total surgical time as well as the number of performed surgeries by 5%.     

Operating theatre scheduling with patient recovery in both operating rooms and recovery beds

This paper investigates the impact of allowing patient recovery in the operating room when no recovery bed is available. Three types of identical resources are considered: transporters, operating rooms and recovery beds. A fixed number of patients must be planned over a term horizon, usually one or two weeks. The surgery process is modelled as follows: each patient is transported from the ward to the operating theatre. Then the patient visits an operating room for surgery operation and is transferred to the recovery room. If no recovery bed is available, the patient wakes up in the operating room until a bed becomes available. The operating room needs to be cleaned after the patient’s departure, before starting another operation. Finally, the patient is transported back to the ward after his recovery. We consider several criteria based on patients’ completion times. We propose a Lagrangian relaxation-based method to solve this operating theatre scheduling problem. The efficiency of this method is then validated by numerical experiments. A comprehensive numerical experiment is then performed to quantify the benefit of allowing patient recovery in operating rooms. We show that the benefit is high when the workload of the recovery beds is high.     

A hybrid genetic approach for solving an integrated multi-objective operating room planning and scheduling problem

In this paper, we propose a multi-objective integer linear programming model aiming at efficiently planning and managing hospital operating room suites. By effectively exploiting a novel hybrid genetic solution approach, the devised optimization model is able to determine, in an integrated way, (i) the operating room time assigned to each surgical specialty, (ii) the operating room time assigned to each surgical team, (iii) the surgery admission planning and (iv) the surgery scheduling. The resulting Pareto frontiers provide a set of “optimal” solutions able to support hospital managers in efficiently orchestrating the involved resources and planning surgeons and surgeries. On this basis, the proposed solution framework could represent a suitable engine for the development of advanced and effective health care management decision support systems.     

Dynamic patient admission scheduling with operating room constraints,flexible horizons,and patient delays

We revisit and extend the patient admission scheduling problem, in order to make it suitable for practical applications. The main novelty is that we consider constraints on the utilisation of operating rooms for patients requiring a surgery. In addition, we propose a more elaborate model that includes a flexible planning horizon, a complex notion of patient delay, and new components of the objective function. We design a solution approach based on local search, which explores the search space using a composite neighbourhood. In addition, we develop an instance generator that uses real-world data and statistical distributions so as to synthesise realistic and challenging case studies, which are made available on the web along with our solutions and the validator. Finally, we perform an extensive experimental evaluation of our solution method including statistically principled parameter tuning and an analysis of some features of the model and their corresponding impact on the objective function.     

Time-constrained project scheduling

We propose a new approach for scheduling with strict deadlines and apply this approach to the Time-Constrained Project Scheduling Problem (TCPSP). To be able to meet these deadlines, it is possible to work in overtime or hire additional capacity in regular time or overtime. For this problem, we develop a two stage heuristic. The key of the approach lies in the first stage in which we construct partial schedules. In these partial schedules, jobs may be scheduled for a shorter duration than required. The second stage uses an ILP formulation of the problem to turn a partial schedule into a feasible schedule, and to perform a neighborhood search. The developed heuristic is quite flexible and, therefore, suitable for practice. We present experimental results on modified RCPSP benchmark instances. The two stage heuristic solves many instances to optimality, and if we substantially decrease the deadline, the rise in cost is only small.     

Maximizing the efficiency of use of nurses under uncertain surgery durations: A case study

This paper studies a nurse scheduling problem of assigning a set of nurses to surgeries scheduled on each workday in an operating room (OR) suite. This problem plays a decisive role in utilizing nurses efficiently, which is of paramount importance for OR suites to provide high-quality service at ever reduced cost. Due to significant uncertainty in surgery durations, designing schedules that achieve high nurse efficiency is complicated by the competing objective of ensuring on-time starts of surgeries. For trading off between the two performance criteria, we formulate the problem as a mixed integer programming (MIP) model with explicit probability modeling of uncertainty. We are concerned about improving nurse efficiency in terms of overtime and idle time of nurses while mastering the risk of delay of surgeries. The MIP model is applied in a large size Chinese hospital, and the results are compared with the actual performance of the OR suite. The comparisons reveal that through examining the trade-off between the performance criteria, important nurse efficiency improvements can be achieved with good on-time start performance. Moreover, the applicability of the MIP model in various problem settings is also investigated.     

