The Critical Few Minutes in Scheduling Time‐Varying Queuing Systems

For nonstationary queuing systems where demand varies over time, an important practical issue is scheduling the number of servers to be available at various times of the day. Widely used scheduling procedures typically involve adding servers at natural time points (e.g., on the hour or at half past the hour) during peak demand periods. Scheduling is often complicated by restrictions on the minimum amount of time (human) servers must work, the earliest (or latest) time a server is available, and limits on the maximum number of servers that can be used at any one time. This paper was motivated by experience with actual queuing systems that embodied such complications. For these systems common scheduling methods that used “natural” starting times for servers resulted in needlessly long customer waits. This research demonstrates that changing the starting times of servers by only a few minutes can have dramatic impacts on customer waiting times for extended periods. In addition, the results highlight the importance of server punctuality.     

Social Optimal Location of Facilities with Fixed Servers,Stochastic Demand,and Congestion

We consider two capacity choice scenarios for the optimal location of facilities with fixed servers, stochastic demand, and congestion. Motivating applications include virtual call centers, consisting of geographically dispersed centers, walk‐in health clinics, motor vehicle inspection stations, automobile emissions testing stations, and internal service systems. The choice of locations for such facilities influences both the travel cost and waiting times of users. In contrast to most previous research, we explicitly embed both customer travel/connection and delay costs in the objective function and solve the location–allocation problem and choose facility capacities simultaneously. The choice of capacity for a facility that is viewed as a queueing system with Poisson arrivals and exponential service times could mean choosing a service rate for the servers (Scenario 1) or choosing the number of servers (Scenario 2). We express the optimal service rate in closed form in Scenario 1 and the (asymptotically) optimal number of servers in closed form in Scenario 2. This allows us to eliminate both the number of servers and the service rates from the optimization problems, leading to tractable mixed‐integer nonlinear programs. Our computational results show that both problems can be solved efficiently using a Lagrangian relaxation optimization procedure.     

APPROXIMATIONS FOR THE GI/G/m QUEUE

Queueing models can usefully represent production systems experiencing congestion due to irregular flows, but exact analyses of these queueing models can be difficult. Thus it is natural to seek relatively simple approximations that are suitably accurate for engineering purposes. Here approximations for a basic queueing model are developed and evaluated. The model is the GI/G/m queue, which has m identical servers in parallel, unlimited waiting room, and the first-come first-served queue discipline, with service and interarrival times coming from independent sequences of independent and identically distributed random variables with general distributions. The approximations depend on the general interarrival-time and service-time distributions only through their first two moments. The main focus is on the expected waiting time and the probability of having to wait before beginning service, but approximations are also developed for other congestion measures, including the entire distributions of waiting time, queue-length and number in system. These relatively simple approximations are useful supplements to algorithms for computing the exact values that have been developed in recent years. The simple approximations can serve as starting points for developing approximations for more complicated systems for which exact solutions are not yet available. These approximations are especially useful for incorporating GI/G/m models in larger models, such as queueing networks, wherein the approximations can be components of rapid modeling tools.     

Appointment Overbooking in Health Care Clinics to Improve Patient Service and Clinic Performance

The problem of no‐shows (patients who do not arrive for scheduled appointments) is particularly significant for health care clinics, with reported no‐show rates varying widely from 3% to 80%. No‐shows reduce revenues and provider productivity, increase costs, and limit patient access by reducing effective clinic capacity. In this article, we construct a flexible appointment scheduling model to mitigate the detrimental effects of patient no‐shows, and develop a fast and effective solution procedure that constructs near‐optimal overbooked appointment schedules that balance the benefits of serving additional patients with the potential costs of patient waiting and clinic overtime. Computational results demonstrate the efficacy of our model and solution procedure, and connect our work to prior research in health care appointment scheduling.     

APPOINTMENT POLICIES IN SERVICE OPERATIONS: A CRITICAL ANALYSIS OF THE ECONOMIC FRAMEWORK

In this paper we review the literature on appointment policies, specifically in terms of the objective function commonly used and the assumptions made about the behavior of demand. First, we provide an economic framework to analyze the problem. Based on this framework we make a critical analysis of the objective functions used in the literature. We also question the validity of the assumption made throughout the literature that demand is exogenous and independent of customers' waiting times. We conclude that the objective functions used in the literature are appropriate only in the case of a central planner facing a demand that is unresponsive to waiting time. For other scenarios, such as a private server facing a demand that does react to waiting time, these objective functions are only shortcuts for the real objective functions that must be used. A more general model is then proposed that fits these scenarios well. Finally, we determine the impact of using the literature's objective functions on optimal appointment policies.     

