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### Browsing by Author "Gürler, Ülkü"

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Item Open Access The effect of economies-of-scale on the performance of lot-sizing heuristics in rolling horizon basis(Taylor & Francis, 2020-02-26) Kian, R.; Berk, Emre; Gürler, Ülkü; Rezazadeh, H.; Yazdani, B.; Berk, Emre; Gürler, ÜlküShow more In this article, we consider the production planning problem in the presence of (dis)economies-of-scale in production costs on a rolling horizon basis with a fixed forecast horizon. We propose variants of three well-known and commonly used heuristics (Wagner–Whitin, Silver–Meal and Least Unit Cost) adapted for this particular setting. In an extensive numerical study with demands exhibiting stationary, increasing and decreasing trends and seasonality, we demonstrate that having longer forecast horizon is less effective in obtaining more cost effective production plans when the production cost function is convex and also when fixed setup cost is lower, which both are proxy to lack of economies-of-scale.Show more Item Open Access An exact analysis on age-based control policies for perishable inventories(Taylor and Francis, 2020-09-01) Poormoaied, S.; Gürler, Ülkü; Berk, E.; Gürler, ÜlküShow more We investigate the impact of effective lifetime of items in an age-based control policy for perishable inventories, a so-called (Q, r, T) policy, with positive lead time and fixed lifetime. The exact analysis of this control policy in the presence of a service level constraint is available in the literature under the restriction that the aging process of a batch begins when it is unpacked for consumption, and that at most one order can be outstanding at any time. In this work, we generalize those results to allow for more than one outstanding order and assume that the aging process of a batch starts since the time that it is ordered. Under this aging process, we derive the effective lifetime distribution of batches at the beginning of embedded cycles in an embedded Markov process. We provide the operating characteristic expressions and construct the cost rate function by the renewal reward theorem approach. We develop an exact algorithm by investigating the cost rate and service level constraint structures. The proposed policy considerably dominates its special two-parameter policies, which are time-dependent (Q, T) and stock-dependent (Q, r) policies. Numerical studies demonstrate that the aging process of items significantly influences the inventory policy performance. Moreover, allowing more than one outstanding order in the system reaps considerable cost savings, especially when the lifetime of items is short and the service level is high.Show more Item Open Access Hazard change point estimation(John Wiley & Sons, 2006) Gürler, Ülkü; Kotz, S.; Read, C. B.; Balakrishnan, N.; Vidakovic, B.; Johnson, N. L.Show more Item Open Access The impact of abusing return policies: a newsvendor model with opportunistic consumers(Elsevier, 2018) Ülkü, M. A.; Gürler, Ülkü; Gürler, ÜlküShow more Consumers may return a product for a variety of reasons, such as the product having the wrong color or size, having poor functionality, being damaged during shipment, or simply prompting regret for an impulsive purchase. Retailers generally provide lenient return policies not only because they may signal high quality but also because they act as risk relievers for consumers’ purchasing decision processes. However, increasing product returns have become particularly challenging for the efficient management of inventory. As such, at the crux of a holistic inventory model lies the understanding of consumer return behavior. In this study, we introduce a variant of the classical single-period inventory (newsvendor) model with returns, in which heterogeneous consumers decide, based on their post-purchase valuation of the product, whether to return the product after using it. From the perspective of the retailer, such deliberate returns may abuse the return policy, which in turn may exacerbate reverse logistics and environmental costs. To that end, we incorporate demand uncertainty and consumer valuation uncertainty by explicitly gauging return probabilities and differentiated salvage values into a newsvendor model. We derive analytical results for the profit-maximizing order quantity for a single-period product that comes with a retailer return policy and exclusively identify the impact of return type as abused or normal. Also offered are closed-form optimal solutions in the cases where market demand is exponentially or uniformly distributed. Structural and numerical results lend managerial insight into how optimal ordering amount, profit, return rates and salvage values change with the price, return window, and hassle cost of returning the product.Show more Item Open Access An integrated replenishment and transportation model: Computational performance assessment(CRC Press, 2014) Kian, R.; Berk, Emre; Gürler, Ülkü; Kara, B. Y.; Sabuncuoğlu, İ.; Bidanda, B.Show more Item Open Access Inventory theory(Taylor & Francis, 2016) Gürler, Ülkü; Berk, Emre; Sengupta, R. N.; Dutta, J.; Gupta, A.Show more Inventory theory is concerned with management of the quantity and timing of the replenishment of