Design and analysis of an outpatient orthopaedic clinic performance with discrete event simulation and design of experiments

Considering that demand for healthcare services is constantly increasing, outpatient services must improve their performance. Being able to satisfy the demand with a limited outpatient service capacity is an important operational challenge. The objective of our research consists in studying the relationships and interactions between patient flows, resource capacity (number of consulting rooms and number of nurses) and appointment scheduling rules in order to improve an outpatient orthopaedic clinic performance. Discrete event simulation is used to model outpatient flows. An experimental design was developed to test how to assign consulting rooms and nurses to each orthopedist considering four appointment scheduling rules and three patient flow types of varied complexity. Analysis of variance and the Tukey test are used to evaluate the simulation results. Our conclusion is that in order to improve the outpatient orthopaedic clinic performance, resources (consulting rooms, nurses) and appointment scheduling rules must be adapted to the different patient flows.     

基于负荷平衡的柔性预约决策

针对目前国内医疗机构普遍以步入病人求诊为主且个别时段密集到达的就诊需求特点,引入负荷均衡的思想,提出一种多目标优化的柔性门诊调度决策方法.根据实际负荷分布,合理利用柔性的预约负荷平衡调整各时段的总负荷,基于多种预约率、预约和排队规则形成方案集,在多目标灰靶决策模型下,优化出各应用场景下的最优调度方案.数值实验表明,所提出模型较其他模型能够有效降低等待时间高达77.2%.在实际应用分析中,所提出模型能够提高有效资源利用率66.7%,降低高空闲时间导致的资源敏感度.     

Simulation modeling and analysis of tool sharing and part scheduling decisions in single-stage multimachine flexible manufacturing systems

This paper focuses on a simulation-based study of tool sharing problem in single-stage multimachine Flexible Manufacturing Systems. Three different scenarios are considered for investigation. A simulation model has been developed for each of these scenarios. A number of scheduling rules are incorporated in the simulation models for the decisions such as tool request selection and part launching in the context of tool sharing environment. The performance measures evaluated are mean tardiness, conditional mean tardiness and mean flow time. Based on the analysis of the simulation results, the best possible scheduling rule combinations for part launching and tool request selection have been identified for the three scenarios.     

Simulation modelling and analysis of part and tool flow control decisions in a flexible manufacturing system

This paper presents the details of a simulation study carried out for analyzing the impact of scheduling rules that control part launching and tool request selection decisions of a flexible manufacturing system (FMS) operating under tool movement along with part movement policy. Two different scenarios have been investigated with respect to the operation of FMS. In scenario 1, the facilities such as machines, tool transporter and part transporter are assumed to be continuously available without breakdowns, whereas in scenario 2, these facilities are prone to failures. For each of these scenarios, a discrete-event simulation model is developed for the purpose of experimentation. A number of scheduling rules are incorporated in the simulation models for the part launching and tool request selection decisions. The performance measures evaluated are mean flow time, mean tardiness, mean waiting time for tool and percentage of tardy parts. The results obtained through the simulation have been statistically analyzed. The best possible scheduling rule combinations for part launching and tool request selection have been identified for the chosen FMS.     

Single versus hybrid time horizons for open access scheduling

Difficulty in scheduling short-notice appointments due to schedules booked with routine check-ups are prevalent in outpatient clinics, especially in primary care clinics, which lead to more patient no-shows, lower patient satisfaction, and higher healthcare costs. Open access scheduling was introduced to overcome these problems by reserving enough appointment slots for short-notice scheduling. The appointments scheduled in the slots reserved for short-notice are called open appointments. Typically, the current open access scheduling policy has a single time horizon for open appointments. In this paper, we propose a hybrid open access policy adopting two time horizons for open appointments, and we investigate when more than one time horizon for open appointments is justified. Our analytical results show that the optimized hybrid open access policy is never worse than the optimized current single time horizon open access policy in terms of the expectation and the variance of the number of patients consulted. In nearly 75% of the representative scenarios motivated by primary care clinics, the hybrid open access policy slightly improves the performance of open access scheduling. Moreover, for a clinic with strong positive correlation between demands for fixed and open appointments, the proposed hybrid open access policy can considerably reduce the variance of the number of patients consulted.     