Stochastic programming analysis and solutions to schedule overcrowded operating rooms in China

As a result of the growing demand for health services, China's large city hospitals have become markedly overstretched, resulting in delicate and complex operating room scheduling problems. While the operating rooms are struggling to meet demand, they face idle times because of (human) resources being pulled away for other urgent demands, and cancellations for economic and health reasons. In this research we analyze the resulting stochastic operating room scheduling problems, and the improvements attainable by scheduled cancellations to accommodate the large demand while avoiding the negative consequences of excessive overtime work. We present a three-stage recourse model which formalizes the scheduled cancellations and is anticipative to further uncertainty. We develop a solution method for this three-stage model which relies on the sample average approximation and the L-shaped method. The method exploits the structure of optimal solutions to speed up the optimization. Scheduled cancellations can significantly and substantially improve the operating room schedule when the costs of cancellations are close to the costs of overtime work. Moreover, the proposed methods illustrate how the adverse impact of cancellations (by patients) for economic and health reasons can be largely controlled. The (human) resource unavailability however is shown to cause a more than proportional loss of solution value for the surgery scheduling problems occurring in China's large city hospitals, even when applying the proposed solution techniques, and requires different management measures.     

Evolutionary algorithm for advanced process planning and scheduling in a multi-plant

Integration of process planning and scheduling is one of the most important functions to support flexible planning in a multi-plant. The planning and scheduling are actually interrelated and should be solved simultaneously. In this paper, we propose an advanced process planning and scheduling model for the multi-plant. The objective of the model is to decide the schedules for minimizing makespan and operation sequences with machine selections considering precedence constraints, flexible sequences, and alternative machines. The problem is formulated as a mathematical model, and an evolutionary algorithm is developed to solve the model. Numerous experiments are carried out to demonstrate the efficiency of the proposed approach.     

最小化空闲时间的Job-shop调度进化算法

为了研究Job-shop调度问题,分析了调度结果和调度过程,认为传统Job-shop调度模型的调度过程,实质是减少并减小空闲时间的组合优化过程,而且不同空闲时间对调度结果的影响程度不同。据此提出了最小化空闲时间的两个处理过程和不同空闲时间的处理顺序规则;并设计了进化算法中最小化空闲时间的初始种群生成过程、重组算子和变异算子。经典的调度基准问题对比测试表明最小化空闲时间的分析结论是正确的;最小化空闲时间过程高效可靠;最小化空闲时间的进化算法缩小了算法的搜索空间,大大提高了搜索效率,有效避免了早熟收敛现象,稳定可靠。     

Logistical support scheduling under stochastic travel times given an emergency repair work schedule

Stochastic factors during the operational stage could have a significant influence on the planning results of logistical support scheduling for emergency roadway repair work. An optimal plan might therefore lose its optimality when applied in real world operations where stochastic disturbances occur. In this study we employ network flow techniques to construct a logistical support scheduling model under stochastic travel times. The concept of time inconsistency is also proposed for precisely estimating the impact of stochastic disturbances arising from variations in vehicle trip travel times during the planning stage. The objective of the model is to minimize the total operating cost with an unanticipated penalty cost for logistical support under stochastic traveling times in short term operations, based on an emergency repair work schedule, subject to related operating constraints. This model is formulated as a mixed-integer multiple-commodity network flow problem and is characterized as NP-hard. To solve the problem efficiently, a heuristic algorithm, based on problem decomposition and variable fixing techniques, is proposed. A simulation-based evaluation method is also presented to evaluate the schedules obtained using the manual method, the deterministic model and the stochastic model in the operation stage. Computational tests are performed using data from Taiwan’s 1999 Chi-Chi earthquake. The preliminary test results demonstrate the potential usefulness of the proposed stochastic model and solution algorithm in actual practice.     

An exact approach to early/tardy scheduling with release dates

In this paper, we consider the single machine earliness/tardiness scheduling problem with different release dates and no unforced idle time. The problem is decomposed into weighted earliness and weighted tardiness subproblems. Lower bounding procedures are proposed for each of these subproblems, and the lower bound for the original problem is the sum of the lower bounds for the two subproblems. The lower bounds and several versions of a branch-and-bound algorithm are then tested on a set of randomly generated problems, and instances with up to 30 jobs are solved to optimality. To the best of our knowledge, this is the first exact approach for the early/tardy scheduling problem with release dates and no unforced idle time.     

