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.     

ANALYSIS OF ALTERNATIVE SCHEDULING POLICIES FOR HOSPITAL NURSES

The persistent shortage of nurses adversely affects the productivity, quality of care, and operating costs in most acute care hospitals. Aggravating the shortage are high nurse turnover rates, approaching 200% in some institutions. Policies to ensure adequate staffing levels and provide more attractive work schedules are alleged to improve nurse retention. However, their cost is seldom discussed. We compared expected nursing expense and workforce requirements to staff eight medical and surgical nursing units of a large hospital for 1 month, under 12 different scheduling policies alleged to improve turnover. Using simulation and an integrated staffing and scheduling methodology, we found that the expected nursing wages and workforce requirements for some policies differed by as much as 33%. In this hospital, the expected labor costs for certain policies could erode the benefits expected from improved retention. In contrast, other policies appear to allow high utilization of nursing resources, enhancing the expected benefits of reduced turnover with significant reductions in expenses for labor, recruiting, training, and fringe benefits.     

Time‐Staged Overtime Staffing for Services with Updated Forecasts and Availabilities

This article develops a framework for staffing in a service environment when multiple opportunities exist for prescheduling overtime prior to the start of a shift. Demand forecasts improve as the shift approaches, while the availability of workers to be scheduled for overtime decreases. First, a single‐shift model is developed and used in computational studies to evaluate the benefits of time‐staged overtime staffing, which include slightly lower costs and significant reductions in unscheduled overtime and outside agents. A multishift model is then developed to consider constraints on consecutive hours worked and minimum rest intervals between shifts. A multishift computational study shows how the benefits of time‐staged overtime staffing depend on problem characteristics when interactions between shifts are considered. The article discusses how single‐shift and multishift models relate to each other and alternative ways the models may be used in practice, including decentralized open shift management and centralized overtime scheduling.     

Structural sources of personnel problems in multinational corporations: Third-country nationals

The paper examines the extent to which multinational corporations (MNCs) whose staffing policies approach the genuine multinational model are free of the dysfunctions found by the authors in earlier studies of ethnocentric MNCs. The findings are based on comparative research in 51 MNCs, and intensive diagnostic studies of seven subsidiaries of MNCs operating and headquartered in four continents. The findings may be summed up as follows: (1) certain, but very few, morale problems have indeed been eliminated; (2) others are still present; (3) others are still present and their effect has intensified; and (4) new problems have appeared which are unique to the staffing policy approximating to the genuine multinational model. These findings shed new light on several of the assumptions underlying this model. The general conclusion is that each prevalent type of staffing policy has several sources of morale problems—some inherent in its uniqueness, and others shared by the alternative staffing policies—irrespective of the personal qualifications of the managers. Therefore, it is unrealistic to expect that a change toward the genuine multinational model would solve the basic morale problems prevalent in the dominant type of MNCs.     

Physician executives: where they are and what they do

As hospital operations become increasingly complex, so does the institution's management and organizational structure. Physician executives with titles of medical director, vice president for medical affairs, medical administrator, chief of staff, medical staff president, etc., are playing more important roles than ever before. This article will briefly review some recent literature describing physician executive profiles. The results from a survey of ten university teaching hospitals are also presented as supplementary information regarding current staffing models. Finally, several physician executive staffing-related issues will be discussed in light of the literature and the survey results.     

Development and analysis of mathematical and simulation models of decision-making tools for remanufacturing