Optimal loan periods for undergraduate recommended reading

A model is developed for the total expected utility to borrowers of an undergraduate text book recommended by a lecturer. It takes account of the peaked demand for a book following a recommendation, measures of borrower satisfaction which involve both waiting time and reading time (loan period), and the persistence of would-be borrowers in requesting books not found on the shelves. Some parameters of the model were estimated by a method which elicited preferences of students in various choice situations; other parameters were estimated by librarians. Some specific conclusions are drawn regarding the optimal loan period of books in terms of their type and the number of copies held.     

Would Allowing Privately Funded Health Care Reduce Public Waiting Time? Theory and Empirical Evidence from Canadian Joint Replacement Surgery Data

This study develops a theoretical model and then, using Canadian joint replacement surgery data, empirically tests the relationship between government policies that promote privately funded health care and patients’ waiting time in the public health care system. Two policies are tested: one policy allows opt‐out physicians to extra‐bill private patients, and the other provides public subsidies to private patients. We find that both policies are associated with shorter public waiting time, and that the subsidy policy appears to be more effective in waiting time reduction than the extra‐billing policy. Our findings are consistent with a dominant demand‐side effect in that these policies would provide patients an option, and some incentive, to opt out of the public health system, shifting the demand from the public health system to the private care market.     

An EOQ inventory model for items with Weibull distribution deterioration,ramp type demand rate and partial backlogging

In this paper, an EOQ inventory model is presented depleted not only by demand but also by Weibull distribution deterioration, in which the demand rate is assumed that with a ramp type function of time. In the model, shortages are allowed partial backlogging and the backlogging rate is variable and is dependent on waiting time for the next replenishment. The method is illustrated by three numerical examples, and sensitivity analysis of the optimal solution with respect to parameters of the system is carried out.     

多渠道医疗门诊挂号的时间策略研究

现阶段多种门诊挂号方式并存时,根据患者特性制定不同的等待时间策略尤为重要。本文考虑门诊挂号的三种渠道：直接排队挂号渠道、电话预约挂号渠道与O2O预约挂号渠道。在价格外生前提下,综合考虑患者的渠道偏好程度、时间敏感性与提前支付敏感性,基于效用理论构建患者的渠道选择模型。根据该模型推导得出不同市场条件下医院的需求,医院再据此制定患者的等待时间策略以达到利润最大化的目的。研究发现：当医院仅开通单一挂号渠道时,若患者的时间敏感度越大、渠道偏好程度越小,等待时间均越小;开通某两种挂号渠道时,还需考虑患者对两种渠道的偏好比例,偏好某种渠道的患者比例增加,选择该渠道的患者等待时间增加,选择另一渠道的患者等待时间减小;同时开通三种渠道时,最偏好某渠道的患者比例越大,选择该渠道的患者的等待时间也越大;在所有情况下,患者对提前支付的敏感度均不影响最优等待时间的制定。     

Estimation of Tuberculosis Risk and Incidence under Upper Room Ultraviolet Germicidal Irradiation in a Waiting Room in a Hypothetical Scenario

Environmental control measures (ventilation, high-efficiency particulate air filtration, and upper room ultraviolet germicidal irradiation [UVGI]) are recommended to effectively control tuberculosis (TB) transmission from unsuspected TB patients in high-risk settings, but the effectiveness of their use is not often clear. This study presents a simulation model for a hypothetical hospital waiting room, in which the number of susceptible immunocompetent people in the waiting room follows a Poisson distribution (M = 5) in either low (annual number of TB patients = 5) or high TB risk settings (annual number of TB patients = 50), and used the model to evaluate the reduction of TB transmission risk by upper room UVGI. An exponential dose-response model was used for TB transmission and a two-zone model was used for evaluating the effect of upper room UVGI. Upper room UVGI reduced TB risk by 1.6-fold at 3 microW/cm2 UV irradiance in the upper room in the low TB risk setting and by 4.1-fold at 15 microW/cm2 UV irradiance in the upper room in the high TB risk setting. Use of upper room UVGI also reduced the mean annual new infection rate from 2.2 to 1.3 infections per year at 3 microW/cm2 and to 0.6 infections per year at 15 microW/cm2 in our hypothetical high-risk settings. The effect of upper room UVGI was sensitive to both vertical air velocity (air mixing) and UV irradiance level. Results from partitioning variability indicate that most variability of TB transmission risk came from waiting time in our hypothetical hospital.     