A model with a solution algorithm for the cash transportation vehicle routing and scheduling problem

Cash transportation vehicle routing and scheduling are essential for security carriers to minimize their operating costs and ensure safe cash conveyance. In real operations, to increase cash conveyance safety, there must be significant variation in daily cash transportation vehicle routes and schedules, making such vehicle routes and schedules difficult to formulate. However, for convenient planning purposes, security carriers normally plan such routes and schedules based on personal experience, without considering variations in routes and schedules from a system perspective. As a result, the obtained routes and schedules are neither safe nor efficient for transporting cash. In this study, a model is developed where the time–space network technique is utilized to formulate the potential movements of cash transportation vehicles among all demand points in the dimensions of time and space. This model incorporates a new concept of similarity of time and space for routing and scheduling, which is expected to help security carriers formulate more flexible routing and scheduling strategies. This is helpful to reduce the risk of robbery. Mathematically, the model is formulated as an integer multiple-commodity network flow problem. A solution algorithm, based on a problem decomposition/collapsing technique, coupled with the use of a mathematical programming software, is developed to efficiently solve the problem. The case study results show that our model and solution algorithm could be useful references for security carriers in actual practice.     

An elective surgery scheduling problem considering patient priority

This paper addresses a scheduling problem where patients with different priorities are scheduled for elective surgery in a surgical facility, which has a limited capacity. When the capacity is available, patients with a higher priority are selected from the waiting list and put on the schedule. At the beginning of each period, a decision of the number of patients to be scheduled is made based on the trade-offs between the cost for overtime work and the cost for surgery postponement. A stochastic dynamic programming model is formulated to address this problem. A structural analysis of the proposed model is conducted to understand the properties of an optimal schedule policy. Based on the structural analysis, bounds on feasible actions are incorporated into a value iteration algorithm, and a brief computation experiment shows the improvement in computational efficiency. Numerical examples show that the consideration of patient priority results in significant differences in surgery schedules from the schedule that ignores the patient priority.     

The effect of few historical data on the performance of sample average approximation method for operating room scheduling

We model the scheduling problem of a single operating room for outpatient surgery, with uncertain case durations and an objective function comprising waiting time, idle time, and overtime costs. This stochastic scheduling problem has been studied in diverse forms. One of the most common approaches used is the sample average approximation (SAA). Our contribution is to study the use of SAA to solve this problem under few historical data using families of log t distributions with varying degrees of freedom. We analyze the results of the SAA method in terms of optimality convergence, the effect of the number of scenarios, and average computational time. Given the case sequence, computational results demonstrate that SAA with an adequate number of scenarios performs close to the exact method. For example, we find that the optimality gap, in units of proportional weighted time, is relatively small when 500 scenarios are used: 99% of the instances have an optimality gap of less than 2.6 7% (1.74%, 1.23%) when there are 3 (9, many) historical samples. Increasing the number of SAA scenarios improves performance, but is not critical when the case sequence is given. However, choosing the number of SAA scenarios becomes critical when the same method is used to choose among sequencing heuristics when there are few historical data. For example, when there are only three (nine, many) historical samples, 99% of the instances have less than 25.38% (13.15%, 6.87%) penalty in using SAA with 500 scenarios to choose the best sequencing heuristic.     

Dynamic task scheduling using online optimization

Algorithms for scheduling independent tasks on to the processors of a multiprocessor system must trade-off processor load balance, memory locality, and scheduling overhead. Most existing algorithms, however, do not adequately balance these conflicting factors. This paper introduces the self-adjusting dynamic scheduling (SADS) class of algorithms that use a unified cost model to explicitly account for these factors at runtime. A dedicated processor performs scheduling in phases by maintaining a tree of partial schedules and incrementally assigning tasks to the least-cost schedule. A scheduling phase terminates whenever any processor becomes idle, at which time partial schedules are distributed to the processors. An extension of the basic SADS algorithm, called DBSADS, controls the scheduling overhead by giving higher priority to partial schedules with more task-to-processor assignments. These algorithms are compared to two distributed scheduling algorithms within a database application on an Intel Paragon distributed memory multiprocessor system.     

How Lean transformation affects scheduling

The Lean paradigm transforms a production company from utilisation-centric planning into a system in which other operating conditions such as short flow times, local control, reduction in variation, and first-in-first-out control are weighted as well. This paper studies how the scheduling of production changes when the above four conditions are implemented. Their effects are studied by constructing an optimisation model for the scheduling of a flow shop. The optimisation model is based on the following ideas. First, when the flow time is emphasised, the objective of the scheduling changes from utilisation to a short flow time. Second, if local control is used, it means that the optimisation is performed locally, i.e. individually at each station, and it concerns the makespan at the station. Third, if the variation is reduced, the processing times and arrival times have less variation and, fourth, the scheduling can force the flow times to have less variation by using first-in-first-out (FIFO) sequencing. The experimental results achieved using the model describe how and in which order the operating conditions under study should be implemented in the scheduling. For example, if utilisation is important, local control and FIFO should not be used before variation is reduced.