Browsing by Author "Berk, E."

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Open Access
Age-based vs. stock level control policies for a perishable inventory system
(2001) Tekin, E.; Gürler Ü.; Berk, E.
In this study, we investigate the impact of modified lotsize-reorder control policy for perishables which bases replenishment decisions on both the inventory level and the remaining lifetimes of items in stock. We derive the expressions for the key operating characteristics of a lost sales perishable inventory model, operating under the proposed age-based policy, and examine the sensitivity of the optimal policy parameters with respect to various system parameters. We compare the performance of the suggested policy to that of the classical (Q,r) type policy through a numerical study over a wide range of system parameters. Our findings indicate that the age-based policy is superior to the stock level policy for slow moving perishable inventory systems with high service levels.
Open Access
Analysis of maintenance policies for M machines with deteriorating performance
(Taylor & Francis, 2000) Berk, E.; Moinzadeh, K.
In this paper, we consider the maintenance scheduling of a group of M identical machines, the performance of which deteriorates with usage. Examples of such situations are frequently found in the heavy machine tooling, petro-chemical and semi-conductor industries among others. Assuming a limited maintenance resource and that the maintenance times are i.i.d., we propose a dynamic maintenance policy which utilities the information about the number of operating machines and their ages. We analyze the system for the special cases of constant and exponentially distributed maintenance times. We investigate the impact of maintenance time variability on system performance and evaluate the performance of various maintenance policies within the proposed policy class when the expected profit rate is maximized.
Open Access
Analysis of the (Q, r) inventory model for perishables with positive lead times and lost sales
(Institute for Operations Research and the Management Sciences (INFORMS), 2008) Berk, E.; Gürler, Ü.
We consider a perishable inventory system with Poisson demands, fixed shelf lives, constant lead times, and lost sales in the presence of nonnegligible fixed ordering costs. The inventory control policy employed is the continuous-review (Q, r) policy, where r < Q. The system is modeled using an embedded Markov process approach by introducing the concept of the effective shelf life of a batch in use. Using the stationary distribution of the effective shelf life, we obtain the expressions for the operating characteristics and construct the expected cost rate function for the inventory system. Our numerical study indicates that the determination of the policy parameters exactly as modeled herein results in significant improvements in cost rates with respect to a previously proposed heuristic. We also compare the (Q, r) policy with respect to a time-based benchmark policy and find that the (Q, r) policy might be impractical for rare events, but overall appears to be a good heuristic policy.
Open Access
An archiving model for a hierarchical information storage environment
(Elsevier, 2000) Moinzadeh, K.; Berk, E.
We consider an archiving model for a database consisting of secondary and tertiary storage devices in which the query rate for a record declines as it ages. We propose a `dynamic' archiving policy based on the number of records and the age of the records in the secondary device. We analyze the cases when the number of new records inserted in the system over time are either constant or follow a Poisson process. For both scenarios, we characterize the properties of the policy parameters and provide optimization results when the objective is to minimize the average record retrieval times. Furthermore, we propose a simple heuristic method for obtaining near-optimal policies in large databases when the record query rate declines exponentially with time. The e ectiveness of the heuristic is tested via a numerical experiment. Finally, we examine the behavior of performance measures such as the average record retrieval time and the hit rate as system parameters are varied.
Open Access
Bayesian demand updating in lost sales newsvendor: a two moment approximation
(Elsevier, 2007-10) Berk, E.; Gürler, Ü.; Levine, R. A.
We consider Bayesian updating of demand in a lost sales newsvendor model with censored observations. In a lost sales environment, where the arrival process is not recorded, the exact demand is not observed if it exceeds the beginning stock level, resulting in censored observations. Adopting a Bayesian approach for updating the demand distribution, we develop expressions for the exact posteriors starting with conjugate priors, for negative binomial, gamma, Poisson and normal distributions. Having shown that non-informative priors result in degenerate predictive densities except for negative binomial demand, we propose an approximation within the conjugate family by matching the first two moments of the posterior distribution. The conjugacy property of the priors also ensure analytical tractability and ease of computation in successive updates. In our numerical study, we show that the posteriors and the predictive demand distributions obtained exactly and with the approximation are very close to each other, and that the approximation works very well from both probabilistic and operational perspectives in a sequential updating setting as well.
Open Access
Centralized and decentralized management of groundwater with multiple users
(Elsevier, 2011) Saleh, Y.; Gürler, Ü.; Berk, E.
