Department of Industrial Engineering

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Open Access
4-generated pseudo symmetric monomial curves with not Cohen–Macaulay tangent cones
(TUBITAK, 2020) Şahin, Nil
In this article, standard bases of some toric ideals associated to 4-generated pseudo symmetric semigroups with not Cohen-Macaulay tangent cones at the origin are computed. As the tangent cones are not Cohen-Macaulay, nondecreasingness of the Hilbert function of the local ring was not guaranteed. Therefore, using these standard bases, Hilbert functions are explicitly computed as a step towards the characterization of Hilbert function. In addition, when the smallest integer satisfying k(α2 + 1) < (k − 1)α1 + (k + 1)α21 + α3 is 1, it is proved that the Hilbert function of the local ring is nondecreasing.
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A mean-CVaR approach to the risk-averse single allocation hub location problem with flow-dependent economies of scale
(Elsevier Ltd, 2022-11-29) Ghaffarinasab, Nader; Çavuş, Ö.; Kara, B. Y.
The hub location problem (HLP) is a fundamental facility planning problem with various applications in transportation, logistics, and telecommunication systems. Due to strategic nature of the HLP, considering uncertainty and the associated risks is of high practical importance in designing hub networks. This paper addresses a risk-averse single allocation HLP, where the traffic volume between the origin–destination (OD) pairs is considered to be uncertain. The uncertainty in demands is captured by a finite set of scenarios, and a flow-dependent economies of scale scheme is used for transportation costs, modeled as a piece-wise concave function of flow on all network arcs. The problem is cast as a risk-averse two-stage stochastic problem using mean-CVaR as the risk measure, and a novel solution approach combining Benders decomposition and scenario grouping is proposed. An extensive set of computational experiments is conducted to study the effect of different input parameters on the optimal solution, and to evaluate the performance of the proposed solution algorithm. Managerial insights are derived and presented based on the obtained results.
Open Access
A new formulation and an effective matheuristic for the airport gate assignment problem
(Elsevier, 2023-03) Karsu, Özlem; Solyalı, Oğuz
This study considers an airport gate assignment problem where a set of aircraft arriving to an airport are assigned to the fixed gates of the airport terminal or to the apron. The aim is to lexicographically minimize the number of aircraft assigned to the apron, and then the total walking distance by passengers. A new mixed integer linear programming formulation and a matheuristic is proposed for the problem. The proposed formulation is based on the idea of flow of passengers and has smaller size compared to the existing formulations in the literature. The proposed matheuristic, which relies on solving a restricted version of the proposed formulation of the problem, is not only easy to implement but is also very effective. A computational study performed on benchmark instances reveals that the proposed formulation and the matheuristic outperform the existing exact and heuristic algorithms in the literature.
Open Access
A planar facility location–allocation problem with fixed and/or variable cost structures for rural electrification
(2023-06) Akbaş, Beste; Kocaman, Ayşe Selin
One major impediment to developing countries’ economic growth is the lack of access to affordable, sustainable, and reliable modern energy systems. Even today, hundreds of millions of people live in rural areas and do not have access to essential electricity services. In this study, we present a planar facility location–allocation problem for planning decentralized energy systems in rural development. We consider nano-grid and micro-grid systems to electrify rural households. While micro-grids serve multiple households with a common generation facility, nano-grids are small-scale systems serving individual consumers. The households served by micro-grids are connected to the generation facilities with low-voltage cables, for which we employ a distance limit constraint due to technical concerns, including power loss and allowable voltage levels. In this problem, we minimize the total investment cost that consists of the facility opening and the low-voltage cable costs. In order to capture the diversity of cost structures in renewable energy investments, we consider three versions of the objective function where we incorporate different combinations of fixed and variable cost components for facilities. For this problem, we provide mixed-integer quadratically constrained problem formulations and propose model-based and clustering-based heuristic approaches. Model-based approaches are multi-stage, in which we solve the discrete counterparts of the problem and employ alternative selection methods for the candidate facility locations. Clustering-based approaches utilize faster clustering techniques to identify the type and location of the facilities. We conduct computational experiments on real-life instances from villages in Sub-Saharan Africa and perform a comparative analysis of the suggested heuristic approaches.
