Dept. of Industrial Engineering - Master's degree
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Item Open Access A replenishment policy for perishable items with cold chain transportation and lead time reduction options(Bilkent University, 2023-07) Bayır, AtahanPerishability relates to products that have limited shelf life and are prone to spoilage, decay, or becoming unsafe for use over time. Although perishability is a common aspect in several product categories such as fresh produce, pharmaceuticals, blood product and fashion industry, many inventory models assume that products have an infinite shelf life. In this work, we introduce a novel approach that integrates inventory replenishment and cold chain technology decisions to replenishment policy of inventories with the aim of better preserving the effective shelf life of products. We focus on a single product, single location, continuous review inventory model with positive lead time, where products have fixed lifetimes. Demand arrivals are assumed to follow a Poisson process. If there are two batches in stock, items in the old batch is disposed with a salvage value. We assume that a cold chain technology is available to maintain the items in a preservative environment, protecting them against temperature and moisture during lead time, thereby providing an extended shelf life when the items arrive in the inventory. In particular, we adopt a modified lot size/reorder point (Q,r) policy that allows for a cold chain technology. The model also allows for a scenario where lead time is reduced through expedited transportation, which directly increases shelf life of arriving batch while decreases the time spent during transportation. The objective is to minimize the expected cost per unit time over an infinite horizon the decision variables of order quantity, reorder level, and cold chain technology level. A numerical study is provided to demonstrate the model performance, its sensitivity to system parameters and to compare all the policies we present.Item Open Access Adopting the parallel strategy in a R&D project task(Bilkent University, 1997) Jelassi, Mohamed MehdiFunding more than one research team in a R&D project task can increase the chance that at least one of them will achieve a timely breakthrough. However resource limitations imply that the budget allocated to each team declines with the amount of parallelism, reducing the chance that the team will be successful. This tradeoff between level of support and degree of parallelism was explicitly modeled for distinct goals in an environment of uncertain achievements, in order to decide on the number of parallel research teams to fund. In this study which is mainly based on the work done by Gerchak et al, we present the suggested model together with its underlying assumptions and give a detailed mathematical ananlysis. Furthermore, we analytically and numerically analyse the problem of allocating a fixed budget over two research activities and deciding on the number of parallel teams within each activity. Moreover we come out with an analytical result for the general problem of having M activities.Item Open Access Air traffic flow management problem with stochastic capacities(Bilkent University, 2021-09) Sertkaya, EfeAir traffic systems have substantial effects on transportation, logistics, and economics in a global scope. Due to both practical significance and intellectual challenges, air traffic flow management problems have been extensively studied for many decades. The aim of air traffic flow management problems is to plan the flow throughout the air traffic network while satisfying capacity constraints. In this study, we consider the case of stochastic capacities in the air traffic network. We propose both stochastic multistage integer and stochastic two-stage integer modeling approaches for the problem. In multistage and two-stage models, we aim to resolve the demand-capacity imbalances at each element of the air traffic network. To achieve this, we decide on the take-off times and routes of each flight for a given time horizon. We propose integer L-shaped and partial Benders’ decomposition approaches to solve the two-stage model. Additionally, we analyze the effect of conditional value-at-risk constraints on delay time distributions. To incorporate conditional value-at-risk to solution methodologies, we propose a novel approximation technique. We present a detailed analysis of delay distributions, demonstrate the effect of the approximation technique on solution quality and computational performance. For computational experiments, we explicitly describe data generation procedures to obtain realistic instances. We demonstrate that the Partial Benders’ modification outperforms the commercial solver (CPLEX) in almost every instance.Item Open Access Airline rescheduling with aircraft unavailability period(Bilkent University, 2019-06) Yetimoğlu, Yücel NazAirlines design their initial schedules under the assumption that all resources will be available on time and ights 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 the literature, it is a common practice to develop sequential approaches at which aircraft and passenger recovery problems are consecutively handled. In this study, we address them simultaneously and propose an integrated math-heuristic framework with an aim to maximize the profit of the airline. In the first phase, we develop a nonlinear mixed integer optimization model for aircraft recovery and utilize conic programming approach to mitigate computational difficulty. We incorporate cancellation and re-routing decisions for ights utilizing cruise time controllability which results in nonlinear fuel burn and CO2 emission cost functions. In the second phase, we develop a passenger recovery algorithm that makes individual itinerary based recovery decisions under the seat capacity restrictions and provide realistic cancellation cost formulations. Lastly, we propose an integrated search algorithm to maintain the integration between two phases through fixing assignment variables in the first phase. We compare the performance of the proposed algorithm to the base policy where all disrupted ights are