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.     

The Modern Call Center: A Multi‐Disciplinary Perspective on Operations Management Research

Call centers are an increasingly important part of today's business world, employing millions of agents across the globe and serving as a primary customer‐facing channel for firms in many different industries. Call centers have been a fertile area for operations management researchers in several domains, including forecasting, capacity planning, queueing, and personnel scheduling. In addition, as telecommunications and information technology have advanced over the past several years, the operational challenges faced by call center managers have become more complicated. Issues associated with human resources management, sales, and marketing have also become increasingly relevant to call center operations and associated academic research. In this paper, we provide a survey of the recent literature on call center operations management. Along with traditional research areas, we pay special attention to new management challenges that have been caused by emerging technologies, to behavioral issues associated with both call center agents and customers, and to the interface between call center operations and sales and marketing. We identify a handful of broad themes for future investigation while also pointing out several very specific research opportunities.     

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 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 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.     

Call Center Delay Announcement Using a Newsvendor‐Like Performance Criterion

The problem of estimating delays experienced by customers with different priorities, and the determination of the appropriate delay announcement to these customers, in a multi‐class call center with time varying parameters, abandonments, and retrials is considered. The system is approximately modeled as an M(t)/M/s(t) queue with priorities, thus ignoring some of the real features like abandonments and retrials. Two delay estimators are proposed and tested in a series of simulation experiments. Making use of actual state‐dependent waiting time data from this call center, the delay announcements from the estimated delay distributions that minimize a newsvendor‐like cost function are considered. The performance of these announcements is also compared to announcing the mean delay. We find that an Erlang distribution‐based estimator performs well for a range of different under‐announcement penalty to over‐announcement penalty ratios.     

Optimizing the Staffing and Routing of Small‐Size Hierarchical Call Centers

Multiple‐skill call centers propagate rapidly with the development of telecommunications. An abundance of literature has already been published on call centers. Here, we want to focus on centers that would typically occur in business‐to‐business environments; these are call centers that handle many types of calls but where the arrival rate for each type is low. To find an optimal configuration, the integrality of the decision variables is a much more important issue than for larger call centers. The present paper proposes an approach that uses elements of combinatorial optimization to find optimal configurations. We develop an approximation method for the evaluation of the service performance. Next, we search for the minimum‐cost configuration subject to service‐level constraints using a branch‐and‐bound algorithm. What is at stake is to find the right balance between gains resulting from the economies of scale of pooling and the higher cost or cross‐trained agents. The article shows that in most cases this method significantly decreases the staffing cost compared with configurations with only cross‐trained or dedicated operators.     

Analysis of the Market‐Based Adjustable Outsourcing Contract under Uncertainties

The market‐based adjustable contract for customized goods or services has emerged in outsourcing practices. Its objective is to minimize the operational risks inherent in today's volatile environment of operations. Our research reveals several important properties of this contract through a continuous‐time analytical approach. Specifically, we consider the determination of this contract between two risk‐averse firms through a Nash bargaining process. We derive the optimal adjusting mechanism analytically and extensively analyze the application boundary of the market‐based adjustable outsourcing contract. We conclude by discussing implications for practice and research.     

Outsourcing Manufacturing: Secure Price‐Masking Mechanisms for Purchasing Component Parts

This paper develops and tests a privacy‐preserving business process that supports the selection of a contract manufacturer by an original equipment manufacturer (OEM), and the determination of whether the OEM or the chosen contract manufacturer will procure each of the components to be used in the manufacture of the OEM's branded product. Our “secure price‐masking (SPM)” technology contributes to procurement theory and practice in four significant ways: First, it preserves the privacy of every party's individual component prices. Second, SPM assures that the contract manufacturers will bid their own private purchase cost (i.e., not add a margin to their cost). Third, SPM is not invertible; i.e., none of the participants can “solve” for the private inputs of any other participant based on its own inputs and the outputs provided to it by SPM. Fourth, the posterior distribution of any other participant's private inputs is practically indistinguishable from its prior distribution. We also describe the results of a proof‐of‐concept implementation.     

The Impact of Switching Costs on the Outsourcing of Knowledge‐Intensive Business Processes

This study examines the impact of switching costs on vendor selection and contract efficiency in the outsourcing of knowledge‐intensive business services (KIBS). We show that under most plausible scenarios in KIBS outsourcing, there is an intrinsic tension between vendor selection and contract efficiency: in the process in which the winning vendor's bid constitutes the terms of the contract between client and vendor (e.g., competitive bidding), there is good selection but contract inefficiency (positive information rent paid by the client). If, by contrast, the client establishes the contract terms, then its performance yields contract efficiency but poor selection. We also highlight the implications of performance metrics for contract design in KIBS outsourcing.     