assets typically stored to satisfy future demands. In this chapter, we introduce the fundamentals of inventory theory and the basic models that constitute the technical core of supply chain management. The purpose of the chapter is to expose the reader to the basic concepts, models, and theoretical results that would serve as a foundation to build upon and to introduce the existing literature. The exposition follows the common classification of inventory models on the basis of echelon structures (single vs. multiple locations/levels), demand processes (deterministic vs. random demands), problem horizon lengths (finite vs. infinite), and perishability (nonperishables vs. perishables). Specifically, the chapter introduces the basic terminology and inventory-related costs and proceeds to construct the continuous and periodic review models with deterministic demands. The models considered herein establish the fundamental trade-offs between the cost components. In each category, the stylistic models are presented first to develop intuition, followed by relaxations of the basic assumptions that result in more realistic models and richer insights. Stochastic demands are treated extensively as they constitute not only the more general contexts but also a vaster portion of the existing literature. For the continuous-review, stochastic demand setting, three different modeling approaches are illustrated in detail to provide a foundation for different solution methodologies encountered in the literature. Special cases are also treated in detail to the same end. The multiple-item and multiple-echelon inventory systems are discussed concisely but all the basic models and results are presented. For such systems, extensive references are given. The modeling approaches assume a basic familiarity with probability and stochastic processes; in cases of specialized techniques, sufficient intuition is provided for the uninitiated. The emphasis is on the model development and codification of the existing knowledge. Where available, optimal control policies are established and presented. In the absence of such policies, commonly used approximations and/or heuristics are given. To illustrate some of the heuristic methods and models, simple numerical examples are also provided. The chapter concludes with some discussion of issues and practices encountered in the implementation of the discussed models.Show more Item Open Access Minimal conic quadratic reformulations and an optimization model(Elsevier, 2019) Kian, R.; Berk, Emre; Gürler, Ülkü; Berk, Emre; Gürler, ÜlküShow more In this paper, we consider a particular form of inequalities which involves product of multiple variables with rational exponents. These inequalities can equivalently be represented by a number of conic quadratic forms called cone constraints. We propose an integer programming model and a heuristic algorithm to obtain the minimum number of cone constraints which equivalently represent the original inequality. The performance of the proposed algorithm and the computational effect of reformulations are numerically illustrated.Show more Item Open Access Newsboy inventory problem(John Wiley & Sons, 2006) Gürler, Ülkü; Berk, Emre; Kotz, S.; Read, C. B.; Balakrishnan, N.; Vidakovic, B.; Johnson, N. L.Show more A definition and classical formulation of the newsboy inventory model as a profit maximization problem is provided. The structure of the optimal stocking policy is given. Alternative formulations of mean-variance, down-side risk, VaR (value-at-risk), and CVaR (conditional value-at-risk) for general demand distributions and a minimax formulation for the distribution-free newsboy model are also presented. Demand estimation in the presence of fully observable and censored sales is discussed from the frequentist and Bayesian perspectives. Explicit formulas are provided for Bayesian updating of a comprehensive set of demand functions.Show more Item Open Access Newsboy inventory problem [reprint](John Wiley & Sons, 2010) Gürler, Ülkü; Berk, Emre; Balakrishnan, N.Show more A definition and classical formulation of the newsboy inventory model as a profit maximization problem is provided. The structure of the optimal stocking policy is given. Alternative formulations of mean-variance, down-side risk, VaR (value-at-risk), and CVaR (conditional value-at-risk) for general demand distributions and a minimax formulation for the distribution-free newsboy model are also presented. Demand estimation in the presence of fully observable and censored sales is discussed from the frequentist and Bayesian perspectives. Explicit formulas are provided for Bayesian updating of a comprehensive set of demand functions.Show more Item Open Access Nonparametric bivariate estimation with randomly truncated observations(Elsevier, 2003) Gürler, Ülkü; Balakrishnan, N.; Rao, C. R.Show more This chapter focuses on the nonparametric estimation of the bivariate hazard and distribution functions (d.f.) when observations are subject to random truncation. Estimation of bivariate distribution and hazard functions is discussed, and as an application of the results on bivariate d.f., bivariate kernel density estimation is presented. The chapter highlights randomly truncated models, which are conveniently used to model several aspects