A hybrid simulation and genetic algorithm approach to determine the optimal scheduling templates for open access clinics admitting walk-in patients

With the pressing demand for improving patient accessibility, the traditional scheduling system may not be effective for mitigating the adverse effects caused by no-shows, appointment cancellations and late arrivals. For this reason, open access scheduling, which specifies that a portion of clinic appointment slots be reserved for short-notice appointments, was proposed and adopted in recent years. In literature, many studies have developed a variety of approaches and models to optimize the open access scheduling systems, while few considers the inclusion of walk-in patients and the optimal allocation of reserved slots on the scheduling template under the open access configuration. In this paper, we propose a Discrete Event Simulation and Genetic Algorithm (DES–GA) approach to find the heuristic optimal scheduling template under the clinic setting that allows both open access and walk-in patients. The solution can provide scheduling templates consisting of not only the optimal number of reservations for open access appointments and walk-ins, but also the optimized allocation of these reserved slots, by minimizing the average cost per admission of open access or walk-in patient. In this approach, the cost is measured by the weighted summation of patient waiting time, provider idle time, and provider overtime. A case study and sensitivity analysis are conducted to show how the heuristic optimal scheduling template generated from the proposed approach could vary under different scenarios. This also illustrates the viability of our model. The results show that the heuristic optimal scheduling templates are significantly affected by the patient attendance rate, level of demands of same-day appointment and walk-in admissions, as well as the cost coefficients associated with patient waiting time, provider idle time and provider overtime.     

Designing cyclic appointment schedules for outpatient clinics with scheduled and unscheduled patient arrivals

We present a methodology to design appointment systems for outpatient clinics and diagnostic facilities that offer both walk-in and scheduled service. The developed blueprint for the appointment schedule prescribes the number of appointments to plan per day and the moment on the day to schedule the appointments. The method consists of two models; one for the day process that governs scheduled and unscheduled arrivals on the day and one for the access process of scheduled arrivals. Appointment schedules that balance the waiting time at the facility for unscheduled patients and the access time for scheduled patients are calculated iteratively using the outcomes of the two models. Two methods to calculate appointment schedules, complete enumeration and a heuristic procedure, are compared in various numerical experiments. Furthermore, an appointment schedule for the CT-scan facility at the Academic Medical Center Amsterdam, The Netherlands, is developed to demonstrate the practical merits of the methodology. The method is of general nature and can therefore also be applied to scheduling problems in other sectors than health care.     

Appointment scheduling algorithm considering routine and urgent patients

This paper derives a solution approach to solve the outpatient appointment schedule problem for given numbers of routine and urgent patients considering a no-show probability to minimize the weighted sum of average patient wait time, physician idle time and overtime. An exact deterministic service time method is proposed to find the optimal schedule. An exponentially distributed service time property is presented to show that the objective function for routine and urgent patients is not multimodular, and consequently a local search algorithm based on multimodulary does not guarantee global optimality. Thus, a heuristic algorithm based on two kinds of shifting policies (HE-TKS) is developed to solve the appointment schedule, which gives a local optimal solution as an upper bound for the optimal schedule. Numerical experiments are conducted to illustrate how the critical factors affect service efficiency of the clinic in practice. It reveals that lower no-show probability, smaller interval lengths, shorter service times, and more urgent patients will benefit both patients and clinics.     

Allocation and scheduling of Conditional Task Graphs

We propose an original, complete and efficient approach to the allocation and scheduling of Conditional Task Graphs (CTGs). In CTGs, nodes represent activities, some of them are branches and are labeled with a condition, arcs rooted in branch nodes are labeled with condition outcomes and a corresponding probability. A task is executed at run time if the condition outcomes that label the arcs in the path to the task hold at schedule execution time; this can be captured off-line by adopting a stochastic model. Tasks need for their execution either unary or cumulative resources and some tasks can be executed on alternative resources. The solution to the problem is a single assignment of a resource and of a start time to each task so that the allocation and schedule is feasible in each scenario and the expected value of a given objective function is optimized. For this problem we need to extend traditional constraint-based scheduling techniques in two directions: (i) compute the probability of sets of scenarios in polynomial time, in order to get the expected value of the objective function; (ii) define conditional constraints that ensure feasibility in all scenarios. We show the application of this framework on problems with objective functions depending either on the allocation of resources to tasks or on the scheduling part. Also, we present the conditional extension to the timetable global constraint. Experimental results show the effectiveness of the approach on a set of benchmarks taken from the field of embedded system design. Comparing our solver with a scenario based solver proposed in the literature, we show the advantages of our approach both in terms of execution time and solution quality.     

