Staffing Call Centers with Uncertain Arrival Rates and Co‐sourcing

In a call center, staffing decisions must be made before the call arrival rate is known with certainty. Once the arrival rate becomes known, the call center may be over‐staffed, in which case staff are being paid to be idle, or under‐staffed, in which case many callers hang‐up in the face of long wait times. Firms that have chosen to keep their call center operations in‐house can mitigate this problem by co‐sourcing; that is, by sometimes outsourcing calls. Then, the required staffing N depends on how the firm chooses which calls to outsource in real time, after the arrival rate realizes and the call center operates as a M/M/N + M queue with an outsourcing option. Our objective is to find a joint policy for staffing and call outsourcing that minimizes the long‐run average cost of this two‐stage stochastic program when there is a linear staffing cost per unit time and linear costs associated with abandonments and outsourcing. We propose a policy that uses a square‐root safety staffing rule, and outsources calls in accordance with a threshold rule that characterizes when the system is “too crowded.” Analytically, we establish that our proposed policy is asymptotically optimal, as the mean arrival rate becomes large, when the level of uncertainty in the arrival rate is of the same order as the inherent system fluctuations in the number of waiting customers for a known arrival rate. Through an extensive numerical study, we establish that our policy is extremely robust. In particular, our policy performs remarkably well over a wide range of parameters, and far beyond where it is proved to be asymptotically optimal.     

Should Cities Invest in Sheltering‐in‐Place Measures Against Chlorine Truck Attacks by Terrorists?

After an intentional release of chlorine in an office district, public responses such as sheltering‐in‐place could save many lives if rapid enough. However, previous work does not estimate how fast and effective such responses would be for several possible investments in attack detection, public alert, and building ventilation, nor whether such measures would be cost effective. We estimate public response times with investment options in place, and resulting changes in fatalities as well as system costs, including false alarm costs, and cost effectiveness in terms of cost per net death avoided. The measures do have life‐saving potential, especially if all response times are at or near the lower limits of the ranges assumed in this article. However, due to uncertainties, it is not clear that responses would be rapid enough to save many people. In some cases total fatalities would increase, since sheltering after chlorine vapor has already entered buildings can increase occupants’ chlorine exposure. None of the options considered have median cost per statistical life saved meeting a cost‐effectiveness threshold of $6.5 million across all of the chlorine exposure dose‐response and ingress‐delay models considered here, even if there were one attack per year in the area covered by the system. Given these and other issues discussed in this article, at this point investments to improve sheltering‐in‐place capability appear not to be robust strategies for reducing fatalities from chlorine attack in an office district.     

A Capacitated Multi‐echelon Inventory Placement Model under Lead Time Constraints

We develop an inventory placement model in the context of general multi‐echelon supply chains where the delivery lead time promised to the customer must be respected. The delivery lead time is calculated based on the available stocks of the different input and output products in the different facilities and takes into account the purchasing lead times, the manufacturing lead times, and the transportation lead times. We assume finite manufacturing capacities and consider the interactions of manufacturing orders between time periods. Each facility manages the stocks of its input and output products. The size of customer orders and their arrival dates and due dates are assumed to be known as in many B2B situations. We perform extensive computational experiments to derive managerial insights. We also derive analytical insights regarding the manufacturing capacities to be installed and the impacts of the frequency of orders on the system cost.     

Analysis of Two‐Level Support Systems with Time‐Dependent Overflow—A Banking Application

In this paper, we analyze the performance of call centers of financial service providers with two levels of support and a time‐dependent overflow mechanism. Waiting calls from the front‐office queue flow over to the back office if a waiting‐time limit is reached and at least one back‐office agent is available. The analysis of such a system with time‐dependent overflow is reduced to the analysis of a continuous‐time Markov chain with state‐dependent overflow probabilities. To approximate the system with time‐dependent overflow, some waiting‐based performance measures are modified. Numerical results demonstrate the reliability of this Markovian performance approximation for different parameter settings. A sensitivity analysis shows the impact of the waiting‐time limit and the dependence of the performance measures on the arrival rate.     

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).     

Real‐Time Delay Estimation Based on Delay History in Many‐Server Service Systems with Time‐Varying Arrivals

Motivated by interest in making delay announcements in service systems, we study real‐time delay estimators in many‐server service systems, both with and without customer abandonment. Our main contribution here is to consider the realistic feature of time‐varying arrival rates. We focus especially on delay estimators exploiting recent customer delay history. We show that time‐varying arrival rates can introduce significant estimation bias in delay‐history‐based delay estimators when the system experiences alternating periods of overload and underload. We then introduce refined delay‐history estimators that effectively cope with time‐varying arrival rates together with non‐exponential service‐time and abandonment‐time distributions, which are often observed in practice. We use computer simulation to verify that our proposed estimators outperform several natural alternatives.     

