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When a manufacturer places repeated orders with a supplier to meet changing production requirements, he faces the challenge of finding the right balance between holding costs and the operational costs involved in adjusting the shipment sizes. We consider an inventory whose content fluctuates as a Brownian motion in the absence of control. At any moment, a controller can adjust the inventory level by any positive or negative quantity, but incurs both a fixed cost and a cost proportional to the magnitude of the adjustment. The inventory level must be nonnegative at all times and continuously incurs a linear holding cost. The objective is to minimize long-run average cost. We show that control band policies are optimal for the average cost Brownian control problem and explicitly calculate the parameters of the optimal control band policy. This form of policy is described by three parameters { q,Q,S }, 0 < q Q < S . When the inventory falls to zero (rises to S ), the controller expedites (curtails) shipments to return it to q ( Q ). Employing apparently new techniques based on methods of Lagrangian relaxation, we show that this type of policy is optimal even with constraints on the size of adjustments and on the maximum inventory level. We also extend these results to the discounted cost problem.

A DEA-based stochastic frontier estimation framework is presented to evaluate contextual variables affecting productivity that allows for both one-sided inefficiency deviations as well as two-sided random noise. Conditions are identified under which a two-stage procedure consisting of DEA followed by ordinary least squares (OLS) regression analysis yields consistent estimators of the impact of contextual variables. Conditions are also identified under which DEA in the first stage followed by maximum likelihood estimation (MLE) in the second stage yields consistent estimators of the impact of contextual variables. This requires the contextual variables to be independent of the input variables, but the contextual variables may be correlated with each other. Monte Carlo simulations are carried out to compare the performance of our two-stage approach with one-stage and two-stage parametric approaches. Simulation results indicate that DEA-based procedures with OLS, maximum likelihood, or even Tobit estimation in the second stage perform as well as the best of the parametric methods in the estimation of the impact of contextual variables on productivity. Simulation results also indicate that DEA-based procedures perform better than parametric methods in the estimation of individual decision-making unit (DMU) productivity. Overall, the results establish DEA as a nonparametric stochastic frontier estimation (SFE) methodology.

Delay announcements informing customers about anticipated service delays are prevalent in service-oriented systems. How delay announcements can influence customers in service systems is a complex problem that depends on both the dynamics of the underlying queueing system and on the customers' strategic behavior. We examine this problem of information communication by considering a model in which both the firm and the customers act strategically: the firm in choosing its delay announcement while anticipating customer response, and the customers in interpreting these announcements and in making the decision about when to join the system and when to balk. We characterize the equilibrium language that emerges between the service provider and her customers. The analysis of the emerging equilibria provides new and interesting insights into customer-firm information sharing. We show that even though the information provided to customers is nonverifiable, it improves the profits of the firm and the expected utility of the customers. The robustness of the results is illustrated via various extensions of the model. In particular, studying models with incomplete information on the system parameters allows us also to highlight the role of information provision in managing customer expectations regarding the congestion in the system. Further, the information could be as simple as \"high congestion\"/\"low congestion\" announcements, or it could be as detailed as the true state of the system. We also show that firms may choose to shade some of the truth by using intentional vagueness to lure customers.

\"Bucket brigades\" are a way of sharing work on a flow line that results in the spontaneous emergence of balance and consequent high throughput. All this happens without a work-content model or traditional assembly line balancing technology. Here we show that bucket brigades can be effective even in the presence of variability in the work content. In addition, we report confirmation at the national distribution center of a major chain retailer, which experienced a 34% increase in productivity after the workers began picking orders by bucket brigade.

In a call center, arriving customers must be routed to available servers, and servers that have just become available must be scheduled to help waiting customers. These dynamic routing and scheduling decisions are very difficult, because customers have different needs and servers have different skill levels. A further complication is that it is preferable that these decisions are made blindly; that is, they depend only on the system state and not on system parameter information such as call arrival rates and service speeds. This is because this information is generally not known with certainty. Ideally, a dynamic control policy for making routing and scheduling decisions balances customer and server needs by keeping customer delays low but still fairly dividing the workload amongst the various servers. In this paper, we propose a blind dynamic control policy for parallel-server systems with multiple customer classes and server pools that is based on the number of customers waiting and the number of agents idling. We show that in the Halfin-Whitt many-server heavy-traffic limiting regime, our proposed blind policy performs extremely well when the objective is to minimize customer holding costs subject to \"server fairness,\" as defined by how the system idleness is divided among servers. To do this, we formulate an approximating diffusion control problem (DCP) and compare the performance of the nonblind DCP solution to a feasible policy for the DCP that is blind. We establish that the increase in the DCP objective function value is small over a wide range of parameter values. We then use simulation to validate that a small increase in the DCP objective function value is indicative of our proposed blind policy performing very well.