Non-binary quantified CSP: algorithms and modelling

The Quantified Constraint Satisfaction Problem (QCSP) extends classical CSP in a way which allows reasoning about uncertainty. In this paper I present novel algorithms for solving QCSP. Firstly I present algorithms to perform constraint propagation on reified disjunction constraints of any length. The algorithms make full use of quantifier information to provide a high level of consistency. Secondly I present a scheme to enforce the non-binary pure value rule. This rule is capable of pruning universal variables. Following this, two problems are modelled in non-binary QCSP: the game of Connect 4, and a variant of job-shop scheduling with uncertainty, in the form of machine faults. The job shop scheduling example incorporates probability bounding of scenarios (such that only fault scenarios above a probability threshold are considered) and optimization of the schedule makespan. These contribute to the art of modelling in QCSP, and are a proof of concept for applying QCSP methods to complex, realistic problems. Both models make use of the reified disjunction constraint, and the non-binary pure value rule. The example problems are used to evaluate the QCSP algorithms presented in this paper, identifying strengths and weaknesses, and to compare them to other QCSP approaches.     

Optimal booking and scheduling in outpatient procedure centers

Patient appointment booking, sequencing, and scheduling decisions are challenging for outpatient procedure centers due to uncertainty in procedure times and patient attendance. We extend a previously developed appointment scheduling model to formulate a model based on a two-stage stochastic mixed integer program for optimizing booking and appointment times in the presence of uncertainty. The objective is to maximize expected profit. Analytical insights are reported for special cases and experimental results show that they provide useful rules of thumb for more general problems. Three solution methods are described which take advantage of the underlying structure of the stochastic program, and a series of experiments are performed to determine the best method. A case study based on an endoscopy suite at a large medical center is used to draw a number of useful managerial insights for procedure center managers.     

Dispatching rule selection using artificial neural networks for dynamic planning and scheduling

To schedule a job shop, the first task is to select an appropriate scheduling algorithm or rule. Because of the complexity of scheduling problems, no general algorithm sufficient for solving all scheduling problems has yet been developed. Most job-shop scheduling systems offer alternative algorithms for different situations, and experienced human schedulers are needed to select the best dispatching rule in these systems. This paper proposes a new algorithm for job-shop scheduling problems. This algorithm consists of three stages. First, computer simulation techniques are used to evaluate the efficiency of heuristic rules in different scheduling situations. Second, the simulation results are used to train a neural network in order to capture the knowledge which can be used to select the most efficient heuristic rule for each scheduling situation. Finally, the trained neural network is used as a dispatching rule selector in the real-time scheduling process. Research results have shown great potential in using a neural network to replace human schedulers in selecting an appropriate approach for real-time scheduling. This research is part of an ongoing project of developing a real-time planning and scheduling system.     

The impact of predictive inaccuracies on execution scheduling

This paper investigates the underlying impact of predictive inaccuracies on execution scheduling, with particular reference to execution time predictions. This study is conducted from two perspectives: from that of job selection and from that of resource allocation, both of which are fundamental components in execution scheduling. A new performance metric, termed the degree of misperception, is introduced to express the probability that the predicted execution times of jobs display different ordering characteristics from their real execution times due to inaccurate prediction. Specific formulae are developed to calculate the degree of misperception in both job selection and resource allocation scenarios. The parameters which influence the degree of misperception are also extensively investigated. The results presented in this paper are of significant benefit to scheduling approaches that take into account predictive data; the results are also of importance to the application of these scheduling techniques to real-world high-performance systems.     

Performance evaluation of candidate appointment schedules using clearing functions

This study is concerned with the problem of reducing the waiting times of outpatients. Both scheduled patients and walk-ins are included among the outpatients to reflect the typical medical environment in Japan. The consultation time of a hospital is divided into several blocks, and each scheduled patient is given the start time of a block as his or her scheduled time of the consultation as an appointment. It is assumed that all scheduled patients arrive at the hospital at their scheduled times, while walk-ins arrive randomly. A set of candidate appointment schedules is given, and the process of selecting promising schedules in terms of average waiting times is the focus of the work. To support the selection process without conducting a conventional simulation, the notion of a clearing function is adopted to evaluate each candidate schedule. The clearing function of a system gives the expected output or throughput of the system under varying levels of workload of the system. Although it is necessary to conduct exploratory experiments in advance to obtain the clearing function, the expected waiting time can be estimated by simple calculations with the aid of the clearing function. The average waiting times of four schedules in two scenarios are calculated and compared with those obtained from conventional simulations. It is revealed that the proposed procedure based on the clearing function gives acceptable estimated average values.     