Waiting Line Effects in Analytical Maintenance Float Policy

The equipment failure distributions commonly identified in practice pose great difficulties in the establishment of sound maintenance total float policy. Some of the existing analytical constructs utilize the reliability ratio of the equipment in operations in order to bypass the obstacles and arrive at applicable solutions. In this paper we give a summary of these theoretical models. In addition, we provide insight by testing the significance of factors utilized in maintenance total float determination. The paper examines the effect of the assumption made by the analytical model of no waiting time for repair. Our test showed that there is no statistically significant difference between the analytical model and simulation when waiting is allowed for the normal and uniform distributions. The analytical model thus offers some advantage in its use to estimate maintenance float due to its simplicity. When failure distribution is an exponential, Erlang-2 or lognormal, the assumption of no waiting time for repair must be kept in order to use the analytical model.     

The price-quality relationship: A heuristic model

An on-the-shop-floor experiment is carried out to determine the price-quality relationship for a number of toiletries. Three different and distinct demand curves are obtained. A heuristic model to describe these curves is constructed. The implications of this model for the profit-orientated businessman are then analysed.     

Scheduling and performance analysis under a stochastic model for electric vehicle charging stations

Wide-spread infrastructures for electric vehicle battery charging stations are essential in order to significantly increase the implementation of electric vehicles (EVs) in the foreseeable future. Therefore, we propose a stochastic model and charge scheduling methods for an EV battery charging system. We utilize a flexible Poisson process with a hidden Markov chain for modeling the complexity of the time-varying behavior of the EV stream into the system. Relevant random factors and constraints, which include parking times, requested amounts of electricity, the number of parking lots (charging facilities), and maximal demand level, are considered within the proposed stochastic model. Performance measures for the proposed charge scheduling are analytically derived by obtaining stationary distributions of states concerning the number of inbound EVs, waiting time distributions, and the joint distributions of parking time and electricity charged during random parking times.     

How Long Should a Customer Wait for Service?

A major concern for service managers is the determination of how long a customer should wait to be served. Services, due to the customer's direct interaction with the process, must face a trade-off between minimizing the cost of having a customer wait and the cost of providing good service. A total cost model is presented for determining how long a customer should wait when these two conflicting cost components are considered. An integral part of this model includes a measure of customer satisfaction with waiting time which is used to develop a waiting cost function. The model is then applied to a major fast food chain, using data collected at several locations. Analysis of the data reveals that the “ideal” waiting time for this firm is significantly less than the current corporate waiting time policy. Thus, as indicated by the model, a corporate policy change is recommended to provide much faster service. The adoption of such a policy would result in increased labor costs, and would simultaneously increase the firm's overall profits. Although appearing contradictory, increases in current labor costs and long-term profits are both possible when management takes the long-range perspective suggested in this paper.     

基于系统柔性的MTS-MTO混合生产决策

研究生产商采用MTS、MTO混合作业的方式为不同客户提供产品和服务的策略。计划利用一组可灵活控制的动态设备处理那些不同需求的MTS和MTO生产业务,为此,我们开发了一个多服务台的排队模型,利用拟生灭过程和相位型分布得到了MTS、MTO排队系统平衡条件和稳态概率矩阵几何解。通过求解分块矩阵方程组,给出了系统队列长度、平均等待队长、顾客服务水平等绩效测度指标。建立了系统运作成本最优化的数学模型,采用搜索算法,确定了关键参数的边界值,找到了混合系统运作的最优策略。数值模拟和系统绩效比较分析结果显示：（1）动态切换策略能够更快速的帮助MTS恢复目标库存量,控制系统缺货风险,降低库存持有成本;（2）找到了满足顾客服务水平的最少的设备配置数量和库存成本最低的生产切换时间,且动态系统的平均队列长度低于静态系统;（3）混合运作策略减少了约2/3的静态系统平均队列长度,企业在队列长度减小的窗口期内可以接受更多订单和缩短MTO订单交货时间。     

Preparation of chemotherapy drugs: Planning policy for reduced waiting times

This study investigates the impact of pharmacy policies on patient waiting time in the Chemotherapy Day Unit of the Netherlands Cancer Institute—Antoni van Leeuwenhoek hospital. The project evaluated whether a reduction in waiting time resulting from medication orders being prepared in advance of patient appointments was justified, given that medications prepared in advance are wasted when patients arrive too sick for treatment. Within this context, we derive analytic expressions to approximate patient waiting times and wastage costs, allowing management to see the tradeoff between these two metrics for different policies. Using a case study and a simulation model, the approximations are evaluated. The use of analytic expressions allows the analysis to be easily repeated when medication costs change or when new medications/protocols are introduced. In the same vein, other hospitals with different patient case mixes can easily complete the analysis in their settings. Finally, the outcome from this study resulted in a new policy at the cancer center which is expected to decrease the waiting time by half, while only increasing pharmacy's costs by 1-2%.     