This article presents decision-making tools for remanufacturing. The first decision-making tool was used to address inventory lot-sizing problems in a hybrid remanufacturing–manufacturing system with varying remanufacturing fraction. In this article, the new inventory lot-sizing model with variable remanufacturing lot sizes has been shown to exhibit better performance than the benchmark model with fixed remanufacturing lot sizes. The new inventory lot-sizing model is anticipated to become a valuable decision-making tool in companies that are planning to adopt remanufacturing. The second decision-making tool was applied to address a production and inventory planning problem in a remanufacturing system considering different remanufacturing policies for a given remanufacturing strategy. For a remanufacture-to-stock system with two quality remanufacturables groups four alternative policies were examined, a policy which specifies simultaneous processing utilising dedicated resources was shown to be the best policy to achieve a shorter remanufacturing cycle time. For a remanufacture-to-order system with two quality remanufacturables groups, the three relevant policies of the four alternative policies were examined, a policy which specifies sequential processing and switching between various quality remanufacturables groups was shown to be the best policy to achieve a shorter remanufacturing cycle time. The production and inventory planning simulation models in a remanufacturing system are expected to become significant decision-making tools in remanufacturing operations.     

Sequential and Simultaneous Decision Making for Optimizing Health Care Resource Flexibilities

Health care administrators commonly employ two types of resource flexibilities (demand upgrades and staffing flexibility) to efficiently coordinate two critical internal resources, nursing staff and beds, and an external resource (contract nurses) to satisfy stochastic patient demand. Under demand upgrades, when beds are unavailable for patients in a less acute unit, patients are upgraded to a more acute unit if space is available in that unit. Under staffing flexibility, nurses cross‐trained to work in more than one unit are used in addition to dedicated and contract nurses. Resource decisions (beds and staffing) can be made at a single point in time (simultaneous decision making) or at different points in time (sequential decision making). In this article, we address the following questions: for each flexibility configuration, under sequential and simultaneous decision making, what is the optimal resource level required to meet stochastic demand at minimum cost? Is one type of flexibility (e.g., demand upgrades) better than the other type of flexibility (e.g., staffing flexibility)? We use two‐stage stochastic programming to find optimal resource levels for two nonhomogeneous hospital units that face stochastic demand following a continuous, general distribution. We conduct a full‐factorial numerical experiment and find that the benefit of using staffing flexibility on average is greater than the benefit of using demand upgrades. However, the two types of flexibilities have a positive interaction effect and they complement each other. The type of flexibility and decision timing has an independent effect on system performance (capacity and staffing costs). The benefits of cross‐training can be largely realized even if beds and staffing levels have been determined prior to the establishment of a cross‐training initiative.     

Unemployment Insurance Policy and Union Wage Formation

Abstract. The paper considers the wage and employment effects of alternative social security policies. Such a policy can take the form of a fixed benefit level or linking the level of unemployment benefits to private sector wages. The latter is an important social security policy instrument to guarantee an equitable distribution of income. A fixed benefit level policy yields lower wages and larger employment than an automatic link between the level of benefits and the wage rate. Further, if the government decides to make the link conditional on the stabilization of the tax rate, wages are lower and employment is higher than in both former alternatives. By endogenizing its social security policy, the government is able to reduce the loss in employment that the link policy brings about.     

Experimental Results Indicating Lattice‐Dependent Policies May Be Optimal for General Assemble‐To‐Order Systems

We consider an assemble‐to‐order (ATO) system with multiple products, multiple components which may be demanded in different quantities by different products, possible batch ordering of components, random lead times, and lost sales. We model the system as an infinite‐horizon Markov decision process under the average cost criterion. A control policy specifies when a batch of components should be produced, and whether an arriving demand for each product should be satisfied. Previous work has shown that a lattice‐dependent base‐stock and lattice‐dependent rationing (LBLR) policy is an optimal stationary policy for a special case of the ATO model presented here (the generalized M‐system). In this study, we conduct numerical experiments to evaluate the use of an LBLR policy for our general ATO model as a heuristic, comparing it to two other heuristics from the literature: a state‐dependent base‐stock and state‐dependent rationing (SBSR) policy, and a fixed base‐stock and fixed rationing (FBFR) policy. Remarkably, LBLR yields the globally optimal cost in each of more than 22,500 instances of the general problem, outperforming SBSR and FBFR with respect to both objective value (by up to 2.6% and 4.8%, respectively) and computation time (by up to three orders and one order of magnitude, respectively) in 350 of these instances (those on which we compare the heuristics). LBLR and SBSR perform significantly better than FBFR when replenishment batch sizes imperfectly match the component requirements of the most valuable or most highly demanded product. In addition, LBLR substantially outperforms SBSR if it is crucial to hold a significant amount of inventory that must be rationed.     

