MANAGERIAL ECONOMICS & DECISION SCIENCES; OPERATIONS
Associate Professor of Managerial Economics & Decision Sciences
Ata’s research is on stochastic models of operations management, specifically the design and control of manufacturing service and telecommunications systems, and revenue management.
Ata received his PhD in Operations, Information and Technology from Stanford University. Prior to his appointment at Kellogg in 2003, he worked as an associate for McKinsey & Company in Istanbul.
Queuing Systems
Revenue Management
We investigate how network design impacts capacity requirements and responsiveness, which is a natural performance indicator of quality of service. Inspired by the contrasting network design approaches of FedEx and UPS, we study when two service classes (e.g., express or regular) should be served by dedicated resources (e.g., air or ground) or by an integrated network. We present analytic expressions for the delay distributions and the network integration value, which show how the value of network integration depends on the quality of service guarantees (speed and reliability of service) and the demand characteristics (averages volume and variance of each service class and their correlation). Our results suggests that operating dedicated networks is a fine strategy (meaning that network integration is of little value) if the firm primarily serves express requests with high reliability and if the correlation with regular requests is not strongly negative.
A class of open processing networks operating under a maximum pressure policy is considered in the heavy traffic regime. We prove that the diffusion-scaled workload process for a network with several bottleneck resources converges to a semimartingale reflecting Brownian motion (SRBM) living in a polyhedral cone. We also establish a state space collapse result that the queue length process can be lifted from the lower-dimensional workload process.
A central controller chooses a state-dependent transmission rate for each user in a fading, downlink channel by varying transmission power over time. For each user, the state of the channel evolves over time according to an exogenous continuous-time Markov chain (CTMC), which affects the quality of transmission. The traffic for each user, arriving at the central controller, is modeled as a finite-buffer Markovian queue with adjustable service rates. That is, for each user data packets arrive to the central controller according to a Poisson process and packet size is exponentially distributed; an arriving packet is dropped if the associated buffer is full, which results in degradation of quality of service. The controller forwards (downlink) the arriving packets to the corresponding user according to an optimally chosen transmission rate from a fixed set Ai of available values for each user i, depending on the backlog in the system and the channel state of all users. The objective is to maximize quality of service subject to an upper bound on the long-run average power consumption. We show that the optimal transmission rate for each user is solely a function of his own packet queue length and channel state; the dependence among users is captured through a penalty rate. Further, we explicitly characterize the optimal transmission rate for each user.
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 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 original queueing system, a nested threshold policy is proposed. A simulation experiment is performed to demonstrate the effectiveness of this policy.
We study a service facility in which the system manager dynamically controls the arrival and service rates to maximize the long-run average value generated. We initially consider a rate setting problem where the service facility is modeled as an M/M/1 queue with adjustable arrival and service rates, and solve this problem explicitly. Next, we use this solution to study a price setting problem, where customers are utility maximizing, price- and delay-sensitive, and the system manager chooses state-dependent service rates and prices. We find that the optimal arrival rate is decreasing and the optimal service rate is increasing in the number of customers in the system, however, the optimal price need not be monotone. We also show that under the optimal policy the service facility operates as one with a finite buffer. Finally, we study a numerical example to compare the social welfare achieved using a dynamic policy to that achieved using static policies, and show the dynamic policy offers significant welfare gains.
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 θ that is chosen from a fixed set A of available values. The controlled process evolves according to the differential relationship dZ=dX−θ(Z) dt+dL−dU, where X is a (0,σ) 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 dξ=c(θ(Z)) dt+p dU, where c(⋅) 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.
A controller dynamically chooses a state-dependent transmission rate on a static, point-to-point wireless link by varying tranmission power over time. The transmitter is modeled as a finite-buffer Markovian queue with adjustable service rates. That is, data packets arrive to the system according to a Poisson process and packet size is exponentially distributed. The controller chooses a transmission rate from a fixed set A of available values, depending on the backlog in the system. The objective is to minimize long-run average energy consumption subject to a quality of service constraint, which is expressed as an upper bound on the packet drop rate. An explicit formula is developed for the optimal transmission rate as a function of the packet queue length.
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.
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 non-greedy outsourcing and resource allocation policy is proposed. A simulation experiment is performed to demonstrate the effectiveness of this policy.
We consider a contracting problem in which a firm outsources its call center operations to a service provider. The outsourcing firm (which we term the originator) has private information regarding the rate of incoming calls. The per-call revenue (or margin) earned by the firm and the service level depend on the staffing decisions by the service provider. Initially, we restrict attention to pay-per-call contracts under which the parties contract on a service level and a per-call fee. The service provider is modeled as a multi-server queue with a Poisson arrival process, exponentially distributed service times and customer abandonment. We assume that the service provider's queue is large enough such that the economically sensible mode of operation for staffing it is the Quality-and-Efficiency-Driven regime, which allows tractable approximations of various performance metrics. We first consider a screening scenario with the service provider offering a contract to the originator. Due to the statistical economies of scale phenomenon observed in queueing systems, the allocation of the originator with higher arrival rate is distorted, which reverses the typical "efficiency at top" result present in the literature on monopolist screening. We then consider the alternative scenario with the originator offering a contract to signal her information and show that the service level of the high volume firm is again distorted. The introduction of a fixed payment ameliorates distortions from first-best and may eliminate them.