A Performance Metric and Goal‐Setting Procedure for Deadline‐Oriented Processes

A performance metric and goal‐setting procedure is defined for an order fulfillment operation. In this operation, order requests arrive continuously, and filled orders are shipped at a specific time each day. The metric links the continuous operation of order fulfillment to the scheduled shipment times. To prescribe goals against the metric, a performance model is developed that incorporates the motivational effect of a goal. Goal‐Setting Theory is used to establish the performance goal and to show how to match arriving orders to deadlines based on their arrival times and expected processing times. Monte Carlo simulation on data from a large distribution center is used to demonstrate that setting these two parameters in the light of motivational research yields quite different results than doing so with an intuitive method. Moreover, a motivational goal leads to better operational performance; that is, correctly setting up the metric causes more customers to receive their orders sooner.     

Pool‐Point Distribution of Zero‐Inventory Products

We study zero‐inventory production‐distribution systems under pool‐point delivery. The zero‐inventory production and distribution paradigm is supported in a variety of industries in which a product cannot be inventoried because of its short shelf life. The advantages of pool‐point (or hub‐and‐spoke) distribution, explored extensively in the literature, include the efficient use of transportation resources and effective day‐to‐day management of operations. The setting of our analysis is as follows: A production facility (plant) with a finite production rate distributes its single product, which cannot be inventoried, to several pool points. Each pool point may require multiple truckloads to satisfy its customers' demand. A third‐party logistics provider then transports the product to individual customers surrounding each pool point. The production rate can be increased up to a certain limit by incurring additional cost. The delivery of the product is done by identical trucks, each having limited capacity and non‐negligible traveling time between the plant and the pool points. Our objective is to coordinate the production and transportation operations so that the total cost of production and distribution is minimized, while respecting the product lifetime and the delivery capacity constraints. This study attempts to develop intuition into zero‐inventory production‐distribution systems under pool‐point delivery by considering several variants of the above setting. These include multiple trucks, a modifiable production rate, and alternative objectives. Using a combination of theoretical analysis and computational experiments, we gain insights into optimizing the total cost of a production‐delivery plan by understanding the trade‐off between production and transportation.     

Pre‐Going Private Ownership Around the World

Going private transactions are often highly leveraged, and give rise to potential agency conflicts among existing shareholders. But who exactly are those shareholders, and under what legal conditions are these transactions more likely to occur? We examine ownership structure prior to going private transactions in 33 countries around the world from 2002 to 2014. The data indicate strong and consistent evidence that pre‐going private ownership is characterized by higher institutional and corporate ownership. Family ownership lowers the probability of a public to private transaction. Stronger creditor rights increase the probability of going private, particularly for whole company and institutional buyouts.     

Let's Call it Quits: Break‐Even Effects in the Decision to Stop Taking Risks

“Chasing” behavior, whereby individuals, driven by a desire to break even, continue a risky activity (RA) despite incurring large losses, is a commonly observed phenomenon. We examine whether the desire to break even plays a wider role in decisions to stop engaging in financially motivated RA in a naturalistic setting. We test hypotheses, motivated by this research question, using a large data set: 707,152 transactions of 5,379 individual financial market spread traders between September 2004 and April 2013. The results indicate strong effects of changes in wealth around the break‐even point on the decision to cease an RA. An important mediating factor was the individual's historical long‐term performance. Those with a more profitable trading history were less affected by a fall in cash balance below the break‐even point compared to those who had been less profitable. We observe that break‐even points play an important role in the decision of nonpathological risk takers to stop RAs. It is possible, therefore, that these nonpathological cognitive processes, when occurring in extrema, may result in pathological gambling behavior such as “chasing.” Our data set focuses on RAs in financial markets and, consequently, we discuss the implications for institutions and regulators in the effective management of risk taking in markets. We also suggest that there may be a need to consider carefully the nature and role of “break‐even points” associated with a broader range of nonfinancially‐focused risk‐taking activities, such as smoking and substance abuse.     

Capacity Planning and Allocation for Web‐Based Applications

Motivated by the technology division of a financial services firm, we study the problem of capacity planning and allocation for Web‐based applications. The steady growth in Web traffic has affected the quality of service (QoS) as measured by response time (RT), for numerous e‐businesses. In addition, the lack of understanding of system interactions and availability of proper planning tools has impeded effective capacity management. Managers typically make decisions to add server capacity on an ad hoc basis when systems reach critical response levels. Very often this turns out to be too late and results in extremely long response times and the system crashes. We present an analytical model to understand system interactions with the goal of making better server capacity decisions based on the results. The model studies the relationships and important interactions between the various components of a Web‐based application using a continuous time Markov chain embedded in a queuing network as the basic framework. We use several structured aggregation schemes to appropriately represent a complex system, and demonstrate how the model can be used to quickly predict system performance, which facilitates effective capacity allocation decision making. Using simulation as a benchmark, we show that our model produces results within 5% accuracy at a fraction of the time of simulation, even at high traffic intensities. This knowledge helps managers quickly analyze the performance of the system and better plan server capacity to maintain desirable levels of QoS. We also demonstrate how to utilize a combination of dedicated and shared resources to achieve QoS using fewer servers.     