Outsourcing to a Powerful Contract Manufacturer: The Effect of Learning‐by‐Doing

The contract manufacturing industry has grown rapidly in recent years as firms have increasingly outsourced production to reduce costs. This growth has created powerful contract manufacturers (CMs) in several industries. Achieving a competitive cost position is often a primary motive for outsourcing. Outsourcing influences both the original equipment manufacturer's (OEM) and the CM's production levels, and, therefore, through learning‐by‐doing renders future costs dependent on past outsourcing decisions. As such, outsourcing should not be viewed as a static decision that, once made, is not revisited. We address these considerations by analyzing a two‐period game between an OEM and a powerful CM wherein both firms can reduce their production costs through learning‐by‐doing. We find that partial outsourcing, wherein the OEM simultaneously outsources and produces in‐house, can be an optimal strategy. Also, we find that the OEM's outsourcing strategy may be dynamic—i.e., change from period to period. In addition, we find both that the OEM may engage in production for leverage (i.e., produce internally when at a cost disadvantage) and that the CM may engage in low balling. These and other findings in this paper demonstrate the importance of considering learning, the power of the CM, and future periods when making outsourcing decisions.     

Coping with Time‐Varying Demand When Setting Staffing Requirements for a Service System

We review queueing‐theory methods for setting staffing requirements in service systems where customer demand varies in a predictable pattern over the day. Analyzing these systems is not straightforward, because standard queueing theory focuses on the long‐run steady‐state behavior of stationary models. We show how to adapt stationary queueing models for use in nonstationary environments so that time‐dependent performance is captured and staffing requirements can be set. Relatively little modification of straightforward stationary analysis applies in systems where service times are short and the targeted quality of service is high. When service times are moderate and the targeted quality of service is still high, time‐lag refinements can improve traditional stationary independent period‐by‐period and peak‐hour approximations. Time‐varying infinite‐server models help develop refinements, because closed‐form expressions exist for their time‐dependent behavior. More difficult cases with very long service times and other complicated features, such as end‐of‐day effects, can often be treated by a modified‐offered‐load approximation, which is based on an associated infinite‐server model. Numerical algorithms and deterministic fluid models are useful when the system is overloaded for an extensive period of time. Our discussion focuses on telephone call centers, but applications to police patrol, banking, and hospital emergency rooms are also mentioned.     

中小呼叫中心月度排班优化模型与算法

国内中小呼叫中心制定坐席人员月度排班表时,通常考虑劳动法规合同约束和体现企业自身用工管理诉求。构建坐席人员月度排班优化问题的二次整数规划模型。鉴于问题模型难解性,依据调研企业需求和模型逻辑结构分析,把问题分解成三个子问题。通过构建整数规划模型和提出启发式算法来求出子问题解,从而生成排班问题优化解。问题实例计算表明,模型算法能够有效控制人力成本和兼顾员工同班次管理目标。与周排班方法比较,该方法能够充分体现月度排班人力灵活性来实现人力优化配置。     

Revenue Management Through Dynamic Cross Selling in Call Centers

This paper models the cross‐selling problem of a call center as a dynamic service rate control problem. The question of when and to whom to cross sell is explored using this model. The analysis shows that, under the optimal policies, cross‐selling targets may be a function of the operational system state. Sufficient conditions are established for the existence of preferred calls, i.e., calls that will always generate a cross‐sell attempt. These provide guidelines in segment formation for marketing managers, and lead to a static heuristic policy. Numerical analysis establishes the value of different types of information, and different types of automation available for cross selling. Increased staffing for the same call volume is shown to have a positive and increasing return on revenue generation via cross selling, suggesting the need to staff for lower loads in call centers that aim to be revenue generators. The proposed heuristic leads to near optimal performance in a wide range of settings.     