We consider data transmission through a time selective(correlated) flat Rayleigh fading channel under an average power constraint. The channel is estimated at the receiver with a pilot signal, and the estimate is fed back to the transmitter. The estimate is used for coherent demodulation, and to adapt the data and pilot powers. We start with a block fading channel in which the channel gain changes according to a Gauss-Markov process. The channel estimate is updated during each coherence block with a Kalman filter, and optimizing the data and pilot powers is formulated as a dynamic program. We then study a continuous limit in which the coherence time tends to zero, and the correlation between successive channel gains tends to one, so that the channel process becomes a diffusion process. In this limit it is shown that the optimal pilot power control policy is “bang-bang”, i.e., depending on the current system state (channel estimate and associated error variance) the pilot power is either the maximum allowable, or zero. The associated regions of the state space are illustrated numerically for specific system values. This example shows that the achievable rate with the optimized training policy provides substantial gains relative to constant training power at low SNRs.
Response time is an important dimension of operational excellence in many manufacturing and service sectors. Firms in such settings may find it attractive to dynamically adjust prices based on the state of their order book and the corresponding lead times. Virtually the entire revenue management literature for queues assumes that providers know the distribution of customer demand attributes. However, such precise demand information may hardly be available. We relax this assumption and study the case of an unknown mix of patient and impatient customers who differ in their time-sensitivity. The provider has a Bernoulli prior on the customer mix which corresponds to an optimistic or pessimistic demand scenario and which she updates depending on whether customers buy or not at the posted prices. We characterize the optimal dynamic pricing policy under Bayesian updating and the resulting system performance. It has a threshold structure whereby the provider experiments with a high price as long as her posterior belief that the demand scenario is optimistic exceeds a certain positive threshold and otherwise reverts to charging a low price forever. We analytically characterize the length of the experimentation period and the probability that the provider eventually learns the underlying demand scenario. Finally, we study the provider’s expected revenue gains from acquiring perfect demand information relative to following the optimal Bayesian pricing policy. We discuss how this value of perfect demand information depends on the problem parameters and provide closed form expressions on its upper bound for the case where all customers are patient in the optimistic and impatient in the pessimistic scenario.
This course counts toward the following majors:Operations.
Operations management is the management of business processes--that is, the management of the recurring activities of a firm. This course aims to familiarize students with the problems and issues confronting operations managers, and to provide the language, concepts, insights and tools to deal with these issues to gain competitive advantage through operations. We examine how different business strategies require different business processes and how different operational capabilities allow and support different strategies to gain competitive advantage. A process view of operations is used to analyze different key operational dimensions such as capacity management, cycle time management, supply chain and logistics management, and quality management. Finally, we connect to recent developments such as lean or world-class manufacturing, just-in-time operations, time-based competition and business re-engineering.
Prerequisite: DECS-433 or DECS-436.
Spreadsheet Modeling for Managerial Decisions (OPNS-450-0)
This course counts toward the following majors: Analytical Consulting, Decision Sciences, Operations.
This course focuses on structuring, analyzing and solving managerial decision problems on Excel spreadsheets. We address problems of resource allocation (how to use available resources optimally), risk analysis (how to simulate the effects of uncertainty in problem parameters), decision analysis (how to analyze sequential decisions involving uncertainty), data analysis (how to synthesize the available data into useful information) and forecasting (how to extrapolate past observations into the future). In each area, we pose specific problems from operations, finance and marketing, structure them on Excel spreadsheets, and analyze and solve them using the available Excel commands, tools and add-ins. The course involves a hands-on, in-class learning experience in modeling and analyzing a variety of business decision problems on a common spreadsheet platform. It should, therefore, enhance one's problem-solving capabilities as well as spreadsheet skills. A good working knowledge of Microsoft Excel is required.
Operations Strategy (OPNS-454-0)
This course counts toward the following majors: Analytical Consulting, Operations.
In this course, students learn how operations strategy can add value by tailoring a set of core principles to a specific business setting. The course provides a framework to formulate an operations strategy and analyze, value, and optimize the key decisions involved in operations strategy. The key evaluation metric is how operations strategy impacts the net present value of the firm. The key decisions studied are choosing competitive operational competencies and benchmarking; capacity expansion, timing, flexibility and location; sourcing and contracting; risk management and operational hedging; revenue management; improvement and learning.
This course builds on the core operations class. Students should also be familiar with the basics of finance, economics and strategy, as the strategic decisions studied in this course require a detailed analysis and understanding of the underlying operations. Thus this course has a greater amount of concreteness and detail than a competitive strategy class, and uses a combination of in-depth case analysis, mini-lectures, presentations and qualitative discussions of other examples. The course is intended for students interested in operations and supply chain management, general management, or management consulting.
This course is designed to introduce students to contemporary research topics in the field of Operations Management. Some familiarity with statistical/empirical methods, dynamic programming, mathematical programming, stochastic processes is required.
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