Agent‐Based Simulation for Human‐Induced Hazard Analysis

Terrorism could be treated as a hazard for design purposes. For instance, the terrorist hazard could be analyzed in a manner similar to the way that seismic hazard is handled. No matter how terrorism is dealt with in the design of systems, the need for predictions of the frequency and magnitude of the hazard will be required. And, if the human‐induced hazard is to be designed for in a manner analogous to natural hazards, then the predictions should be probabilistic in nature. The model described in this article is a prototype model that used agent‐based modeling (ABM) to analyze terrorist attacks. The basic approach in this article of using ABM to model human‐induced hazards has been preliminarily validated in the sense that the attack magnitudes seem to be power‐law distributed and attacks occur mostly in regions where high levels of wealth pass through, such as transit routes and markets. The model developed in this study indicates that ABM is a viable approach to modeling socioeconomic‐based infrastructure systems for engineering design to deal with human‐induced hazards.     

Health‐Economics Analyses Applied to ELF Electric and Magnetic Fields

Extremely low frequency electric and magnetic fields (ELF EMFs) are a common exposure for modern populations. The prevailing public‐health protection paradigm is that quantitative exposure limits are based on the established acute effects, whereas the possible chronic effects are considered too uncertain for quantitative limits, but might justify precautionary measures. The choice of precautionary measures can be informed by a health‐economics analysis (HEA). We consider four such analyses of precautionary measures that have been conducted at a national or state level in California, the Netherlands, the United Kingdom, and Israel. We describe the context of each analysis, examine how they deal with some of the more significant issues that arise, and present a comparison of the input parameters and assumptions used. The four HEAs are methodologically similar. The most significant qualitative choices that have to be made are what dose‐response relationship to assume, what allowance if any to make for uncertainty, and, for a CBA only, what diseases to consider, and all four analyses made similar choices. These analyses suggest that, on the assumptions made, there are some low‐cost measures, such as rephasing, that can be applied to transmission in some circumstances and that can be justifiable in cost‐benefit terms, but that higher cost measures, such as undergrounding, become unjustifiable. Of the four HEAs, those in the United Kingdom and Israel were influential in determining the country's EMF policy. In California and Netherlands, the HEA may well have informed the debate, but the policy chosen did not stem directly from the HEA.     

Peakedness‐Based Staffing for Call Center Outsourcing

This study considers the staffing problem of a vendor call center in a co‐sourcing setting. The aim is to take short‐term variability and correlations in time for call arrivals at such a vendor call center into account. To do so, peakedness is proposed as a useful measure of the burstiness in the arrival stream. The study empirically demonstrates the presence of bursty arrivals at a call center and proposes an approach to the measurement of the peakedness of the arrival stream making use of standard call center data. The problematic nature of bursty arrivals in the context of call center co‐sourcing is demonstrated along with an asymptotic result establishing that the problem persists in large call centers. The study then analyzes two peakedness‐based staffing methods: one which is a well known extension of the square root staffing rule and another which makes use of the Hayward approximation principles. Both approaches are simple and enable the vendor to improve its staffing procedure with good accuracy.     

Flexible Backup Supply and the Management of Lead‐Time Uncertainty

We consider replenishment decisions for a constant rate demand environment from a supplier with uncertain lead times. We study the potential use of a flexible backup supplier as an emergency response to accurate lead‐time information arriving at (or close after) the beginning of the demand interval and well after an original order with the stochastic lead‐time supplier has been placed. The emergency response decisions involve whether to order and how much from the flexible backup supplier, with the objective of minimizing the cost of meeting demand. We derive the optimal emergency‐response policy and clearly outline its implications on the optimized safety lead time of the original order placement and on the cost of meeting demand. We examine the impact on the use of the flexible backup supplier of factors like the arrival time of accurate lead‐time information and the response lead time of the backup supplier. We further study the potential benefits of the use of the flexible backup supplier in a dual role: as one of the two suppliers in a redundant supply system assigned to originally meet the demand and as an emergency response to later‐arriving lead‐time information. Our numerical studies illustrate the benefits from the use of the flexible backup supplier as an emergency response, but for reasonable purchase premiums and short lead times of flexible backup supply options, their use in a dual (regular and emergency response) role often leads to improved performance over safety lead‐time single and uncertain lead‐time supplier‐replenishment strategies. The benefits of the backup supply options are accentuated the higher the lead‐time uncertainty of the stochastic lead‐time supplier is.     