A comparison of machine-learning algorithms for dynamic scheduling of flexible manufacturing systems

Dispatching rules are frequently used to schedule jobs in flexible manufacturing systems (FMSs) dynamically. A drawback, however, to using dispatching rules is that their performance is dependent on the state of the system, but no single rule exists that is superior to all the others for all the possible states the system might be in. This drawback would be eliminated if the best rule for each particular situation could be used. To do this, this paper presents a scheduling approach that employs machine learning. Using this latter technique, and by analysing the earlier performance of the system, ‘scheduling knowledge’ is obtained whereby the right dispatching rule at each particular moment can be determined. Three different types of machine-learning algorithms will be used and compared in the paper to obtain ‘scheduling knowledge’: inductive learning, backpropagation neural networks, and case-based reasoning (CBR). A module that generates new control attributes allowing better identification of the manufacturing system's state at any particular moment in time is also designed in order to improve the ‘scheduling knowledge’ that is obtained. Simulation results indicate that the proposed approach produces significant performance improvements over existing dispatching rules.     

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.     

Workload vs scheduling policies in a dual-resource constrained job shop

The purpose of this paper is to report on research conducted to examine the effectiveness of different scheduling policies in a dual-constrained job shop under various workload conditions. The standard assumption in most job shop scheduling research has been that a 90% utilization of the shop is achieved. However, since shop utilization levels vary widely, it was hypothesized that scheduling policies that are optimum under one load condition might not be as effective under other load conditions. The model for this simulation experiment represented a job shop constrained by both labor and machines. The shop contains four machine centers with random routing of jobs through the shop. Shop workload was defined at three levels: 70, 85 and 99% utilization. Four machine scheduling rules and three labor assignment rules were tested for each of the shop workload levels, with mean job flow time as. the performance criterion. The results of the 3 × 4 × 3 factorial experiment showed that the advantage of the SPT (shortest processing time) machine scheduling rule over other rules is diminished dramatically when shop utilization is reduced from 99 to 85% or below. This same observation holds for other rules considered. The LNQ (longest queue length) labor assignment rule outperformed other rules at the 99% utilization level, but yielded no significant difference in performance at the 85% and below workload levels.     

An opportunistic and non-anticipating size-aware scheduling proposal for mean holding cost minimization in time-varying channels

In this paper we study how to design a scheduling strategy aimed at minimizing the average holding cost for flows with general size distribution when the feasible transmission rate of each user varies randomly over time. We employ a Whittle-index-based approach in order to achieve an opportunistic and non-anticipating size-aware scheduling index rule proposal. When the flow size distribution belongs to the Decreasing Hazard Rate class, we propose the so-called Attained Service Potential Improvement index rule, which consists in giving priority to the flows with the highest ratio between the current attained-service-dependent completion probability and the expected potential improvement of this completion probability. We further analyze the performance of the proposed scheduler, concluding that it outperforms well-known opportunistic disciplines.     

Optimization of scheduling patient appointments in clinics using a novel modelling technique of patient arrival

This paper re-visits the question of mapping a probability distribution to patient unpunctuality in appointment-driven outpatient clinics, with reference to published empirical arrival data. This data indicates the possibility of interesting aberrations such as local modes and near-modes, asymmetry and peakedness. We examine the form of some published data on patient unpunctuality, and propose a mixed distribution which we call "F3" to provide a richer representation of shape such as in the shoulders of the distribution. The adequacy of this model is assessed in a worked example referencing a classical study, where a comparison is made of F3 against the normal and Pearson VII distributions with reference to summary statistics, graphical probability plots (P-P and Q-Q), a range of goodness of fitness criteria. Under this patient arrival setting, 2P method is proposed for optimal patient interval setting to minimize waiting time of both patient and the doctor and this 2P method is validated with a tentative simulation example. This study argues that frequency distribution of patient unpunctuality shows asymmetry in shape which is resulted from various types of arrival behaviours. Consequently optimal appointment intervals of scheduled patients, which minimize the total waiting time of patients and the doctor is highly related to patient unpunctuality patterns and this makes the optimal appointment intervals for various patient unpunctualities predictable.     

LEARNING-BASED SCHEDULING OF FLEXIBLE MANUFACTURING SYSTEMS USING SUPPORT VECTOR MACHINES

Dispatching rules are usually applied to dynamically schedule jobs in flexible manufacturing systems (FMSs). Despite their frequent use a significant drawback is that the performance level of the rule is dictated by the current state of the manufacturing system. Because no rule is better than any other for every system state, it would be highly desirable to know which rule is the most appropriate for each given condition. To achieve this goal we propose a scheduling approach using support vector machines (SVMs). By using this technique and by analyzing the earlier performance of the system, “scheduling knowledge” is obtained whereby the right dispatching rule at each particular moment can be determined. Simulation results show that the proposed approach leads to significant performance improvements over existing dispatching rules. In the same way it is also confirmed that SVMs perform better than other traditional machine learning algorithms as the inductive learning when applied to FMS scheduling problem, due to their better generalization capability.