In this work, we investigate two groundwater inventory management schemes with multiple users in a dynamic game-theoretic structure: (i) under the centralized management scheme, users are allowed to pump water from a common aquifer with the supervision of a social planner, and (ii) under the decentralized management scheme, each user is allowed to pump water from a common aquifer making usage decisions individually in a non-cooperative fashion. This work is motivated by the work of Saak and Peterson [14], which considers a model with two identical users sharing a common aquifer over a two-period planning horizon. In our work, the model and results of Saak and Peterson [14] are generalized in several directions. We first build on and extend their work to the case of n non-identical users distributed over a common aquifer region. Furthermore, we consider two different geometric configurations overlying the aquifer, namely, the strip and the ring configurations. In each configuration, general analytical results of the optimal groundwater usage are obtained and numerical examples are discussed for both centralized and decentralized problems.
Open Access
A continuous review replenishment-disposal policy for an inventory system with autonomous supply and fixed disposal costs
(Elsevier, 2008) Pinçe, Ç.; Gürler, Ü.; Berk, E.
In this study, we analyze an inventory system facing stochastic external demands and an autonomous supply (independent return flow) in the presence of fixed disposal costs and positive lead times under a continuous review replenishment-disposal policy. We derive the analytical expressions of the operating characteristics of the system; and, construct the objective function to minimize the total expected costs of ordering, holding, purchasing and disposal per unit time subject to a fill rate constraint. An extensive numerical analysis is conducted to study the sensitivity of the policy parameters and the benefit of employing a policy which allows for disposal of excess stock in this setting. We model the net demand process as the superposition of normally distributed external demand and inflows, which is expressed as a Brownian motion process. Our findings indicate that the disposal option results in considerable savings even (i) in the presence of non-zero fixed disposal costs, (ii) large actual demand rates with high return ratios (resulting in small net demands) and (iii) for moderate return ratios with high demand variability.
Open Access
Dynamic lot sizing for a warm/cold process: heuristics and insights
(Elsevier, 2013-09) Toy, A. Ö.; Berk, E.
We consider the dynamic lot sizing problem for a warm/cold process where the process can be kept warm at a unit variable cost for the next period if more than a prespecified quantity has been produced. Exploiting the optimal production plan structures, we develop nine rule-based forward solution heuristics. Proposed heuristics are modified counterparts of the heuristics developed previously for the classical dynamic lot sizing problem. In a numerical study, we investigate the performance of the proposed heuristics and identify operating environment characteristics where each particular heuristic is the best or among the best. Moreover, for a warm/cold process setting, our numerical studies indicate that, when used on a rolling horizon basis, a heuristic may also perform better costwise than a solution obtained using a dynamic programming approach.
Open Access
Dynamic lot sizing problem for a warm/cold process
(Taylor & Francis, 2006) Toy, A. Ö.; Berk, E.
We consider a dynamic lot sizing problem with finite capacity for a process that can be kept warm until the next production period at a unit variable cost ωt only if more than a threshold value has been produced and is cold, otherwise. That is, the setup cost in period t is Kt if xt-1 < Qt-1 and kt, otherwise (0 ≤ kt ≤ Kt). We develop a dynamic programming formulation of the problem, establish theoretical results on the structure of the optimal production plan and discuss its computational complexity in the presence of Wagner-Whitin-type cost structures. Based on our stuctural results, we present an optimal polynomial-time solution algorithm for kt = 0, and also show that an optimal linear-time solution algorithm exists for a special case. Our numerical study indicates that utilizing the undertime option (i.e., keeping the process warm via reduced production rates) results in significant cost savings, which has managerial implications for capacity planning and selection.
Open Access
The dynamic lot-sizing problem with convex economic production costs and setups
(Elsevier, 2014-09) Kian, R.; Gurler, U.; Berk, E.
In this work the uncapacitated dynamic lot-sizing problem is considered. Demands are deterministic and production costs consist of convex costs that arise from economic production functions plus set-up costs. We formulate the problem as a mixed integer, non-linear programming problem and obtain structural results which are used to construct a forward dynamic-programming algorithm that obtains the optimal solution in polynomial time. For positive setup costs, the generic approaches are found to be prohibitively time-consuming; therefore we focus on approximate solution methods. The forward DP algorithm is modified via the conjunctive use of three rules for solution generation. Additionally, we propose six heuristics. Two of these are single-stepSilver-Meal and EOQ heuristics for the classical lot-sizing problem. The third is a variant of the Wagner-Whitin algorithm. The remaining three heuristics are two-step hybrids that improve on the initial solutions of the first three by exploiting the structural properties of optimal production subplans. The proposed algorithms are evaluated by an extensive numerical study. The two-step Wagner-Whitin algorithm turns out to be the best heuristic.