Staffing a Multiskilled Workforce with Varying Levels of Productivity: An Analysis of Cross-training Policies*

Service operations that utilize cross-trained employees face complex workforce staffing decisions that have important implications for both cost and productivity. These decisions are further complicated when cross-trained employees have different productivity levels in multiple work activity categories. A method for policy analysis in such environments can be beneficial in determining low-cost staffing plans with appropriate cross-training configurations. In this paper, we present an integer linear programming model for evaluating cross-training configurations at the policy level. The objective of the model is to minimize workforce staffing costs subject to the satisfaction of minimum labor requirements across a planning horizon of a single work shift. The model was used to evaluate eight cross-training structures (consisting of 36 unique cross-training configurations) across 512 labor requirement patterns. These structures, as well as the labor requirement patterns, were established based on data collected from maintenance operations at a large paper mill in the United States. The results indicate that asymmetric cross-training structures that permit chaining of employee skill classes across work activity categories are particularly useful.     

Identification and Inference in Nonlinear Difference‐in‐Differences Models

This paper develops a generalization of the widely used difference‐in‐differences method for evaluating the effects of policy changes. We propose a model that allows the control and treatment groups to have different average benefits from the treatment. The assumptions of the proposed model are invariant to the scaling of the outcome. We provide conditions under which the model is nonparametrically identified and propose an estimator that can be applied using either repeated cross section or panel data. Our approach provides an estimate of the entire counterfactual distribution of outcomes that would have been experienced by the treatment group in the absence of the treatment and likewise for the untreated group in the presence of the treatment. Thus, it enables the evaluation of policy interventions according to criteria such as a mean–variance trade‐off. We also propose methods for inference, showing that our estimator for the average treatment effect is root‐N consistent and asymptotically normal. We consider extensions to allow for covariates, discrete dependent variables, and multiple groups and time periods.     

Analysis of an EOQ inventory model with partial backordering and non-linear unit holding cost

In this paper, an economic order quantity inventory model is analyzed, considering that the unit cumulative holding cost has two significant components: a fixed cost which represents the cost of accommodating the item in the warehouse and a variable cost given by a potential function of the length of time over which the item is held in stock. Shortages are allowed and, during the stockout period, only a fraction of demand is partially backordered. The backordering cost includes a fixed cost and a cost linearly dependent on the length of time for which backorder exists. A solution procedure is developed for determining the optimal inventory policy. Moreover, to illustrate the effects of some parameters on the optimal policy and the minimum total inventory cost, a numerical study is developed.     

3 Staffing Twenty‐first‐century Organizations

Abstract

We highlight important differences between twenty‐first‐century organizations as compared with those of the previous century, and offer a critical review of the basic principles, typical applications, general effectiveness, and limitations of the current staffing model. That model focuses on identifying and measuring job‐related individual characteristics to predict individual‐level job performance. We conclude that the current staffing model has reached a ceiling or plateau in terms of its ability to make accurate predictions about future performance. Evidence accumulated over more than 80 years of staffing research suggests that general mental abilities and other traditional staffing tools do a modest job of predicting performance across settings and jobs considering that, even when combined and corrected for methodological and statistical artifacts, they rarely predict more than 50% of the variance in performance. Accordingly, we argue for a change in direction in staffing research and propose an expanded view of the staffing process, including the introduction of a new construct, in situ performance, and an expanded view of staffing tools to be used to predict future in situ performance that take into account time and context. Our critical review offers a novel perspective and research agenda with the goal of guiding future research that will result in more useful, applicable, relevant, and effective knowledge for practitioners to use in organizational settings.     