of AIDS data, such as the incubation time, which is defined as the time from infection to the onset of the disease or the time from the onset of AIDS until death; the time from infection to seroconversion; or in insurance applications, the reporting lags, which is the time between when an accident happens and when it is reported to the insurance company. A few results for the univariate truncation model are also presented.Show more Item Open Access On the (Q,r) policy for perishables with positive lead times and multiple outstanding orders(Springer New York LLC, 2020-01) Berk, Emre; Gürler, Ülkü; Poormoaied, Saeed; Berk, Emre; Gürler, Ülkü; Poormoaied, SaeedShow more We consider an inventory system for perishables with fixed lifetimes, positive replenishment lead times and lost sales in the presence of non-negligible fixed ordering costs. The system is studied under the lotsize reorder level (Q, r) policy. An exact analysis of this system based on the stationary distribution of the remaining lifetime process is provided by Berk and Gürler (Oper Res 56(5):1238-1246, 2008) under the restriction that there is at most one outstanding order at any time (r< Q). In this work, we generalize their results to allow for more than one outstanding orders (r≥ Q). We provide the operating characteristics of the inventory system and construct the exact expected cost rate expression using a renewal theoretic approach. An illustrative numerical study indicates that allowing for multiple outstanding orders (r≥ Q) may result in significant savings in the expected cost rate, compared to the case with r< Q. In particular, when the fixed lifetimes are short and the ordering costs are low, expected costs can be reduced by more than half.Show more Item Open Access On the consistency of a two-sample matching test(Taylor & Francis, 1996) Gürler, Ülkü; Siddiqui, M. M.Show more Let {X k} and {Y k}, 1 ≤ k ≤n be the order statistics of independent random samples from continuous distribution function F and G respectively. To test the null hypothesis H 0 : G = F, known, against the alternative H 1 : G ≠ F, a test S n, based on the number of matches between the two samples was suggested by Siddiqui and Gürler (1992). In this note the asymptotic distribution of S n under the null hypothesis is obtained and its consistency against a fixed alternative is shown.Show more Item Open Access Queueing theory(CRC Press, 2016) Gürler, Ülkü; Berk, Emre; Sengupta, R. N.; Gupta, A.; Dutta, J.Show more Queueing theory is concerned with the quantitative modeling of dynamic systems that generate waiting lines, and the analysis of the behavior of such systems in the short and long time spans. In this chapter, we present a brief overview of the history of queueing theory and the basic concepts of it. The aim of this chapter is to expose the reader to one of the most instrumental and widely applicable topics of stochastic analysis, to provide the basic concepts of it, and to stimulate further interest in it. Some motivating examples of stochastic processes are discussed followed by the main topics in a standard course of stochastic processes. These include the renewal processes, Markov chains, and continuous-time Markov chains. Queueing models are then discussed in more detail, where the focus is mainly restricted to Markovian queues. A more complicated topic of queueing networks is also briefly discussed. Most of the topics discussed are also supported by illustrative examples. The methods are presented mainly under the assumption of a single queue, where a single type of service is provided by possibly several servers under the FIFO (first in first out) service protocol and under the traditional assumption that once a customer enters a queue, she/he stays there until the service has been completed. In an extensive section, we pointed out relaxation of such assumptions and extensions in several directions regarding the queue discipline, service protocol, customer behavior, several service types, estimation of major system parameters, as well as the current research interests in the field. In an appendix, we included a brief review of the background material in probability theory.Show more Item Open Access Reverse Hazard(John Wiley & Sons, 2006) Gürler, Ülkü; Kotz, S.; Read, C. B.; Balakrishnan, N.; Vidakovic, B.; Johnson, N. L.Show more Item Open Access Reverse hazard(Wiley, 2016) Gürler, Ülkü; Balakrishnan, N.Show more As a dual of the hazard rate function, reversed hazard rate characterizes the probability of an immediate past failure, given that a failure has already occurred. This function appears to be important both in survival and reliability studies as it complements a thorough understanding of the failure behavior of the underlying stochastic system. In this article, we provide the basic notions regarding reverse hazard rate function, and compare and contrast its properties with the hazard rate function. We further point to the extension of the concept to bivariate case. The estimation of the distribution function via the reverse hazard rate is also briefly discussed in the context of right truncated data.Show more Item Open Access Two-sample matching test(John Wiley & Sons, 2006) Gürler, Ülkü; Kotz, S.; Read, C. B.; Balakrishnan, N.; Vidakovic, B.; Johnson, N. L.Show more