Adoption of e‐Processes by Service Firms: An Empirical Study of Antecedents

This paper investigates empirically antecedents of the adoption of web‐based processes (e‐processes) by service providers. We examine whether rational efficiency (expressed by expected performance benefits and access to new markets), the bandwagon effect (expressed by external pressure), and barriers (both internal and customer related) influence Internet use for transactions (e‐transactions) and/or to extend the relationships between service providers and their customers (e‐CRM). The findings, based on a sample of 338 service firms, show that rational efficiency and the bandwagon effect drive both types of e‐processes. Conversely, only internal barriers have a negative impact on adoption of e‐processes, while barriers related to customers do not have a significant impact. These findings have important academic and managerial implications, given the limited evidence regarding the implementation of e‐processes in services.     

Dynamic Pricing and Lead‐Time Policies for Make‐to‐Order Systems*

Make‐to‐order firms use different approaches for managing their lead‐times and pricing in the face of changing market conditions. A particular firm's approach may be largely dictated by environmental constraints. For example, it makes little sense to carefully manage lead‐time if its effect on demand is muted, as it can be in situations where leadtime is difficult for the market to gauge or requires investment to estimate. Similarly, it can be impractical to change capacity and price. However, environmental constraints are likely to become less of an issue in the future with the expanding e‐business infrastructure, and this trend raises questions into how to manage effectively the marketing mix of price and lead‐time in a more “friction‐free” setting. We study a simple model of a make‐to‐order firm, and we examine policies for adjusting price and capacity in response to periodic and unpredictable shifts in how the market values price and lead‐time. Our analysis suggests that maintaining a fixed capacity while using lead‐time and/or price to absorb changes in the market will be most attractive when stability in throughput and profit are highly valued, but in volatile markets, this stability comes at a cost of low profits. From a pure profit maximization perspective, it is best to strive for a short and consistent lead‐times by adjusting both capacity and price in response to market changes.     

EXPECTATIONS‐BASED REFERENCE‐DEPENDENT PREFERENCES AND ASSET PRICING

This paper explores the quantitative asset‐pricing implications of expectations‐based reference‐dependent preferences, as introduced by Koszegi and Rabin (2009, American Economic Review, 99(3), 909–936), in an otherwise traditional Lucas‐tree model. I find that the model easily succeeds in matching the historical equity premium and its variability when the preference parameters are calibrated in line with micro evidence. The equity premium is high because expectations‐based loss aversion makes uncertain fluctuations in consumption more painful. Additionally, loss aversion introduces variation in returns because unexpected cuts in consumption are particularly painful, and the agent wants to postpone such cuts to let his reference point decrease. This variation generates strong predictability. However, it also causes counterfactually high volatility in the risk‐free rate, which I address by allowing for variation in expected consumption growth, heteroskedasticity in consumption growth, time‐variant disaster risk, and sluggish belief updating.     

Point‐of‐Use Hybrid Inventory Policy for Hospitals

Modern point‐of‐use technology at hospitals has enabled new replenishment policies for medical supplies. One of these new policies, which we call the hybrid policy, is currently in use at a large U.S. Midwest hospital. The hybrid policy combines a low‐cost periodic replenishment epoch with a high‐cost continuous replenishment option to avoid costly stockouts. We study this new hybrid policy under deterministic and stochastic demand. We develop a parameter search engine using simulation to optimize the long‐run average cost per unit time and, via a computational study, we provide insights on the benefits (reduction in cost, inventory, and number of replenishments) that hospitals may obtain by using the hybrid policy instead of the commonly used periodic policies. We also use the optimal hybrid policy parameters from the deterministic analysis to propose approximate expressions for the stochastic hybrid policy parameters that can be easily used by hospital management.      

Storing Fresh Produce for Fast Retrieval in an Automated Compact Cross‐Dock System

We study temporary storage of fresh produce in a cross‐dock center. In order to minimize cooling cost, compact storage systems are used. A major disadvantage of these systems is that additional retrieval time is needed, caused by necessary reshuffles due to the improper storage sequence of unit loads. In practice therefore, a dedicated storage policy is used in which every storage lane in the system accommodates only one product. However, this policy does not use the planned arrival time information of the outbound trucks. To exploit this information, this study proposes a mathematical model for a shared storage policy that minimizes total retrieval time. The policy allows different products to share the same lane. In order to solve real‐sized problems, an effective and efficient heuristic is proposed, based on a greedy construction and an improvement part, which provides near optimal solutions. The gaps between the results of the heuristic and the lower bound are mostly less than 1%. The resulting shared storage policy is generally robust against disturbances in arrival or departure times. We compare our shared storage heuristic with dedicated storage to determine which policy performs best under which circumstances. For most practical cases, shared storage appears to outperform dedicated storage, with a shorter response time and better storage lane utilization.