Publications with Fulltext
Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/6
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Publication Open Access Structural properties of a class of robust inventory and queueing control problems(Wiley, 2018) Department of Industrial Engineering; N/A; Örmeci, Lerzan; Karaesmen, Fikri; Faculty Member; Faculty Member; Department of Industrial Engineering; College of Engineering; Graduate School of Sciences and Engineering; 32863; 3579; N/AIn standard stochastic dynamic programming, the transition probability distributions of the underlying Markov Chains are assumed to be known with certainty. We focus on the case where the transition probabilities or other input data are uncertain. Robust dynamic programming addresses this problem by defining a min-max game between Nature and the controller. Considering examples from inventory and queueing control, we examine the structure of the optimal policy in such robust dynamic programs when event probabilities are uncertain. We identify the cases where certain monotonicity results still hold and the form of the optimal policy is determined by a threshold. We also investigate the marginal value of time and the case of uncertain rewards.Publication Open Access Distributionally robust optimization under a decision-dependent ambiguity set with applications to machine scheduling and humanitarian logistics(The Institute for Operations Research and the Management Sciences (INFORMS), 2022) Noyan, Nilay; Lejeune, Miguel; Department of Industrial Engineering; Rudolf, Gabor; Faculty Member; Department of Industrial Engineering; College of EngineeringWe introduce a new class of distributionally robust optimization problems under decision-dependent ambiguity sets. In particular, as our ambiguity sets, we consider balls centered on a decision-dependent probability distribution. The balls are based on a class of earth mover's distances that includes both the total variation distance and the Wasserstein metrics. We discuss the main computational challenges in solving the problems of interest and provide an overview of various settings leading to tractable formulations. Some of the arising side results, such as the mathematical programming expressions for robustified risk measures in a discrete space, are also of independent interest. Finally, we rely on state-of-the-art modeling techniques from machine scheduling and humanitarian logistics to arrive at potentially practical applications, and present a numerical study for a novel risk-averse scheduling problem with controllable processing times. Summary of Contribution: In this study, we introduce a new class of optimization problems that simultaneously address distributional and decision-dependent uncertainty. We present a unified modeling framework along with a discussion on possible ways to specify the key model components, and discuss the main computational challenges in solving the complex problems of interest. Special care has been devoted to identifying the settings and problem classes where these challenges can be mitigated. In particular, we provide model reformulation results, including mathematical programming expressions for robustified risk measures, and describe how these results can be utilized to obtain tractable formulations for specific applied problems from the fields of humanitarian logistics and machine scheduling. Toward demonstrating the value of the modeling approach and investigating the performance of the proposed mixed-integer linear programming formulations, we conduct a computational study on a novel risk-averse machine scheduling problem with controllable processing times. We derive insights regarding the decision-making impact of our modeling approach and key parameter choices.Publication Open Access Modeling and analysis of vessel casualties resulting from tanker traffic through narrow waterways(Wiley, 1999) Otay, Emre N.; Department of Business Administration; Tan, Barış; Faculty Member; Department of Business Administration; College of Administrative Sciences and Economics; 28600In this paper, we present a physics-based stochastic model to investigate vessel casualties resulting from tanker traffic through a narrow waterway. A state-space model is developed to represent the waterway and the location of vessels at a given time. We first determine the distribution of surface current at a given location of the waterway depending on channel geometry, bottom topography, boundary conditions, and the distribution of wind. Then we determine the distribution of the angular drift for a given vessel travelling at a given location of a waterway. Finally, we incorporate the drift probabilities and random arrival of vessels into a Markov chain model. By analyzing the time-dependent and the steady-state probabilities of the Markov chain, we obtain risk measures such as the probability of casualty at a given location and also the expected number of casualties for a given number of vessels arriving per unit time. Analysis of the Markovian model also yields an analytical result that shows that the