Disassembly to order system under uncertainty

This paper presents a multi-criteria optimization model of a disassembly-to-order (DTO) system under uncertainty. The goal of the proposed model is to determine the best combination of the number of each product type to be taken back from the last user and/or collectors. The EOL products are then disassembled for the retrieval of reusable components and materials and resold in order to meet a certain level of demand under a variety of physical, financial and environmental constraints. The surplus components are recycled, stored for usage in subsequent periods or properly disposed. The problem is modeled as a multi-criteria decision-making problem under uncertainty, where the aspiration levels for various goals are more likely to be in the “approximately more (less) than” and/or “more (less) is better” form. We employ fuzzy goal programming technique to solve the problem. When solved, the model provides the number of EOL products to be taken back as well as the number of items reused, recycled, stored and disposed. The values of a host of other performance measures are also obtained, including total profit, materials and items sales revenues, take back cost, transportation costs as well as costs of preparation of EOL products, destructive disassembly, non-destructive disassembly, recycling, storage and disposal. A case example is presented to illustrate the model's implementation.     

Design Principles for Flexible Systems

A fundamental aspect of designing systems with dedicated servers is identifying and improving the system bottlenecks. We extend the concept of a bottleneck to networks with heterogeneous, flexible servers. In contrast with a network with dedicated servers, the bottlenecks are not a priori obvious, but can be determined by solving a number of linear programming problems. Unlike the dedicated server case, we find that a bottleneck may span several nodes in the network. We then identify some characteristics of desirable flexibility structures. In particular, the chosen flexibility structure should not only achieve the maximal possible capacity (corresponding to full server flexibility), but should also have the feature that the entire network is the (unique) system bottleneck. The reason is that it is then possible to shift capacity between arbitrary nodes in the network, allowing the network to cope with demand fluctuations. Finally, we specify when certain flexibility structures (in particular chaining, targeted flexibility, and the “N” and “W” structures from the call center literature) possess these desirable characteristics.     

Access to Long‐Term Care: The True Cause of Hospital Congestion?

Much attention has been paid to lengthy wait times in emergency departments (EDs) and much research has sought to improve ED performance. However, ED congestion is often caused by the inability to move patients into the wards while the wards in turn are often congested primarily due to patients waiting for a bed in a long‐term care (LTC) facility. The scheduling of clients to LTC is a complex problem that is compounded by the variety of LTC beds (different facilities and room accommodations), the presence of client choice and the competing demands of the hospital and community populations. We present a Markov decision process (MDP) model that determines the required access in order for the census of patients waiting for LTC in the hospitals to remain below a given threshold. We further present a simulation model that incorporates both hospital and community demand for LTC in order to predict the impact of implementing the policy derived from the MDP on the community client wait times and to aid in capacity planning for the future. We test the MDP policy vs. current practice as well as against a number of other proposed policy changes.     

A multi-objective vehicle routing and scheduling problem with uncertainty in customers’ request and priority

In this paper, a multi-objective vehicle routing and scheduling problem with uncertainty in priority and request of customers is presented. In the proposed model, a set of dynamic requests is received over time, and the planner does not have any information regarding their location and size until they arrive. Moreover, the routing model aims to satisfy different customers according to their specific time windows which were predefined by an expert as (being very important, important, casual or unimportant). This paper uses the proposed model as a multi-objective problem where the total required number of vehicles, the total distance travelled and the waiting time imposed on vehicles are minimized, and the total customers’ satisfaction for service is maximized. An efficient framework for solving this model is designed and its performance is evaluated in different steps for various test problems generalized from Solomon’s VRPTW benchmark problems. The various heuristics and improvement concepts incorporate local exploitation in the evolutionary search, and the concept of Pareto optimality for the multi-objective optimization is used in the proposed procedure. The computational experiments on data sets illustrate the efficiency and effectiveness of the proposed approach.