带学习效应的双渠道供应链库存策略研究

针对具有学习行为的双渠道供应链问题,本文研究了两种分销渠道并存下的最优库存策略。有限计划期内,分销商通过传统销售和在线销售来满足下游顾客的需求。两种分销渠道下的销售单价为时变不减线性函数,当系统中各周期的生产订购固定成本以一定的概率具有学习效应行为时,分别建立了非变质产品生产存贮问题的混合整数约束优化模型以及易变质产品存贮问题的无约束混合整数优化模型,所建立模型的目标为极大化分销商总利润函数。对于这两类模型,通过分析其最优解的性质,利用将生产订购次数松弛为连续变量的技巧证明了最优解存在的唯一性。给出了最优策略的求解方法并比较了两类模型最优利润函数值的大小。最后通过数值算例对上述模型进行了验证,数值结果表明当供应链系统中存在学习效应行为时,该系统能够获得更多的利润。     

Optimal Dynamic Pricing of Perishable Items by a Monopolist Facing Strategic Consumers

We introduce a dynamic pricing model for a monopolistic company selling a perishable product to a finite population of strategic consumers (customers who are aware that pricing is dynamic and may time their purchases strategically). This problem is modeled as a stochastic dynamic game in which the company's objective is to maximize total expected revenues, and each customer maximizes the expected present value of utility. We prove the existence of a unique subgame‐perfect equilibrium pricing policy, provide equilibrium optimality conditions for both customer and seller, and prove monotonicity results for special cases. We demonstrate through numerical examples that a company that ignores strategic consumer behavior may receive much lower total revenues than one that uses the strategic equilibrium pricing policy. We also show that, when the initial capacity is a decision variable, it can be used together with the appropriate pricing policy to effectively reduce the impact of strategic consumer behavior. The proposed model is computationally tractable for problems of realistic size.     

Equity in Social Risk: Some Empirical Observations

In societal risk analysis the equity of the distribution of risks is often an important consideration owing to the special nature of health risks. We empirically validate some assumptions about equity that have been discussed in the decision analytic literature. Our results show that the way fatalities are distributed throughout a society is considered along with the number of fatalities in evaluating alternative policies involving mortality risks. The concepts of ex ante equity and ex post equity are both shown to be important in judgments of fairness. We next present a decision model based on multiattribute preference theory incorporating the number of fatalities, as well as ex ante equity and ex post equity. When ex ante equity and ex post equity are positively weighted in this fair-risk model , options with more equal risk distributions are ranked higher. Next we empirically show that the distribution of benefits has an impact on judgments of fairness. The fair-risk model does not include information on the benefits distribution, so it would apply when benefits are distributed equally or when the decision maker wishes to not include benefits in the model. We briefly discuss how the notion of proportional equity can incorporate benefits into judgments of the fairness of risk distributions. We then include benefits in a more general model in which fair risk-benefit combinations are those that are exchange equitable. A key implication of this envy-free risk–benefit model is that an unequal distribution of risks may be preferred if it is accompanied by a compensatory differential in benefits consistent with peoples' preference tradeoffs between received benefits and assumed risks. Finally, we discuss how perceived deservedness may influence judgments about equity. We conclude with a discussion of the implications of research on alternative notions of equity for policy makers dealing with social risks.     

Joint Ordering and Pricing Strategies for Managing Substitutable Products

Starr and Rubinson (1978) develop a model to establish the relationship between product demand and relative prices. The notion of relative prices motivates us to consider a situation in which a retailer would either charge the same retail price for all products if he adopts a ‘fixed’ pricing strategy or charge different prices for different products if he adopts a ‘variable’ pricing strategy. In this paper, we develop a base model with deterministic demand that is intended to examine how a retailer should jointly determine the order quantity and the retail price of two substitutable products under the fixed and variable pricing strategies. Our analysis indicates that the optimal retail price under the variable pricing strategy is equal to the optimal retail price under the fixed pricing strategy plus or minus an adjustment term. This adjustment term depends on product substitutability and price sensitivity. We also present two different extensions of our base model. In the first extension, our analysis indicates that the underlying structure of the optimal retail price and order quantity is preserved when there is a limit on the total order quantity. The second extension deals with the issue of retail competition. Relative to the base case, we show that the underlying structure of the optimal retail price and order quantity is preserved in a duopolistic environment. Moreover, our analysis suggests that both retailers would adopt the variable pricing strategy at the equilibrium.     

