Figure 3 - uploaded by Shane G. Henderson
Content may be subject to copyright.
Source publication
We consider the problem of minimizing staffing costs in an inbound call center, while maintaining an acceptable level of service in multiple time periods. The problem is complicated by the fact that staffing level in one time period can affect the service levels in subsequent periods. Moreover, staff schedules typically take the form of shifts cove...
Contexts in source publication
Context 1
... of a function is a weaker property than concavity; see also Figure 3.12 in Bazaraa et al. (1993). ...
Context 2
... above procedure is then repeated. An illustration of the localization set and the feasible regions and solutions of problems (9) and (10) in each iteration is shown in Figure 3. The picture The weight parameter w on the optimality cut can be increased to "push" the weighted analytic center away from the optimality cuts. ...
Similar publications
We address a multi-skill staffing problem in a call center where the agent skill sets are exogenously specified and the call routing policy has well-specified features of overflow between different agent types. Constraints are imposed on the service level for each call class, defined here as the steady-state fraction of calls served within a given...
For nearly all call centers, agent schedules are typically created several days or weeks before 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 practit...
Citations
... Moreover, the objective function can be defined in terms of minimizing the completion time, maximizing the quality of the output, or minimizing the cost of the assignment. For example, Atlason et al. [27] introduced a method using simulation for optimal staffing levels in call centers. In another study, Brunner et al. [28] proposed a mixed-integer approach to solve the shift scheduling problem of physicians in hospitals while considering legal and institutional constraints imposed by a national labor agreement. ...
... In a single-skill setting, Koole & van der Sluis [85] use SIPP to determine staffing levels and show that under a very simple shift structure, a suitable local algorithm can find optimal schedules. In a transient single-skill setting, Atlason et al. [16] integrate staffing and shift scheduling and use simulation to generate cutting planes used in the shift optimization module. Liao et al. [96] also use simulation. ...
... Moreover, service levels cannot be approximated, because the models are based on rejection models without queues. Again using simulation, Cezik & l'Ecuyer [32] extend the approach of Atlason et al. [16] to multi-skill staffing. Avramidis et al. [18] extend the cutting plane method to solve scheduling problem over a day (i.e., multiple periods). ...
We give an overview of the practice and science of call center workforce planning, in which we evaluate the commonly used methods by their quality and the theory by its applicability. As such, this paper is useful for developers and consultants interested in the background and advanced methodology of workforce management and for researchers interested in practically relevant science.
Supplemental Material: The e-companion is available at https://doi.org/10.1287/stsy.2021.0008 .
... Chiu et al. (2009) developed a constraint-based particle swarm optimization method for scheduling. Atlason et al. (2008), however, utilized a robust non-traditional method that performs well over a range of different problems. It is precisely these schedules on which we wish to test our simulation models. ...
... Simulation can also be combined into optimization procedures to search for the optimal solution, known as simulation(-based) optimization, or optimization via simulation. For example, Atlason et al. (2008) and Cezik and L'Ecuyer (2008) solved call center staffing problems with non-closed-form servicelevel functions evaluated via simulation; Tsai and Zheng (2013) addressed a two-echelon inventory problem, where one constraint requires the expected response time at each depot to be within a threshold; Guo et al. (2017) and Chen et al. (2020) studied staffing problems in hospital EDs while satisfying stochastic service quality requirements. This paper contributes to the above literature on studying a generalized resource allocation problem in service systems, where two unique structures exist: (1) The performance of neighboring resource allocation scenarios may be correlated and the modeler can obtain prior knowledge on their joint distribution; and (2) the objective and multiple constraints are stochastic and in the form of probabilistic measures. ...
The service sector has become increasingly important in today's economy. To meet the rising expectation of high‐quality services, efficiently allocating resources is vital for service systems to balance service qualities with costs. In particular, this paper focuses on a class of resource allocation problems where the service‐level objective and constraints are in the form of probabilistic measures. Further, process complexity and system dynamics in service systems often render their performance evaluation and optimization challenging and relying on simulation models. To this end, we propose a generalized resource allocation model with probabilistic measures, and subsequently, develop an optimal computing budget allocation (OCBA) formulation to select the optimal solution subject to random noises in simulation. The OCBA formulation minimizes the expected opportunity cost that penalizes based on the quality of the selected solution. Further, the formulation takes a Bayesian approach to consider the prior knowledge and potential performance correlations on candidate solutions. Then, the asymptotic optimality conditions of the formulation are derived, and an iterative algorithm is developed accordingly. Numerical experiments and a case study inspired by a real‐world problem in a hospital emergency department demonstrate the effectiveness of the proposed algorithm for solving the resource allocation problem via simulation. This article is protected by copyright. All rights reserved
... Atlason et al. (2004) propose a method that combines cut generation and linear programming to solve a scheduling problem in a single call type and single-skill call center with long-term expected SL constraints. Çezik and L'Ecuyer (2008) adapt the cutting plane method to solve large-size staffing problems in a single time period for multi-skill call centers and Atlason et al. (2008) have also developed a cutting plane method in conjunction with simulation and analytic call centers to solve the scheduling problem with more factors such as work requirements and shift construction. Another algorithm based on the cutting plane method to solve the scheduling problem in multiple time periods and constraints on work schedules is developed in Avramidis et al. (2010). ...
