Baris Ata

Drift rate control of a Brownian processing system

A system manager dynamically controls a diffusion process Z that lives in a finite interval [0,b]. Control takes the form of a negative drift rate \theta that is chosen from a fixed set A of available values. The controlled process evolves according to the differential relationship dZ=dX-\theta(Z) dt+dL-dU, where X is a (0,\sigma) Brownian motion, and L and U are increasing processes that enforce a lower reflecting barrier at Z=0 and an upper reflecting barrier at Z=b, respectively. The cumulative cost process increases according to the differential relationship d\xi =c(\theta(Z)) dt+p dU, where c(\cdot) is a nondecreasing cost of control and p>0 is a penalty rate associated with displacement at the upper boundary. The objective is to minimize long-run average cost. This problem is solved explicitly, which allows one to also solve the following, essentially equivalent formulation: minimize the long-run average cost of control subject to an upper bound constraint on the average rate at which U increases. The two special problem features that allow an explicit solution are the use of a long-run average cost criterion, as opposed to a discounted cost criterion, and the lack of state-related costs other than boundary displacement penalties. The application of this theory to power control in wireless communication is discussed.

Heavy traffic analysis of open processing networks with complete resource pooling: Asymptotic optimality of discrete review policies

We consider a class of open stochastic processing networks, with feedback routing and overlapping server capabilities, in heavy traffic. The networks we consider satisfy the so-called complete resource pooling condition and therefore have one-dimensional approximating Brownian control problems. We propose a simple discrete review policy for controlling such networks. Assuming 2+\epsilon moments on the interarrival times and processing times, we provide a conceptually simple proof of asymptotic optimality of the proposed policy.

Revenue management by sequential screening

Using a mechanism design approach, we consider a firms optimal pricing policy when consumers are heterogeneous and learn their valuations at different times. We show that by offering a menu of advance-purchase contracts that differ in when, and for how much, the product can be returned, a firm can more easily price discriminate between privately-informed consumers. In particular, we show that screening on when the return option can be exercised increases firm profits, relative to screening on the size of the refund alone, only if the expected gains from trade are higher for consumers who learn later. We show that in some settings (mean-preserving spread) the firm can achieve the complete-information profits and analyze the optimal contract in other settings (first-order stochastic dominance) in which the first-best allocation is not always feasible.

Structural Estimation of Callers' Delay Sensitivity in Call Centers

We model the decision-making process of callers in call centers as an optimal stopping problem. After each waiting period, a caller decides whether to abandon a call or continue to wait. The utility of a caller is modeled as a function of her waiting cost and reward for service. We use a random-coefficients model to capture the heterogeneity of the callers and estimate the cost and reward parameters of the callers using the data from individual calls made to an Israeli call center. We also conduct a series of counterfactual analyses that explore the effects of changes in service discipline on resulting waiting times and abandonment rates. Our analysis reveals that modeling endogenous caller behavior can be important when major changes such as a change in service discipline are implemented and that using a model with an exogenously specified abandonment distribution may be misleading. This paper was accepted by Assaf Zeevi, stochastic models and simulation.

Dynamic Control of a Multiclass Queue with Thin Arrival Streams

As a model of make-to-order production, we consider an admission control problem for a multiclass, single-server queue. The production system serves multiple demand streams, each having a rigid due-date lead time. To meet the due-date constraints, a system manager may reject orders when a backlog of work is judged to be excessive, thereby incurring lost revenues. The system manager strives to minimize long-run average lost revenues by dynamically making admission control and sequencing decisions. Under heavy-traffic conditions the scheduling problem is approximated by a Brownian control problem, which is solved explicitly. Interpreting this solution in the context of the original queueing system, a nested threshold policy is proposed. A simulation experiment is performed to demonstrate the effectiveness of this policy.

Dynamic Control of a Make-to-Order, Parallel-Server System with Cancellations

Motivated by make-to-order production systems, we consider a dynamic control problem for a multiclass, parallel-server queueing system. The production system serves multiple classes of customers who require rigid due-date lead times and may cancel their order subject to a cancellation penalty. To meet the due-date constraints, a system manager may outsource orders when the backlog of work is judged excessive, thereby incurring outsourcing costs. The system manager strives to minimize long-run average costs by dynamically making outsourcing and resource allocation decisions. Under heavy-traffic conditions, the scheduling problem is approximated by a Brownian control problem. Interpreting the solution of the Brownian control problem in the context of the original queueing system, a nongreedy outsourcing and resource allocation policy is proposed. A simulation experiment is performed to demonstrate the effectiveness of this policy.

