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Publication Open Access Analysis of copositive optimization based linear programming bounds on standard quadratic optimization(Springer, 2015) Department of Industrial Engineering; Sağol, Gizem; Yıldırım, Emre Alper; Faculty Member; Department of Industrial Engineering; Graduate School of Sciences and Engineering; College of EngineeringThe problem of minimizing a quadratic form over the unit simplex, referred to as a standard quadratic optimization problem, admits an exact reformulation as a linear optimization problem over the convex cone of completely positive matrices. This computationally intractable cone can be approximated in various ways from the inside and from the outside by two sequences of nested tractable convex cones of increasing accuracy. In this paper, we focus on the inner polyhedral approximations due to YA +/- ldA +/- rA +/- m (Optim Methods Softw 27(1):155-173, 2012) and the outer polyhedral approximations due to de Klerk and Pasechnik (SIAM J Optim 12(4):875-892, 2002). We investigate the sequences of upper and lower bounds on the optimal value of a standard quadratic optimization problem arising from these two hierarchies of inner and outer polyhedral approximations. We give complete algebraic descriptions of the sets of instances on which upper and lower bounds are exact at any given finite level of the hierarchy. We identify the structural properties of the sets of instances on which upper and lower bounds converge to the optimal value only in the limit. We present several geometric and topological properties of these sets. Our results shed light on the strengths and limitations of these inner and outer polyhedral approximations in the context of standard quadratic optimization.
Publication Metadata only Bayesian analysis of Markov modulated Bernoulli processes(Springer, 2003) Soyer, R.; Department of Industrial Engineering; Özekici, Süleyman; Faculty Member; Department of Industrial Engineering; College of Engineering; 32631We consider Markov Modulated Bernoulli Processes (MMBP) where the success probability of a Bernoulli process evolves over time according to a Markov chain. The MMBP is applied in reliability modeling where systems and components function in a randomly changing environment. Some of these applications include, but are not limited to, reliability assessment in power systems that are subject to fluctuating weather conditions over time and reliability growth processes that are subject to design changes over time. We develop a general setup for analysis of MMBPs with a focus on reliability modeling and present Bayesian analysis of failure data and illustrate how reliability predictions can be obtained.Publication Metadata only Modeling and simulation of metabolic networks for estimation of biomass accumulation parameters(Elsevier, 2009) Biegler, L.; Karasozen, Bülent; N/A; Department of Industrial Engineering; Kaplan, Uğur; Türkay, Metin; PhD Student; Faculty Member; Department of Industrial Engineering; Graduate School of Sciences and Engineering; College of Engineering; N/A; 24956Metabolic networks are defined as the collection of biochemical reactions within a cell that define the functions of that cell. Due to the growing need to understand the functions of biological organisms for industrial and medical purposes, modeling and simulation of metabolic networks has attracted a lot of attention recently. Traditionally, metabolic networks are modeled such as flux-balance analysis that considers the steady state nature of the cell. However, it is important to consider the dynamic behavior of a cell since the environmental conditions change continuously. Sometimes due to the critical changes in the environment some of the reactions exhibit completely different behavior leading to discrete changes in the metabolic network. Therefore, a cell exhibits discrete-continuous behavior in continuous time. Since hybrid systems exhibit the same characteristics modeling a cell as a hybrid system gives an accurate representation. The aim of this paper is to develop a simulation framework to model the evolving structure of the cell metabolism under changes in the environment. The metabolic responses that cell gives, against multiple changes in the environment are not fully understood. Therefore, in this study, a cell is modeled as a hybrid system that is composed of a system of differential and algebraic equations. The changes in the concentration of metabolites in the environment are represented by Ordinary Differential Equations and the intracellular cell metabolism is represented by a set of algebraic equations. TO understand the feedback relationship between intracellular and extracellular changes, the system is solved considering the effects of extracellular stresses on the metabolic responses. (c) 2008 Elsevier B.V. .Publication Metadata only Newsvendor models with dependent random supply and demand(Springer Heidelberg, 2014) N/A; N/A; Department of Industrial Engineering; Department of Industrial Engineering; Okyay, Hayrettin Kaan; Karaesmen, Fikri; Özekici, Süleyman; Master Student; Faculty Member; Faculty Member; Department of Industrial Engineering; Graduate School of Sciences and Engineering; College of Engineering; College of Engineering; N/A; 3579; 32631The newsvendor model is perhaps the most widely analyzed model in inventory management. In this single-period model, the only source of randomness is the demand during the period and one tries to determine the optimal order quantity in view of various cost factors. We consider an extention where supply is also random so that the quantity ordered is not necessarily received in full at the beginning of the period. Such models have been well-received in the literature with the assumption of independence between demand and supply. In this setting, we suppose that the random demand and supply are not necessarily independent. We focus on the resulting optimization problem and provide interesting characterizations on the optimal order quantity.Publication Metadata only Optimal policies under different pricing strategies in a production system with Markov-modulated demand(Springer, 