... In general, the joint probability function has some properties distinguishing it with the separate chance-constraints and expected SL constraints, raising a question that whether standard methods used to solve the separate CC and expected SL problems (Atlason et al. 2008;Ta et al. 2020) still apply. We discuss this in the next section, where we show that the joint probability function still displays a S-shaped curve, but identifying the concave region of the function is more challenging, thus requires new investigations. ...
... In this section, we describe a simulation-based method to solve the joint CC staffing optimization problem. Similar to previous studies (Atlason et al. 2008;Çezik and L'Ecuyer 2008;Ta et al. 2020), to make the problem practical, we use simulation to approximate the joint probability function. We then show that the joint probability function also has an S-shaped curve, suggesting that the standard cutting plane method (Atlason et al. 2008;Çezik and L'Ecuyer 2008) would be still useful. ...
This paper concerns the staffing optimization problem in multi-skill call centers. The objective is to find a minimal cost staffing solution while meeting a target level for the quality of service (QoS) to customers. We consider a staffing problem in which joint chance constraints are imposed on the QoS of the day. Our joint chance-constrained formulation is more rational capturing the correlation between different call types, as compared to separate chance-constrained versions considered in previous studies. We show that, in general, the probability functions in the joint-chance constraints display S-shaped curves, and the optimal solutions should belong to the concave regions of the curves. Thus, we propose an approach combining a heuristic phase to identify solutions lying in the concave part and a simulation-based cut generation phase to create outer-approximations of the probability functions. This allows us to find good staffing solutions satisfying the joint-chance constraints by simulation and linear programming. We test our formulation and algorithm using call center examples of up to 65 call types and 89 agent groups, which shows the benefits of our joint-chance constrained formulation and the advantage of our algorithm over standard ones.
... To address these challenges, many researchers use the sample average approximation (SAA) method to approximate these constraints. The corresponding model is an integer program which is easier to solve using commercial solvers [3,25,31]. ...
... Moisture content of the biomass that flows from the equipment i ∈ E g in period t in scenario s d its Density of biomass flowing from the equipment i ∈ E g ∪ E m in time period t in scenario s (in tons/inch 3 ) ρ j its ...
Variations of physical and chemical characteristics of biomass lead to an uneven flow of biomass in a biorefinery, which reduces equipment utilization and increases operational costs. Uncertainty of biomass supply and high processing costs increase the risk of investing in the US’s cellulosic biofuel industry. We propose a stochastic programming model to streamline processes within a biorefinery. A chance constraint models system’s reliability requirement that the reactor is operating at a high utilization rate given uncertain biomass moisture content, particle size distribution, and equipment failure. The model identifies operating conditions of equipment and inventory level to maintain a continuous flow of biomass to the reactor. The sample average approximation method approximates the chance constraint and a bisection search-based heuristic solves this approximation. A case study is developed using real-life data collected at Idaho National Laboratory’s biomass processing facility. An extensive computational analysis indicates that sequencing of biomass bales based on moisture level, increasing storage capacity, and managing particle size distribution, increases utilization of the reactor and reduces operational costs.
... They then serve as constraints in deterministic shift scheduling, see, for example, [2]. Iterative approaches: In contrast to sequential approaches, such methods iterate between an evaluation part and an optimization part to get a new candidate solution, see, for example, [1]. Queueing approaches or simulation evaluates the candidate solution. ...
... Schwarz et al. (2016) report that the pioneering analysis of time-dependent queuing systems date back to the work of Kolmogorov in 1931. Since then, some studies analyzed the time-dependent behavior in a variety of queuing systems, such as air terminals , air traffic (Wang et al., 2018), healthcare (Brahimi and Worthington, 1991;de Bruin et al., 2007), emergency medical services (Singer and Donoso, 2008;Vile et al., 2016, Beojene andSouza, 2020), call centers (Atlason et al., 2008;Dietz, 2011;Green et al., 2001), computer and communication networks (Lackman et al., 1992), repair facilities (Lau and Song, 2008), and police patrols (Alfa and Margolius, 2008;Ingolfsson et al., 2002;Kolesar et al., 1975). ...
