Elsevier

Omega

Volume 58, January 2016, Pages 4-25
Omega

Review
Staffing and scheduling under nonstationary demand for service: A literature review☆

https://doi.org/10.1016/j.omega.2015.04.002Get rights and content

Highlights

  • •

    We provide a literature review on staffing and scheduling approaches for nonstationary demand.

  • •

    We categorize articles according to system assumptions and performance metrics.

  • •

    We categorize articles based on optimization approach and application context.

  • •

    We develop recommendations to achieve a better integration of theory and practice.

Abstract

Many service systems display nonstationary demand: the number of customers fluctuates over time according to a stochastic—though to some extent predictable—pattern. To safeguard the performance of such systems, adequate personnel capacity planning (i.e., determining appropriate staffing levels and/or shift schedules) is often crucial. This paper provides a state-of-the-art literature review on staffing and scheduling approaches that account for nonstationary demand. Among references published during 1991–2013, it is possible to categorize relevant contributions according to system assumptions, performance evaluation characteristics, optimization approaches and real-life application contexts. Based on their findings, the authors develop recommendations for further research.

Section snippets

Introduction and scope

In most service systems, staffing drives both costs and service quality. Personnel capacity planning for these systems tends to be non-trivial though, due to the many sources of variability inherent in real-life service systems (e.g., nonstationary demand, stochastic service times, and different customer classes) and phenomena like customer abandonment, balking, retrials, etc. The personnel capacity planning process usually gets decomposed into four steps [1], [2], [3], [4], [5], [6], [7]:

  • 1.

Overview of classification criteria

Fig. 1 displays a simple representation of a (single-stage) service system with nonstationary demand. Customers arrive according to a nonstationary arrival process with time-varying arrival rate λt (where t represents time). Typically, the arrival pattern repeats over a given cycle (e.g., day, week, month, and year). The service process (with per server service rate μ) starts immediately if a server is available on arrival; otherwise, the customer joins the queue. The aggregate service rate

Classification by system assumptions

Table 3 displays the literature classification based on the system assumptions. These assumptions are often linked with the choice of a performance evaluation method and/or capacity optimization approach, as discussed further in 4 Classification by performance evaluation methods and performance metrics, 5 Classification by optimization approach, respectively.

A large majority of extant studies assume that both customer types and server types are homogenous and that the system consists of a

Classification by performance evaluation methods and performance metrics

This section highlights the performance metrics evaluated in each article, and classifies articles according to the methodology used to evaluate system performance for given capacities.

The number of performance metrics actually used is vast, as the overview in Table 5 reveals (this table also clarifies the more concise notation we use in Table 6, Table 7, Table 8). We distinguish metrics based on number in system/number in queue, waiting time, abandonments/throughput, length of stay, and

Classification by optimization approach

In this section, we classify previous publications according to the approach used to optimize personnel capacity. We make a distinction between articles that solely focus on staffing optimization, and thus ignore shift schedule considerations (Section 5.1) and articles that take into account shift schedule requirements (Section 5.2).

Classification by application areas

Finally, Table 9 classifies articles on the basis of their application context. For each reference, we indicate whether the model was implemented (and the results reported), or if it was validated using real-life data or fictive examples. We only consider implementations reported in the academic literature and acknowledge that this is an incomplete indicator of practical implementation. For ease of reference, we repeat the methodology used for staffing and scheduling. As is evident from this

Conclusions and implications for future research

The extensive review of extant literature we have reported leads us to draw several conclusions that may be useful for guiding further research. First, it becomes clear that this research field is growing rapidly. Researchers have become very creative in applying multiple methodologies to optimize staffing and/or scheduling in systems with nonstationary demand, and thus meet a myriad of objectives and performance constraints. Unfortunately, our analysis of the system assumptions in Section 3

Acknowledgments

This research was supported by the Research Foundation-Flanders (FWO) (Grant no. G.0547.09). We also thank the three anonymous referees for their remarks, which have considerably improved this paper.

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