expected number of casualties is proportional to square of the tanker arrival rate. We present our methodology on an experimental model of a hypothetical narrow waterway.Publication Open Access Dynamics of price premiums in loyalty programs(Emerald, 2014) Hoch, Stephen J.; Department of Business Administration; Department of Business Administration; Sayman, Serdar; Faculty Member; Department of Business Administration; College of Administrative Sciences and Economics; 112222Purpose - A loyalty program might influence buyer behavior in several ways. Prior research offers evidence that buyers might increase the frequency of purchases and volume per occasion in a loyalty program; however, the effect on buyers' price tolerance has not been studied before. The aim of this paper is to examine buyers' willingness to pay a price premium for a firm offering a loyalty program reward.Design/methodology/approach - An analytical model of dynamic consumer choice is developed, where one of the two selling firms offers a reward for a certain number of purchases. The maximum price premium that a normatively rational buyer should be willing to pay at each level of accumulated purchases is obtained. A price tolerance in controlled settings is obtained and these are compared with normative solutions. Findings - Analytically, it is shown that the maximum price premium increases as purchases are accumulated; and the exact solutions can be found, given the price distributions and program design parameters. In the empirical studies it is found that individuals' maximum premiums are less than the normative levels. On the other hand, as buyers accumulate purchases from the reward offering firm, and get closer to the reward, maximum premiums paid increase - particularly when the reward is immediate. Originality/value - This paper contributes to the loyalty programs literature by examining the price premium, or switching barrier, aspect of buyer response. Furthermore, the paper not only models and solves the normative strategy, but also obtains actual price tolerance in laboratory settings.Publication Open Access Analysis of a group purchasing organization under demand and price uncertainty(Springer, 2018) Department of Business Administration; Department of Industrial Engineering; Tan, Barış; Karabağ, Oktay; Faculty Member; Resercher; Department of Business Administration; Department of Industrial Engineering; College of Administrative Sciences and Economics; College of Engineering; 28600; N/ABased on an industrial case study, we present a stochastic model of a supply chain consisting of a set of buyers and suppliers and a group purchasing organization (GPO). The GPO combines orders from buyers in a two-period model. Demand and price in the second period are random. An advance selling opportunity is available to all suppliers and buyers in the first-period market. Buyers decide how much to buy through the GPO in the first period and how much to procure from the market at a lower or higher price in the second period. Suppliers determine the amount of capacity to sell through the GPO in the first period and to hold in reserve in order to meet demand in the second period. The GPO conducts a uniform-price reverse auction to select suppliers and decides on the price that will be offered to buyers to maximize its profit. By determining the optimal decisions of buyers, suppliers, and the GPO, we answer the following questions: Do suppliers and buyers benefit from working with a GPO? How do the uncertainty in demand, the share of GPO orders in the advance sales market, and the uncertainty in price influence the players' decisions and profits? What are the characteristics of an environment that would encourage suppliers and buyers to work with a GPO? We show that a GPO helps buyers and suppliers to mitigate demand and price risks effectively while collecting a premium by serving as an intermediary between them.Publication Open Access Inventory policies for two products under Poisson demand: interaction between demand substitution, limited storage capacity and replenishment time uncertainty(Wiley, 2018) Burnetas, Apostolos; Department of Industrial Engineering; Kanavetas, Odysseas; Faculty Member; Department of Industrial Engineering; College of EngineeringWe consider a two-product inventory system with independent Poisson demands, limited joint storage capacity and partial demand substitution. Replenishment is performed simultaneously for both products and the replenishment time may be fixed or exponentially distributed. For both cases we develop a Continuous Time Markov Chain model for the inventory levels and derive expressions for the expected profit per unit time. We establish analytic expressions for the profit function and show that it satisfies decreasing differences properties in the order quantities, which allows for a more efficient algorithm to determine the optimal ordering policy. Using computational experiments, we assess the effect of substitution and replenishment time uncertainty on the order quantities and the profit as a function of the storage capacity.