Open Access
A stochastic programming approach to surgery scheduling under parallel processing principle
(Elsevier Ltd, 2023-11-06) Çelik, Batuhan; Gül, Serhat; Çelik, Melih
Parallel processing is a principle which enables simultaneous implementation of anesthesia induction and operating room (OR) turnover with the aim of improving OR utilization. In this article, we study the problem of scheduling surgeries for multiple ORs and induction rooms (IR) that function based on the parallel processing principle under uncertainty. We propose a two-stage stochastic mixed-integer programming model considering the uncertainty in induction, surgery and turnover durations. We sequence patients and set appointment times for surgeries in the first stage and assign patients to IRs at the second stage of the model. We show that an optimal myopic policy can be used for IR assignment decisions due to the special structure of the model. We minimize the expected total cost of patient waiting time, OR idle time and IR idle time in the objective function. We enhance the model formulation using bounds on variables and symmetry-breaking constraints. We implement a novel progressive hedging algorithm by proposing a penalty update method and a variable fixing mechanism. Based on real data of a large academic hospital, we compare our solution approach with several scheduling heuristics from the literature. We assess the additional benefits and costs associated with the implementation of parallel processing using near-optimal schedules. We examine how the benefits are inflated by increasing the number of IRs. Finally, we estimate the value of stochastic solution to underline the importance of considering uncertainty in durations. © 2022 Elsevier Ltd
Open Access
Accounting for parameter uncertainty in large-scale stochastic simulations with correlated inputs
(Institute for Operations Research and the Management Sciences (I N F O R M S), 2011) Biller, B.; Corlu, C. G.
This paper considers large-scale stochastic simulations with correlated inputs having normal-to-anything (NORTA) distributions with arbitrary continuous marginal distributions. Examples of correlated inputs include processing times of workpieces across several workcenters in manufacturing facilities and product demands and exchange rates in global supply chains. Our goal is to obtain mean performance measures and confidence intervals for simulations with such correlated inputs by accounting for the uncertainty around the NORTA distribution parameters estimated from finite historical input data. This type of uncertainty is known as the parameter uncertainty in the discrete-event stochastic simulation literature. We demonstrate how to capture parameter uncertainty with a Bayesian model that uses Sklar's marginal-copula representation and Cooke's copula-vine specification for sampling the parameters of the NORTA distribution. The development of such a Bayesian model well suited for handling many correlated inputs is the primary contribution of this paper. We incorporate the Bayesian model into the simulation replication algorithm for the joint representation of stochastic uncertainty and parameter uncertainty in the mean performance estimate and the confidence interval. We show that our model improves both the consistency of the mean line-item fill-rate estimates and the coverage of the confidence intervals in multiproduct inventory simulations with correlated demands.
Open Access
Accurate calculation of hazardous materials transport risks
(Elsevier, 2003-07) Kara, B.; Erkut, E.; Verter, V.
We propose two path-selection algorithms for the transport of hazardous materials. The algorithms can deal with link impedances that are path-dependent. This approach is superior to the use of a standard shortest path algorithm, common in the literature and practice, which results in inaccuracies.
Open Access
An adaptive bayesian replacement policy with minimal repair
(Institute for Operations Research and the Management Sciences (INFORMS), 2002) Gürler, Ü.; Dayanık, S.
In this study, an adaptive Bayesian decision model is developed to determine the optimal replacement age for the systems maintained according to a general age-replacement policy. It is assumed that when a failure occurs, it is either critical with probability p or noncritical with probability1−p, independently. A maintenance policy is considered where the noncritical failures are corrected with minimal repair and the system is replaced either at the first critical failure or at age , whichever occurs first. The aim is to find the optimal value of that minimizes the expected cost per unit time. Two adaptive Bayesian procedures that utilize different levels of information are proposed for sequentiallyupdating the optimal replacement times. Posterior density/mass functions of the related variables are derived when the time to failure for the system can be expressed as a Weibull random variable. Some simulation results are also presented for illustration purposes.
Open Access
Adjusted hazard rate estimator based on a known censoring probability
(Taylor & Francis, 2011) Gürler, Ü.; Kvam, P.
In most reliability studies involving censoring, one assumes that censoring probabilities are unknown. We derive a nonparametric estimator for the survival function when information regarding censoring frequency is available. The estimator is constructed by adjusting the Nelson-Aalen estimator to incorporate censoring information. Our results indicate significant improvements can be achieved if available information regarding censoring is used. We compare this model to the Koziol-Green model, which is also based on a form of proportional hazards for the lifetime and censoring distributions. Two examples of survival data help to illustrate the differences in the estimation techniques.
Open Access
Advances in business analytics at HP laboratories
(Springer, Boston, 2010) Beyer, D.; Clearwater, S.; Chen, K. Y.; Feng, Q.; Huberman, B. A.; Jain, S.; Jamal, Z.; Şen, Alper; Tang, H. K.; Tarjan, B.; Ward, J.; Zhang, A.; Zhang, B.; Sodhi, M. S.; Tang, C. S.