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.
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.
Open Access
The impact of discharge decisions on health care quality
(Institute for Operations Research and the Management Sciences (INFORMS), 1998) Berk, E.; Moinzadeh, K.
In this paper, we present a normative study that describes the impact of discharging decisions in the face of resource shortages. We develop a model that represents the dynamics of a health care unit. Then, to capture the essence of discharge decisions, we consider discharge policies that incorporate both the occupancy level of the unit and the status of patients measured by their stage of recovery and the time they have spent in that stage. We believe that our model can be used as an aid to physicians and administrators to better assess discharge and/or capacity decisions. In addition, we investigate the impact of discharge decisions on the measures that represent the quality of care at a facility such as average hospital stays, system accessibility, and average complication risk of discharged patients. Our findings illustrate that inclusion of early discharge option improves system accessibility significantly and does not jeopardize care equity among patients. Furthermore, introduction of early discharge option has more pronounced effects on increasing care unit capacity than addition of open beds with no early discharges.
Open Access
The impact of small lot ordering on traffic congestion in a physical distribution system
(Taylor & Francis, 1997) Moinzadeh, K.; Klastorin, T.; Berk, E.
In recent years, some managers and researchers have advocated reducing lot sizes by decreasing setup costs, arguing that smaller lot sizes improve quality while reducing inventory levels and associated holding costs. However, smaller lot sizes result in an increased number of shipments which, in turn, exacerbates traffic congestion. This results in longer delivery times and, thereby, higher inventory levels. In this paper we study the relation between lot sizes and traffic congestion by constructing a model with numerous retailers who share a common congested delivery road. Using a numerical example, we illustrate the model's managerial implications with respect to several factors, including lot sizes, traffic congestion, and inventory levels. Our findings suggest that in a physical distribution system, if there are a relatively large number of retailers, no single retailer has an incentive to increase batch sizes because one retailer's effect on reducing traffic congestion will be negligible. If all retailers increase their lotsizes, however, traffic congestion will be reduced and all retailers will experience lower costs.
Open Access
On pricing of perishable assets with menu costs
(Elsevier, 2009-10) Berk, E.; Gürler, Ü.; Yıldırım, G.
We consider dynamic pricing of perishable assets in the presence of price-sensitive renewal demand processes. Unlike the existing works in the literature, we explicitly incorporate non-negligible price change costs which reflects the revenue management practice more realistically. These costs are also known as menu costs in the economic literature. The objective is to maximize the discounted expected profit for an initial inventory of Q items by determining the selling prices dynamically. We employ a dynamic programming approach and formulate a model that captures the price– demand relationship. We establish some theoretical results on the properties of the problem at hand. Specifically, we establish the sufficient conditions under which the within-period profit is concave in the selling price and in the remaining shelf life and, furthermore, show the structure of the myopically and asymptotically optimal pricing policy. In a numerical study, we investigate the impact of various system parameters and, in particular, the existence of menu costs, on pricing decisions. We observe that ignoring menu costs may be significantly misleading for the implementation of revenue management. We also propose four implementable policy heuristics and examine their performances. Our findings support some results previously obtained in settings with continuous pricing and negligible price change costs; and, contradict some others.
Open Access
On the modeling of CO2 EUA and CER prices of EU-ETS for the 2008–2012 period
(John Wiley and Sons, 2016) Gürler, Ü.; Yenigün, D.; Çağlar, M.; Berk, E.
Increased consumption of fossil fuels in industrial production has led to a significant elevation in the emission of greenhouse gases and to global warming. The most effective international action against global warming is the Kyoto Protocol, which aims to reduce carbon emissions to desired levels in a certain time span. Carbon trading is one of the mechanisms used to achieve the desired reductions. One of the most important implications of carbon trading for industrial systems is the risk of uncertainty about the prices of carbon allowance permits traded in the carbon markets. In this paper, we consider stochastic and time series modeling of carbon market prices and provide estimates of the model parameters involved, based on the European Union emissions trading scheme carbon allowances data obtained for 2008–2012 period. In particular, we consider fractional Brownian motion and autoregressive moving average–generalized autoregressive conditional heteroskedastic modeling of the European Union emissions trading scheme data and provide comparisons with benchmark models. Our analysis reveals evidence for structural changes in the underlying models in the span of the years 2008–2012. Data-driven methods for identifying possible change-points in the underlying models are employed, and a detailed analysis is provided. Our analysis indicated change-points in the European Union Allowance (EUA) prices in the first half of 2009 and in the second half of 2011, whereas in the Certified Emissions Reduction (CER) prices three change-points have appeared, in the first half of 2009, the middle of 2011, and in the second half of 2012. These change-points seem to parallel the global economic indicators as well.
