LETRIS: Staffing service systems by means of simulation

Purpose: This paper introduces a procedure for solving the staffing problem in a service system (i.e., determining the number of servers for each staffing period). Design/methodology: The proposed algorithm combines the use of queueing theory to find an initial solution with the use of simulation to adjust the number of servers to meet previously specified target non-delay probabilities. The basic idea of the simulation phase of the procedure is to successively fix the number of servers from the first staffing period to the last, without backtracking. Findings: Under the assumptions that the number of servers is not upper-bounded and there are no abandonments and, therefore, no retrials, the procedure converges in a finite number of iterations, regardless of the distributions of arrivals and services, and requires a reasonable amount of computing time. Originality / value: The new procedure proposed in this paper is a systematic, robust way to find a good solution to a relevant problem in the field of service management and it is very easy to implement using no more than commonly accessible tools.Peer Reviewe

A queueing theoretic approach to set staffing levels in time-dependent dual-class service systems

This article addresses the optimal staffing problem for a nonpreemptive priority queue with two customer classes and a time-dependent arrival rate. The problem is related to several important service settings such as call centers and emergency departments where the customers are grouped into two classes of “high priority” and “low priority,” and the services are typically evaluated according to the proportion of customers who are responded to within targeted response times. To date, only approximation methods have been explored to generate staffing requirements for time-dependent dual-class services, but we propose a tractable numerical approach to evaluate system behavior and generate safe minimum staffing levels using mixed discrete-continuous time Markov chains (MDCTMCs). Our approach is delicate in that it accounts for the behavior of the system under a number of different rules that may be imposed on staff if they are busy when due to leave and involves explicitly calculating delay distributions for two customer classes. Ultimately, we embed our methodology in a proposed extension of the Euler method, coined Euler Pri, that can cope with two customer classes, and use it to recommend staffing levels for the Welsh Ambulance Service Trust (WAST)

Managing Trade-Offs in Call Center Agent Scheduling: Methodology and Case Study

This paper develops a flexible and tractable scheduling methodology that produces near-optimal call center agent schedules while taking into account the costs associated with customer waiting time, customer abandonment, and call center agents. Our methodology combines integer programming (to find a desirable staffing plan for a given total number of agents) and simulation modeling (to evaluate the weekly costs of a given staffing plan). We describe the advantages of this approach over the traditional scheduling method, and test both methods by building schedules based on actual demand and shift data from an actual call center operated by Expedia.com under a variety of cost scenarios. The new scheduling approach not only out-performs the traditional staffing approach in all scenarios examined, it reduces total weekly costs of the call center\u27s existing agent schedule by 8-25%, depending on the scenario

Intelligent Procedures for Intra-Day Updating of Call Center Agent Schedules

For nearly all call centers, agent schedules are typically created several days or weeks prior to the time that agents report to work. After schedules are created, call center resource managers receive additional information that can affect forecasted workload and resource availability. In particular, there is significant evidence, both among practitioners and in the research literature, suggesting that actual call arrival volumes early in a scheduling period (typically an individual day or week) can provide valuable information about the call arrival pattern later in the same scheduling period. In this paper, we develop a flexible and powerful heuristic framework for managers to make intra-day resource adjustment decisions that take into account updated call forecasts, updated agent requirements, existing agent schedules, agents’ schedule flexibility, and associated incremental labor costs. We demonstrate the value of this methodology in managing the trade-off between labor costs and service levels to best meet variable rates of demand for service, using data from an actual call center

Modeling And Optimization Of Non-Profit Hospital Call Centers With Service Blending

This dissertation focuses on the operations problems in non-profit hospital call centers with inbound and outbound calls service blending. First, the routing policy for inbound and outbound calls is considered. The objective is to improve the system utilization under constraints of service quality and operators\u27 quantity. A collection of practical staffing assignment methods, separating and mixing staffing policy are evaluated. Erlang C queuing model is used to decide the minimum number of operators required by inbound calls. Theoretical analysis and numerical experiments illustrate that through dynamically assigning the inbound and outbound calls to operators under optimal threshold policy, mixing staffing policy is efficient to balance the system utilization and service quality. Numerical experiments based on real-life data demonstrate how this method can be applied in practice. Second, we study the staffing shift planning problem based on the inbound and outbound calls routing policies. A mathematical programming model is developed, based on a hospital call center with one kind of inbound calls and multiple kinds of outbound calls. The objective is to minimize the staffing numbers, by deciding the shift setting and workload allocation. The inbound calls service level and staffing utilization are taken into consideration in the constraints. Numerical experiments based on actual operational data are included. Results show that the model is effective to optimize the shift planning and hence reduce the call centers\u27 cost. Third, we model the staffing shift planning problem for a hospital call center with two kinds of service lines. Each kind of service is delivered through both inbound calls and outbound calls. The inbound calls can be transferred between these two service lines. A mathematical programming model is developed. The objective is to minimize the staffing cost, by deciding the shift setting and workload allocation. The inbound calls service level and staffing utilization are taken into consideration in the constraints. Numerical experiments are carried out based on actual operational data. Results show that the model is effective to reduce the call centers\u27 labor cost