A Social Decision Analysis of the Earthquake Safety Problem: The Case of Existing Los Angeles Buildings

In this paper we propose a framework for conducting a decision analysis for a societal problem such as earthquake safety. The application deals with the formulation and evaluation of alternative policies for the seismic safety problem faced by the city of Los Angeles with regard to its old masonry buildings. A social decision analysis compares the costs and benefits of the alternative policies from the viewpoints of the impacted constituents. The emphasis is on identifying acceptable policy that considers the interests of the impacted constituents and provides incentives for their cooperation. Alternatives ranging from strict regulation to free market are examined. In order to evaluate the trade-offs between additional cost and savings in lives, a direct willingness-to-pay and an economic approach, based on property value differential, are used. Recommendations range from strict regulation for the residential and critical buildings (schools, hospitals, fire stations, etc.) to simply informing the occupants (in the case of commercial and industrial buildings) of the risks involved.     

Characterizing the Structure of Optimal Stopping Policies

This paper studies a stochastic model of optimal stopping processes, which arise frequently in operational problems (e.g., when a manager needs to determine an optimal epoch to stop a process). For such problems, we propose an effective method of characterizing the structure of the optimal stopping policy for the class of discrete‐time optimal stopping problems. Using this method, we also derive a set of metatheorems that can help identify when a threshold or control‐band type stopping policy is optimal. We show that our proposed method can determine the structure of the optimal policy for some stopping problems that conventional methods fail to do so. In some cases, our method also simplifies the analysis of some existing results. Moreover, the metatheorems we propose help identify sufficient conditions that yield simple optimal policies when such policies are not generally optimal. We demonstrate these benefits by applying our method to several optimal stopping problems frequently encountered in, for example, the operations, marketing, finance, and economics literatures. We note that with structural results, optimal‐stopping policies are easier to follow, describe, and compute and hence implement. They also help determine how a stopping policy should be adjusted in response to changes in the operational environment. In addition, as structural results are critical for the development of efficient algorithms to solve optimal stopping problems numerically, we hope that the method and results provided in the study will contribute to that effort.     

The Value of Information in Decision‐Analytic Modeling for Malaria Vector Control in East Africa

Decision analysis tools and mathematical modeling are increasingly emphasized in malaria control programs worldwide to improve resource allocation and address ongoing challenges with sustainability. However, such tools require substantial scientific evidence, which is costly to acquire. The value of information (VOI) has been proposed as a metric for gauging the value of reduced model uncertainty. We apply this concept to an evidenced‐based Malaria Decision Analysis Support Tool (MDAST) designed for application in East Africa. In developing MDAST, substantial gaps in the scientific evidence base were identified regarding insecticide resistance in malaria vector control and the effectiveness of alternative mosquito control approaches, including larviciding. We identify four entomological parameters in the model (two for insecticide resistance and two for larviciding) that involve high levels of uncertainty and to which outputs in MDAST are sensitive. We estimate and compare a VOI for combinations of these parameters in evaluating three policy alternatives relative to a status quo policy. We find having perfect information on the uncertain parameters could improve program net benefits by up to 5–21%, with the highest VOI associated with jointly eliminating uncertainty about reproductive speed of malaria‐transmitting mosquitoes and initial efficacy of larviciding at reducing the emergence of new adult mosquitoes. Future research on parameter uncertainty in decision analysis of malaria control policy should investigate the VOI with respect to other aspects of malaria transmission (such as antimalarial resistance), the costs of reducing uncertainty in these parameters, and the extent to which imperfect information about these parameters can improve payoffs.