Questions regarding the relative value and frequency of mammography screening for premenopausal women versus postmenopausal women remain open due to the conflicting age-based dynamics of both the disease (increasing incidence, decreasing aggression) and the accuracy of the test results (increasing sensitivity and specificity). To investigate these questions, we formulate a partially observed Markov chain model that captures several of these age-based dynamics not previously considered simultaneously. Using sample-path enumeration, we evaluate a broad range of policies to generate the set of \"efficient\" policies, as measured by a lifetime breast cancer mortality risk metric and an expected mammogram count, from which a patient may select a policy based on individual circumstance. We demonstrate robustness with respect to small changes in the input data and conclude that, in general, to efficiently achieve a lifetime risk comparable to the current risk among U.S. women, screening should start relatively early in life and continue relatively late in life regardless of the screening interval(s) adopted. The frontier also exhibits interesting patterns with respect to policy type, where policy type is defined by the relationship between the screening interval prescribed in younger years and that prescribed later in life.

We propose a new method to compute bid prices in network revenue management problems. The novel aspect of our method is that it explicitly considers the temporal dynamics of the arrivals of the itinerary requests and generates bid prices that depend on the remaining leg capacities. Our method is based on relaxing certain constraints that link the decisions for different flight legs by associating Lagrange multipliers with them. In this case, the network revenue management problem decomposes by the flight legs, and we can concentrate on one flight leg at a time. When compared with the so-called deterministic linear program, we show that our method provides a tighter upper bound on the optimal objective value of the network revenue management problem. Computational experiments indicate that the bid prices obtained by our method perform significantly better than the ones obtained by standard benchmark methods.

We study a multicomponent, multiproduct production and inventory system in which individual components are made to stock but final products are assembled to customer orders. Each component is produced by an independent production facility with finite capacity, and the component inventory is controlled by an independent base-stock policy. For any given base-stock policy, we derive the key performance measures, including the probability of fulfilling a customer order within any specified time window. Computational procedures and numerical examples are also presented. A similar approach applies to the generic multi-item make-to-stock inventory systems in which a typical customer order consists of a kit of items.

Many companies have started segmenting customers to better match their products and services to the needs of the customers. We support this development by presenting a stochastic model of a rental system with two customer classes that was motivated by the operations of one of Europe's leading logistics companies. At the company, customers can choose between premium and classic service. Under premium service, customers provide advance demand information (ADI) by reserving cars ahead of the time when they need them, and they receive a service guarantee in return. Under classic service, customers do not make a reservation and do not receive a service guarantee. Because both demand classes access a common pool of cars, the company must decide which demands to fill and which to reject. The admission decision must be made without knowing the rental duration, which is an exponentially distributed random variable. We model the system as a multiserver loss system and prove that the optimal admission policy is a threshold policy. Because computing the parameters of the policy is computationally intractable, we propose an ADI policy that can be implemented and executed with moderate effort. We analyze the performance of our ADI policy by analytically deriving upper and lower bounds on the optimal expected profit and by performing numerical experiments using data from the logistics company that motivated our research. The numerical experiments indicate that the potential benefit of using ADI is significant and that our ADI policy performs close to optimal. Finally, we extend our model to a different cost structure and to multiple ADI classes.

We present a new model for revenue management of product sales that incorporates both dynamic pricing and a price guarantee. The guarantee provides customers with compensation if, prior to a fixed future date, the price of the product drops below a level specified at the time of purchase. We consider the problem of simultaneously determining optimal dynamic price and guarantee policies for items from a fixed stock when demand depends both on the price and on the parameters of the price guarantee. The model can be used for pricing any items with limited availability over a fixed time horizon. We formulate this model as a discrete-time optimal control problem, prove the existence of its optimal solution, explore some of the structural properties of the solution, present lower-bounding heuristics for solving the problem, and report numerical results.