服务外包基地城市BPO发展模式分析

以首批服务外包基地城市:大连、成都、上海、深圳、西安为对象,分析了这5个城市的BPO发展状况和发展模式,指出每种模式的特色之处,对西安进行了SWOT分析,旨在为其他城市发展BPO面临的模式选择问题提供参考。     

资源外包决策的系统分析模型

针对资源外包决策这一复杂系统问题,采用系统分析的方法,从经济学与战略管理2个角度对企业核心活动进行界定,指出企业核心活动具有集中性和独特性,在此基础之上,构建了识别企业核心活动的系统分析模型。最后通过一个制造企业的例证,说明该资源外包决策模型的科学性和有效性。     

信息系统外包决策的AHP/PROMETHEE方法

针对信息系统外包项目优选这一重要问题,在已有方法的基础上,结合层次分析法与偏好顺序结构评估法,提出了一种基于这两种方法相结合的信息系统外包项目选择决策方法。以管理、战略、技术、经济、质量与风险6项因素作为评价准则,用层次分析法确定信息系统外包项目选择问题的层次结构与评价准则的权重,用偏好顺序结构评估法确定信息系统外包项目的排序,并通过算例说明该方法的有效性。     

武器装备保障供应链中基于绩效的整体外包机制

传统的武器装备保障是军方体制内的保障,供应商只负责提供装备,因
而供应商没有动力提高装备可靠性,保障成本也比较高。针对这种弊端,本文提
出了一种基于绩效的保障服务整体外包模式,即由供应商负责从提供装备到完成
装备保障任务的整个供应链,军方根据保障的绩效水平通过合同进行一定的奖励
和惩罚。本文运用委托代理的研究模型,分析了这种保障模式的优势。结果表明,
军方一定的激励政策可以引导供应商努力提高装备可靠性,并使其获得更好的收
入;与此同时,军方保障的总成本也得到降低,供应链绩效得到改善。     

Impact of Customer Traffic and Service Process Outsourcing Levels on e‐Retailer Operational Performance

Many service firms deliver services via a mix of internally developed and delivered (i.e., insourced) and externally developed and delivered (i.e., outsourced) service processes. Service process outsourcing is especially common in e‐retailing. Portions of e‐retail customer ordering processes and delivery processes can be digitized and contracted to third‐party vendors. Via outsourcing, service systems change from dyadic to triadic. Prior research examines consumer perceptions of dyadic (consumer to e‐retailer) outcomes, but little research considers service co‐delivery with outsourcing partners (i.e., triadic systems). Literature also does not focus on joint associations of service process outsourcing and customer traffic with e‐retailer operations. We analyze several years of data on North American e‐retailers. We first examine factors associated with e‐retailer outsourcing levels, for front‐end and back‐end service processes. We observe customer traffic is positively associated with future outsourcing. We then examine how outsourcing moderates associations between contemporaneous customer traffic and e‐retailer operational performance, as measured by numbers of processed orders, website response times, and customer satisfaction. Results suggest outsourcing levels are associated with operational outcomes, yet surprisingly, high outsourcing and high traffic jointly may not benefit e‐retailers.     

外包信息系统脆弱性评价模型研究

针对外包信息系统脆弱性评价问题,从技术脆弱性和管理脆弱性两个方面提出了信息系统脆弱评价指标体系。在此基础上,给出外包信息系统脆弱性评价流程,构建基于技术脆弱性和管理脆弱性的二维评价矩阵模型。最后通过一个制造企业的电子商务外包案例说明该评价模型的科学性和有效性。     

外包联盟中核心技术投入的激励机制研究

发包方如何设置有效的契约来激励接包方进行知识共享和核心技术的投入是外包联盟成功的关键。基于多任务委托代理模型,引入外包联盟的整体绩效作为绩效测量,进而将接包方的收益与绩效挂钩,激励接包方投入核心技术。通过分析,发现核心技术成本的临界值随着核心技术的贡献率的增大而降低,随着绩效测量误差的增大而增大。绩效测量误差还会负向影响接包方的激励系数以及发包方和接包方的效用。     

基于核心制造规范的外包决策模型及实证研究

本文将制造规范概念引入外包决策,从考虑企业长期绩效和长期竞争力的角度提出了一个以制造规范核心度和流失度为控制变量的二维外包决策模型。决策模型将外包环境分为九种类型,涵盖了从内部制造、各种形式的外包,到简单采购等所有"买或做"的决策,尤其是对介于自制与简单采购之间灰色地带的外包,给出了考虑提供制造规范主体和供应商类型的不同类型合作和联盟治理结构策略。对四个不同类型的企业典型产品近1000个零件的外包决策进行了统计分析,实证了模型的有效性。模型对现实世界观察到的制造企业由于没有按照其中规律行事而导致失败的原因做出了合理而明确解释。