HP Labs’ Business Optimization Lab is a group of researchers focused on developing innovations in business analytics that deliver value to HP. This chapter describes several activities of the Business Optimization Lab, including work in product portfolio management, prediction markets, modeling of rare events in marketing, and supply chain network design.
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
Aircraft and passenger recovery during an aircraft’s unexpected unavailability
(Elsevier, 2020-11-14) Aktürk, M. Selim; Yeti̇moğlu, Y. N.
Airlines design their initial schedules under the assumption that all resources will be available on time and flights will operate as planned. However, some disruptions occur due to mechanical failures and unexpected delays of maintenance, making the aircraft unavailable for a certain period of time. These deviations from the initial plan result in high operational costs in addition to the serious inconveniences experienced by passengers. In order to handle aircraft and passenger recovery problems simultaneously, we work on integrated networks at which aircraft routings and passenger itineraries are superimposed. Consequently, we could calculate the actual profit and cancellation cost by evaluating each passenger itinerary while considering the seat capacity limitations. In our computational results, we use a daily schedule of a major U.S. airline and clearly demonstrate that there is an optimal trade-off between operating and passenger-related costs.
Open Access
Aircraft recovery model with flight time controllability
(2011) Akturk, Mehmet Selim; Atamturk, A.; Gurel, S.
[No abstract available]
Open Access
Aircraft rescheduling with cruise speed control
(Institute for Operations Research and the Management Sciences (I N F O R M S), 2014-05-23) Aktürk, M. S.; Atamtürk, A.; Gürel, S.
Airline operations are subject to frequent disruptions typically due to unexpected aircraft maintenance requirements and undesirable weather conditions. Recovery from a disruption often involves propagating delays in downstream flights and increasing cruise stage speed when possible in an effort to contain the delays. However, there is a critical trade-off between fuel consumption (and its adverse impact on air quality and greenhouse gas emissions) and cruise speed. Here we consider delays caused by such disruptions and propose a flight rescheduling model that includes adjusting cruise stage speed on a set of affected and unaffected flights as well as swapping aircraft optimally. To the best of our knowledge, this is the first study in which the cruise speed is explicitly included as a decision variable into an airline recovery optimization model along with the environmental constraints and costs. The proposed model allows one to investigate the trade-off between flight delays and the cost of recovery. We show that the optimization approach leads to significant cost savings compared to the popular recovery method delay propagation. Flight time controllability, nonlinear delay, fuel burn and CO2 emission cost functions, and binary aircraft swapping decisions complicate the aircraft recovery problem significantly. In order to mitigate the computational difficulty we utilize the recent advances in conic mixed integer programming and propose a strengthened formulation so that the nonlinear mixed integer recovery optimization model can be solved efficiently. Our computational tests on realistic cases indicate that the proposed model may be used by operations controllers to manage disruptions in real time in an optimal manner instead of relying on ad-hoc heuristic approaches.
Open Access
An algorithm and a core set result for the weighted euclidean one-center problem
(Institute for Operations Research and the Management Sciences (I N F O R M S), 2009) Kumar, P.; Yıldırım, A. E.
Given a set A of m points in n-dimensional space with corresponding positive weights, the weighted Euclidean one-center problem, which is a generalization of the minimum enclosing ball problem, involves the computation of a point c A n that minimizes the maximum weighted Euclidean distance from c A to each point in A In this paper, given ε > 0, we propose and analyze an algorithm that computes a (1 + ε)-approximate solution to the weighted Euclidean one-center problem. Our algorithm explicitly constructs a small subset X ⊆ A, called an ε-core set of A, for which the optimal solution of the corresponding weighted Euclidean one-center problem is a close approximation to that of A. In addition, we establish that \X\ depends only on ε and on the ratio of the smallest and largest weights, but is independent of the number of points m and the dimension n. This result subsumes and generalizes the previously known core set results for the minimum enclosing ball problem. Our algorithm computes a (1 + ε)-approximate solution to the weighted Euclidean one-center problem for A in O(mn\X\) arithmetic operations. Our computational results indicate that the size of the ε-core set computed by the algorithm is, in general, significantly smaller than the theoretical worst-case estimate, which contributes to the efficiency of the algorithm, especially for large-scale instances. We shed some light on the possible reasons for this discrepancy between the theoretical estimate and the practical performance.
Open Access
An algorithmic proof of the polyhedral decomposition theorem
(John Wiley & Sons, 1988) Akgül, M.
It is well‐known that any point in a convex polyhedron P can be written as the sum of a convex combination of extreme points of P and a non‐negative linear combination of extreme rays of P. Grötschel, Lovász, and Schrijver gave a polynomial algorithm based on the ellipsoidal method to find such a representation for any x in P when P is bounded. Here we show that their algorithm can be modified and implemented in polynomial time using the projection method or a simplex‐type algorithm : in n(2n + 1) simplex pivots, where n is the dimension of x. Extension to the unbounded case is immediate.