... The stationary independent period-by-period approximation (SIPP) segments the entire period into small consecutive independent periods and employs the average arrival rate for each period as the input to a series of stationary analyses. The SIPP has been used by several researchers, for example, Green et al. (2001) and Atlason et al. (2008), to estimate the behavior of M(t)/M/c(t) queuing systems. The pointwise stationary approximation (PSA), on the other hand, consists of an appropriate weighted average of the performance measures in each point in time (the interval length is set to zero). ...
This study presents a stationary backlog-carryover (SBC) approach to deal with hypercube queuing models with time-dependent user arrival rates for the analysis of emergency agricultural systems. It is motivated by practical situations faced by the agricultural stage of sugarcane mills. Due to the frequent changes in the locations of harvest fronts, the emergency calls for tire repair also change their locations over time, and managers should determine the appropriate number and locations of servers and their dispatch policies. This approach is applied to a case study conducted in the tire repair emergency services of a sugarcane mill. A simulation model is also developed to crosscheck the validity of this approach. This work aims at analyzing and highlighting the importance of considering time-dependent changes in arrival rates at different regions of the system. The findings suggest that this approach is flexible enough to deal with alternative dispatch policies, changes in the number of servers, and the increase in server utilization rates.
... (1) Our data points to a considerable variability in the number of available nursing staff (e.g., due to absenteeism) as well as the arrival rate, which were ignored in our formulation. An extended problem can explicitly account for the parameter uncertainty and investigate its impact along the same lines as done in the call center literature, e.g., Harrison and Zeevi (2005) and Atlason et al. (2008) (arrival rate uncertainty) and Whitt (2006) (arrival and capacity uncertainty). In addition to reassignment decision, a two-stage formulation can be considered to determine the number of scheduled staff as well as determining a control policy to assign them to different areas once the available number of staff is realized. ...
... One of the most prevalent and dominant points of interaction between many organizations and their customers and therefore, critical for managing customer experience, are call centers or customer service centers (Whiting & Donthu, 2006). To constantly provide high service quality in the form of short waiting times at this touchpoint, a sufficient number of call center agents is needed (Atlason et al., 2008). Consequently, the process of predicting call arrival volumes and deciding on the required staffing level is a critical success factor in this area. ...
E-commerce has seen a steady increase in usage since its establishment in the 1970s and 80s: By 2025, two-thirds of the world’s population (4,913.9M people) are expected to be e-commerce users. Throughout these decades, e-commerce businesses had to face a variety of different challenges, which, to some extent, determined their survival within their competitive environment. Within this thesis, two selected current phenomena are shed light on with which e-commerce businesses are struggling: A shift within society’s mindset towards environmental awareness and analytical approaches to manage the infinite pool of data about online consumer behavior. Since both research fields have an extremely granular spectrum of different facets, many sub-facets still lack a comprehensive investigation. The overall purpose of this research is thus twofold: (1) Gathering insights on consumers’ sustainable clothing consumption behavior and (2) proposing Artificial Intelligence-driven approaches for analytical problems in the e-commerce context. More specifically, Part A focuses on consumers’ sustainable clothing consumption behavior as the textile industry causes an excessive environmental footprint considering valuable resources as ever inexhaustible and, simultaneously, yields the highest sales among all e-commerce segments. Research Paper No. 1 hence takes a macro-perspective on sustainable clothing consumption behavior by examining the determinants of consumers’ purchase intention for sustainable clothing and factors influencing the intention-behavior gap. Research Paper No. 2 and No. 3 take a deeper dive and provide micro-perspectives on the topic: the impact of specific sustainable clothing attributes on customer satisfaction is investigated (Research Paper No. 2). To complement these findings, the importance of specific sustainable clothing (and online shop) attributes is then compared to the importance of specific conventional clothing (and online shop respectively) attributes (Research Paper No. 3). Within Part B of this thesis, Research Paper No. 4 and No. 5 focus on call center arrivals’ forecasting as call centers still constitute an essential customer touchpoint for e-commerce businesses: Reliable forecasts can enhance customer satisfaction with shortened waiting times and avoid overstaffing (and thus, unnecessary costs). Research Paper No. 4 therefore investigates the trade-off between accuracy and practicability of different machine learning models as these have been neglected by traditional forecasting literature. Research Paper No. 5 draws on these preceding findings and proposes a new dynamic harmonic regression model by incorporating the benefits of both approaches without (i.e., time series models) and with explanatory variables (i.e., machine learning and regression models). Research Paper No. 6 considers another prediction problem, which is particularly inherent to the online context of e-commerce, i.e., online shopping cart abandonment. It investigates the trade-off between accuracy and practicability of machine learning models for shopping cart abandonment prediction. Overall, this thesis allows the reader to gather a better understanding of the underlying challenges by providing fruitful insights and proposes different approaches as a solution. Thereby, it makes several key contributions to extant literature and provides essential insights and implications for practitioners.