Time-dependent stochastic methods for managing and scheduling Emergency Medical Services

Emergency Medical Services (EMS) are facing increasing pressures in many nations given that demands on the service are rising. This article focuses in particular on the operations of the Welsh Ambulance Service Trust (WAST), which is the only organisation that provides urgent paramedical care services on a day-to-day basis across the whole of Wales. In response to WAST’s aspiration to improve the quality of care it provides, this research investigates several interrelated advanced statistical and operational research (OR) methods, culminating in a suite of decision support tools to aid WAST with capacity planning issues. The developed techniques are integrated in a master workforce capacity planning tool that may be independently operated by WAST planners. By means of incorporating methods that seek to simultaneously better predict future demands, recommend minimum staffing requirements and generate low-cost rosters, the tool ultimately provides planners with an analytical base to effectively deploy resources. Whilst the tool is primarily developed for WAST, the generic nature of the methods considered means they could equally be applied to any service subject to demand that is of an urgent nature, cannot be backlogged, is heavily time-dependent and highly variabl

Time-dependent stochastic modelling for predicting demand and scheduling of emergency medical services

As the prominence of the service sector is increasing in developed nations, new and exciting opportunities are arising for operational researchers to develop and apply models which offer managers solutions to improve the quality of their services. The development of time-dependent stochastic models to analyse complex service systems and generate effective personnel schedules are key to this process, enabling organisations to strike a balance between the provision of a good quality service whilst avoiding unnecessary personnel costs. Specifically within the healthcare sector, there is a need to promote efficient management of an Emergency Medical Service (EMS), where the probability of survival is directly related to the speed of assistance. Motivated by case studies investigating the operation of the Welsh Ambulance Service Trust (WAST), this thesis aims to investigate how operational research (OR) techniques can be developed to analyse priority service systems subject to demand that is of an urgent nature, cannot be backlogged, is heavily time-dependent and highly variable. A workforce capacity planning tool is ultimately developed that integrates a combination of forecasting, queueing theory, stochastic modelling and optimisation techniques into a single spreadsheet model in order to predict future demand upon WAST, set staffing levels, and optimise shift schedules and rosters. The unique linking together of the techniques in a planning tool which further captures time-dependency and two priority classes enables this research to outperform previous approaches, which have generally only considered a single class of customer, or generated staffing recommendations using approximation methods that are only reliable under limited conditions. The research presented in this thesis is novel in several ways. Primarily, the first section considers the potential of a nonparametric modelling technique known as Singular Spectrum Analysis (SSA) to improve the accuracy of demand forecasts. Secondly, the main body of work is dedicated to adapting numerical queueing theory techniques to accurately model the behaviour of time-dependent multi-server priority systems across shift boundaries and evaluate the likelihood of excessive waits for service for two customer classes. The final section addresses how shifts can be optimally scheduled using heuristic search techniques. The main conclusions are that in addition to offering a more flexible approach, the forecasts generated by SSA compare favourably to those obtained using traditional methods, and both approximate and numerical modelling techniques may be duly extended to set staffing levels in complex priority systems

Simulation Combined Approach to Police Patrol Services Staffing

Motivated by the squeeze on public service expenditure, staffing is an important issue for service systems, which are required to maintain or even improve their service levels in order to meet general public demand. This paper considers Police Patrol Service Systems (PPSSs) where staffing issues are extremely serious and important because they have an impact on service costs, quality and public-safety. Police patrol service systems are of particularly interest because the demand for service exhibits large time-varying characteristics. In this case, incidents with different urgent grades have different targets of patrol officers’ immediate attendances. A new method is proposed which aims to determine appropriate staffing levels. This method starts at a refinement of the Square Root Staffing (SRS) algorithm which introduces the possibility of a delay in responding to a priority incident. Simulation of queueing systems will then be implemented to indicate modifications in shift schedules. The proposed method is proved to be effective on a test instance generated from real patrol activity records in a local police force

Controlling excessive waiting times in emergency departments: an extension of the ISA algorithm.

In an emergency department (ED), the demand for service is not constant over time. This cannot be accounted for by means of waiting lists or appointment systems, so capacity decisions are the most important tool to influence patient waiting times. Additional complexities result from the relatively small system size that characterizes an ED (i.e. a small number of physicians or nurses) and the presence of customer impatience. Assuming a single-stage multiserver M(t)/G/s(t) + G queueing system with general abandonment and service times and time-varying demand for service, we suggest a method inspired by the simulation-based Iterative Staffing Algorithm (ISA) proposed by Feldman and others (2008) as a method to set staffing levels throughout the day. The main advantage of our extension is that it enables the use of performance measures based on the probability of experiencing an excessive waiting time, instead of the common focus on delay probability as a performance metric.Emergency department; Personnel planning; Time-varying arrival rate;