Open Access
Algorithms to solve unbounded convex vector optimization problems
(Society for Industrial and Applied Mathematics Publications, 2023-10-12) Wagner, A.; Ulus, Firdevs; Rudloff, B.; Kováčová, G.; Hey, N.
This paper is concerned with solution algorithms for general convex vector optimization problems (CVOPs). So far, solution concepts and approximation algorithms for solving CVOPs exist only for bounded problems [\c C. Ararat, F. Ulus, and M. Umer, J. Optim. Theory Appl., 194 (2022), pp. 681-712], [D. Dörfler, A. Löhne, C. Schneider, and B. Weißing, Optim. Methods Softw., 37 (2022), pp. 1006-1026], [A. Löhne, B. Rudloff, and F. Ulus, J. Global Optim., 60 (2014), pp. 713-736]. They provide a polyhedral inner and outer approximation of the upper image that have a Hausdorff distance of at most ε. However, it is well known (see [F. Ulus, J. Global Optim., 72 (2018), pp. 731-742]), that for some unbounded problems such polyhedral approximations do not exist. In this paper, we will propose a generalized solution concept, called an (ε,δ)-solution, that allows one to also consider unbounded CVOPs. It is based on additionally bounding the recession cones of the inner and outer polyhedral approximations of the upper image in a meaningful way. An algorithm is proposed that computes such δ-outer and δ-inner approximations of the recession cone of the upper image. In combination with the results of [A. Löhne, B. Rudloff, and F. Ulus, J. Global Optim., 60 (2014), pp. 713-736] this provides a primal and a dual algorithm that allow one to compute (ε,δ)-solutions of (potentially unbounded) CVOPs. Numerical examples are provided.
Open Access
Allocation Strategies in Hub Networks
(Elsevier, 2011-06-11) Yaman, H.
In this paper, we study allocation strategies and their effects on total routing costs in hub networks. Given a set of nodes with pairwise traffic demands, the p-hub median problem is the problem of choosing p nodes as hub locations and routing traffic through these hubs at minimum cost. This problem has two versions; in single allocation problems, each node can send and receive traffic through a single hub, whereas in multiple allocation problems, there is no such restriction and a node may send and receive its traffic through all p hubs. This results in high fixed costs and complicated networks. In this study, we introduce the r-allocation p-hub median problem, where each node can be connected to at most r hubs. This new problem generalizes the two versions of the p-hub median problem. We derive mixed-integer programming formulations for this problem and perform a computational study using well-known datasets. For these datasets, we conclude that single allocation solutions are considerably more expensive than multiple allocation solutions, but significant savings can be achieved by allowing nodes to be allocated to two or three hubs rather than one. We also present models for variations of this problem with service quality considerations, flow thresholds, and non-stop service.
Open Access
Ambulance location for maximum survival
(John Wiley & Sons, 2008) Erkut, E.; Ingolfsson, A.; Erdoğan, G.
This article proposes new location models for emergency medical service stations. The models are generated by incorporating a survival function into existing covering models. A survival function is a monotonically decreasing function of the response time of an emergency medical service (EMS) vehicle to a patient that returns the probability of survival for the patient. The survival function allows for the calculation of tangible outcome measures-the expected number of survivors in case of cardiac arrests. The survival-maximizing location models are better suited for EMS location than the covering models which do not adequately differentiate between consequences of different response times. We demonstrate empirically the superiority of the survival-maximizing models using data from the Edmonton EMS system.
Open Access
Analysis and applications of replenishment problems under stepwise transportation costs and generalized wholesale prices
(2012) Konur, D.; Toptal, A.
In this study, we analyze the replenishment decision of a buyer with the objective of maximizing total expected profits. The buyer faces stepwise freight costs in inbound transportation and a hybrid wholesale price schedule given by a combination of all-units discounts with economies and diseconomies of scale. This general cost structure enables the model and the proposed solution to be also used for the supplier selection of a buyer under the single sourcing assumption. We show that the buyers replenishment problem reduces to finding and comparing the solutions of the following two subproblems: (i) a replenishment problem involving wholesale prices given by an all-units discount schedule with economies of scale and a lower bound on the replenishment quantity, and (ii) a replenishment problem involving wholesale prices given by an all-units discount schedule with diseconomies of scale and an upper bound on the replenishment quantity. We propose solution methods for these two subproblems, each of which stands alone as practical problems, and utilize these methods to optimally solve the buyers replenishment problem.