2006) Gayon, JP; Talay-Değirmenci, I.; Department of Industrial Engineering; Department of Industrial Engineering; Örmeci, Lerzan; Karaesmen, Fikri; Faculty Member; Faculty Member; Department of Industrial Engineering; College of Engineering; College of Engineering; 32863; 3579We study the effects of different pricing strategies available to a continuous review inventory system with capacitated supply, which operates in a fluctuating environment. The system has a single server with exponential processing time. The inventory holding cost is nondecreasing and convex in the inventory level, the production cost is linear with no set-up cost. The potential customer demand is generated by a Markov-Modulated (environment-dependent) Poisson process, while the actual demand rate depends on the offerred price. For such systems, there are three possible pricing strategies: Static pricing, where only one price is used at all times, environment-dependent pricing, where the price changes with the environment, and dynamic pricing, where price depends on both the current environment and the stock level. The objective is to find an optimal replenishment policy under each of these strategies. This paper presents some structural properties of optimal replenishment policies, and a numerical study which compares the performances of these three pricing strategies.Publication Metadata only Optimal threshold levels in stochastic fluid models via simulation-based optimization(Springer, 2007) Gurkan, Gul; Ozdemir, Ozge; Department of Industrial Engineering; Karaesmen, Fikri; Faculty Member; Department of Industrial Engineering; College of Engineering; 3579A number of important problems in production and inventory control involve optimization of multiple threshold levels or hedging points. We address the problem of finding such levels in a stochastic system whose dynamics can be modelled using generalized semi-Markov processes (GSMP). The GSMP framework enables us to compute several performance measures and their sensitivities from a single simulation run for a general system with several states and fairly general state transitions. We then use a simulation-based optimization method, sample-path optimization, for finding optimal hedging points. We report numerical results for systems with more than twenty hedging points and service-level type probabilistic constraints. In these numerical studies, our method performed quite well on problems which are considered very difficult by current standards. Some applications falling into this framework include designing manufacturing flow controllers, using capacity options and subcontracting strategies, and coordinating production and marketing activities under demand uncertainty.Publication Metadata only Portfolio optimization in stochastic markets(Springer Heidelberg, 2006) Cakmak, U; Department of Industrial Engineering; Özekici, Süleyman; Faculty Member; Department of Industrial Engineering; College of Engineering; 32631We consider a multiperiod mean-variance model where the model parameters change according to a stochastic market. The mean vector and covariance matrix of the random returns of risky assets all depend on the state of the market during any period where the market process is assumed to follow a Markov chain. Dynamic programming is used to solve an auxiliary problem which, in turn, gives the efficient frontier of the mean-variance formulation. An explicit expression is obtained for the efficient frontier and an illustrative example is given to demonstrate the application of the procedure.Publication Metadata only Scheduling chains with identical jobs and constant delays on a single machine(Springer, 2006) Brucker, P; Knust, S; Department of Industrial Engineering; Oğuz, Ceyda; Faculty Member; Department of Industrial Engineering; College of Engineering; 6033In this paper we study the single-machine problem 1|chains(l), p j = p|∑ C j in which jobs with constant processing times and generalized precedence constraints in form of chains with constant delays are given. One has to schedule the jobs on a single machine such that all delays between consecutive jobs in a chain are satisfied and the sum of all completion times of the jobs is minimized. We show that this problem is polynomially solvable.Publication Metadata only Semi-Markov modulated Poisson process: probabilistic and statistical analysis(Springer, 2006) Soyer, R.; Department of Industrial Engineering; Özekici, Süleyman; Faculty Member; Department of Industrial Engineering; College of Engineering; 32631We consider a Poisson process that is modulated in such a way that the arrival rate at any time depends on the state of a semi-Markov process. This presents an interesting generalization of Poisson processes with important implications in real life applications. Our analysis concentrates on the transient as well as the long term behaviour of the arrival count and the arrival time processes. We discuss probabilistic as well as statistical issues related to various quantities of interest.Publication Metadata only Structural results on a batch acceptance problem for capacitated queues(Springer Heidelberg, 2007) N/A; Department of Industrial Engineering; Department of Industrial Engineering; Çil, Eren Başar; Örmeci, Lerzan; Karaesmen, Fikri; Master Student; Faculty Member; Faculty Member; Department of Industrial Engineering; Graduate School of Sciences and Engineering; College of Engineering; College of Engineering; N/A; 32863; 3579The purpose of this paper is to investigate the structural properties of the optimal batch acceptance policy in a Markovian queueing system where different classes of customers arrive in batches and the buffer capacity is finite. We prove that the optimal policy can possess certain monotonicity properties under the assumptions of a single-server and constant batch sizes. Even though our proof cannot be extended to cases where either one of the assumptions is relaxed, we numerically observe that the optimal policy can still possess the same properties when only the single-server assumption is relaxed. Finally, we present counterexamples that show the non-monotone structure of the optimal policy when the batch sizes are not constant.