A Broader View of Designing the Liver Allocation System

We consider the problem of designing an efficient system for allocating donated livers to patients waiting for transplantation. The trade-off between medical urgency and efficiency is at the heart of the liver allocation problem. We model the transplant waiting list as a multiclass fluid model of overloaded queues, which captures the disease evolution by allowing the patients to switch between classes, i.e., health levels. We consider the bicriteria objective of minimizing total number of patient deaths while waiting for transplantation (NPDWT) and maximizing total quality-adjusted life years (QALYs) through a weighted combination. On one hand, under the objective of minimizing NPDWT, the current policy of United Network for Organ Sharing (UNOS) emerges as the optimal policy, providing a theoretical justification for the current practice. On the other hand, under the metric of maximizing QALYs, the optimal policy is an intuitive dynamic index policy that ranks patients based on their marginal benefit from transplantation, i.e., the difference in benefit with versus without transplantation. Finally, we perform a detailed simulation study to compare the performances of our proposed policies and the current UNOS policy along the following metrics: total QALYs, NPDWT, number of patient deaths after transplantation, number of total patient deaths, and number of wasted livers. Numerical experiments show that our proposed policy for maximizing QALYs outperforms the current UNOS policy along all metrics except the NPDWT.

Bid-Price Controls for Network Revenue Management: Martingale Characterization of Optimal Bid Prices

We consider a continuous-time, rate-based model of network revenue management. Under mild assumptions, we construct a simple e-optimal bid-price control, which can be viewed as a perturbation of a bid-price control in the classical sense [Williamson, E. L. 1992. Airline network seat control. Ph.D. thesis, MIT, Cambridge, MA]. We show that the associated bid-price process forms a martingale and the corresponding booking controls converge in an appropriate sense to an optimal control as e tends to 0. Moreover, we show that there exists an optimal generalized bid-price control, where the bid-price process forms a martingale and is used in conjunction with a capacity usage limit process. We also discuss its connection to the bid-price controls in the classical sense and sufficient conditions for the (near) optimality of the latter.

Optimizing Organic Waste to Energy Operations

A waste-to-energy firm that recycles organic waste with energy recovery performs two environmentally beneficial functions: it diverts waste from landfills and it produces renewable energy. At the same time, the waste-to-energy firm serves and collects revenue from two types of customers: waste generators who pay for waste disposal service and electricity consumers who buy energy. Given the process characteristics of the waste-to-energy operation, the market characteristics for waste disposal and energy, and the mechanisms regulators use to encourage production of renewable energy, we determine the profit-maximizing operating strategy of the firm. We also show how regulatory mechanisms affect the operating decisions of the waste-to-energy firm. Our analyses suggest that if the social planners objective is to maximize landfill diversion, offering a subsidy as a per kilowatt-hour for electricity is more cost effective, whereas if the objective is to maximize renewable energy generation, giving a subsidy as a lump sum to offset capital costs is more effective. This has different regulatory implications for urban and rural settings where the environmental objectives may differ.

Dynamic pricing of remanufacturable products under demand substitution: a product life cycle model

We consider a manufacturer who sells both the new and remanufactured versions of a product over its life cycle. The manufacturer’s profit depends crucially on her ability to synchronize product returns with the sales of the remanufactured product. This gives rise to a challenging dynamic optimization problem where the size of both the market and the user pool are dynamic and their current values depend on the entire history. We provide an analytical characterization of the manufacturer’s optimal pricing, production, and inventory policies which lead to a practical threshold policy with a small optimality gap. In addition, our analysis offers a number of interesting insights. First, the timing of remanufacturing activity and its co-occurrence with new product manufacturing critically depends on remanufacturing cost benefits, attractiveness of the remanufactured product and product return rate. Second, there is a small upward jump in the price of the new product when remanufacturing is introduced. Third, the manufacturer keeps the new product longer on the market as the cost of remanufacturing decreases. Fourth, partially satisfying demand for the remanufactured item is never optimal, i.e., it is satisfied either fully or not at all. Finally, user pool and inventory of returned products are substitutes in ensuring the supply for future remanufacturing.