Open Access
Optimal spacing of "covered" and "exposed" time intervals in a stochastic process with high penalty costs: applications to Parking and Insurance
(Taylor & Francis Inc., 2015) Bakhtiari, B.; Berk, E.; Hassini, E.; Parlar, M.
This paper studies a class of policies for a stochastic process that is constituted of several time intervals of total time T. The intervals can be covered (or insured) at a pay-per-use rate or exposed (uninsured) with the risk of a large penalty. A decision maker has the three options: (i) Pay the user fee for the full period, (ii) not pay at all, and (iii) sporadically pay a user fee leaving an uncovered period at the end of each covered one. The penalty risk is assumed to occur during an uncovered interval according to a Poisson process. We present the expected cost model and find the optimal coverage policy. We present conditions under which it is always optimal to pay in full or not pay at all to minimize the expected total cost. Finally, we relax two assumptions and allow for the consideration of setup costs for every time the decision maker pays the coverage fees as well as a random duration T and derive new conditions for optimal strategies. Possible application of our model is paying parking meter fees and deciding between self-insuring one’s property and buying full (or partial) insurance coverage.
Open Access
Quality control chart design under jidoka
(John Wiley & Sons, Inc., 2009) Berk, E.; Toy, A. Ö.
We consider design of control charts in the presence of machine stoppages that are exogenously imposed (as under jidoka practices). Each stoppage creates an opportunity for inspection/repair at reduced cost. We first model a single machine facing opportunities arriving according to a Poisson process, develop the expressions for its operating characteristics and construct the optimization problem for economic design of a control chart. We, then, consider the multiple machine setting where individual machine stoppages may create inspection/repair opportunities for other machines. We develop exact expressions for the cases when all machines are either opportunity-takers or not. On the basis of an approximation for the all-taker case, we then propose an approximate model for the mixed case. In a numerical study, we examine the opportunity taking behavior of machines in both single and multiple machine settings and the impact of such practices on the design of an X̄ - Q C chart. Our findings indicate that incorporating inspection/repair opportunities into QC chart design may provide considerable cost savings.
Open Access
Single item lot-sizing problem for a warm/cold process with immediate lost sales
(Elsevier, 2008-06-16) Berk, E.; Toy, A. Ö.; Hazır, Ö.
We consider the dynamic lot-sizing problem with finite capacity and possible lost sales for a process that could be kept warm at a unit variable cost for the next period t + 1 only if more than a threshold value Qt has been produced and would be cold, otherwise. Production with a cold process incurs a fixed positive setup cost, Kt and setup time, St, which may be positive. Setup costs and times for a warm process are negligible. We develop a dynamic programming formulation of the problem, establish theoretical results on the structure of the optimal production plan in the presence of zero and positive setup times with Wagner–Whitin-type cost structures. We also show that the solution to the dynamic lot-sizing problem with lost sales are generated from the full commitment production series improved via lost sales decisions in the presence of a warm/cold process. 2006 Elsevier B.V. All rights reserved.
Open Access
The stochastic joint replenishment problem: a new policy, analysis, and insights
(John Wiley & Sons, 2006) Özkaya, B. Y.; Gürler, Ü.; Berk, E.
In this study, we propose a new parsimonious policy for the stochastic joint replenishment problem in a single-location, N-item setting. The replenishment decisions are based on both group reorder point-group order quantity and the time since the last decision epoch. We derive the expressions for the key operating characteristics of the inventory system for both unit and compound Poisson demands. In a comprehensive numerical study, we compare the performance of the proposed policy with that of existing ones over a standard test bed. Our numerical results indicate that the proposed policy dominates the existing ones in 100 of 139 instances with comparably significant savings for unit demands. With batch demands, the savings increase as the stochasticity of demand size gets larger. We also observe that it performs well in environments with low demand diversity across items. The inventory system herein also models a two-echelon setting with a single item, multiple retailers, and cross docking at the upper echelon.
Open Access
Supplier diversification under binomial yield
(Elsevier, 2008) Fadıloǧlu, M. M.; Berk, E.; Gürbüz, M. Ç.
We consider supplier diversification in an EOQ type inventory setting with multiple suppliers and binomial yields. We characterize the optimal policy for the model and show that, in this case, it does not pay to diversify, in contrast to previous results in the random yield literature.