directly cancelled. We observe improvements in terms of profit and the number of overnight passengers.Item Open Access Airline scheduling to minimize operational costs and variability(Bilkent University, 2021-08) Şimşek, DenizAirlines tend to design their flights schedules with the primary concern of the minimization of operational costs. However, the recently emerging idea of resilient scheduling defined as staying operational in case of unexpected disruptions and adaptability should be of great importance for airlines as well due to the high opportunity costs caused by the flight cancellations and passenger inconvenience caused by delays in the schedule. In this study, we integrate resilient airline schedule design, aircraft routing and fleet assignment problems with uncertain non-cruise times and controllable cruise times. We follow a data-driven method to estimate flight delay probabilities to calculate the airport congestion coefficients required for the probability distributions of non-cruise time random variables. We formulate the problem as a bi-criteria nonlinear mixed integer mathematical model with chance constraints. The nonlinearity caused by the fuel consumption and CO2 emission function associated with the controllable cruise times in our first objective is handled by second order conic inequalities. We minimize the total absolute deviation of the aircraft path variabilities from the average in our second objective to generate balanced schedules in terms of resilience. We follow an ε-constraint approach to scalarize and solve our problem via commercial solvers and we also devise a discretized approximation and search algorithm to solve large instances. We compare the recovery performances of our proposed schedules to the minimum cost schedules by a scenario-based posterior analysis. As a key contribution, we show that in the schedule generation phase, designing resilient schedules by allowing them to deviate from the minimum cost within the trade-off between the operational costs and the variability, the potential recovery costs in case of unexpected disruptions can be reduced significantly.Item Open Access Algorithms for 2 edge connectivity with fixed costs in telecommunications networks(Bilkent University, 2011) Güzel, UmutIn this thesis, several algorithms are developed in order to provide costeffective and survivable communication in telecommunications networks. In its broadest sense, a survivable network is one which can maintain communication even in the presence of a physical breakdown. There are several ways of providing survivable communication in a given network. Our choice is to hedge against single link failures and provide two edge disjoint paths for every source and destination pair. Each edge in the network is assumed to have a variable unit routing cost and a fixed usage cost. Our objective is the minimization of the total routing cost of the traffic demand and the fixed cost of the utilized links. Several constructive and improvement type heuristics are developed and tested extensively in an experimental design setting.Item Open Access Algorithms for on-line vertex enumeration problem(Bilkent University, 2017-09) Kaya, İrfan CanerVertex enumeration problem is to enumerate all vertices of a polyhedron P which is given by intersection of finitely many halfspaces. It is a basis for many algorithms designed to solve problems from various application areas and there are many algorithms to solve these problems in the literature. On the one hand, there are iterative algorithms which solve the so called 'on-line' vertex enumeration problem in each iteration. In other words, in each iteration of these algorithms, the current polyhedron is intersected with an additional halfspace that defines P. On the other hand, there are simplex-type algorithms which takes the set off all halfspaces as its input from the beginning. One of the usages of the vertex enumeration problem is the Benson-type multiobjective optimization algorithms. The aim of these algorithms is to generate or approximate the Pareto frontier (the set of nondominated points in the objective space). In each iteration of the Benson's algorithm, a polyhedron which contains the Pareto frontier is intersected with an additional halfspace in order tofind a finer outer approximation. The vertex enumeration problem to be used within this algorithm has a special structure. Namely, the polyhedron to be generated is known to be unbounded with a recession cone which is equal to the positive orthant. In this thesis, we consider the double description method which is a method to solve an on-line vertex enumeration problem where the starting polyhedron is bounded. (1) We generate an iterative algorithm to solve the vertex enumeration problem from the scratch where polyhedron P is allowed to be bounded or unbounded. (2) Then, we slightly modify this algorithm to be more efficient while it only works for problems where the recession cone of P is known to be the positive orthant. (3) Finally, we generate an additional algorithm for these problems. For this one, we modify the double description method such that it uses the extreme directions of the recession cone more effectively. We provide an illustrative example to explain the algorithms in detail. We implement the algorithms using MATLAB; employ each of them as a function of a Benson-type multiobjective optimization algorithm; and test the performances of the algorithms for randomly generated linear multiobjective optimization problems. Accordingly, for two dimensional problems, there is no clear distinction between the run-time performances of these algorithms. However, as the dimension of the vertex enumeration problem increases, the last algorithm (Algorithm 3) gets more efficient than the others.Item Open Access Algorithms for some discrete location problems(Bilkent University, 2003-09) Özsoy, F. AykutItem Open Access Algorithms for sparsity constrained principal component analysis(2023-07) Aktaş, Fatih SelimThe classical Principal Component Analysis problem consists of finding a linear transform that reduces the dimensionality of the original dataset while keeping most of the variation. Extra sparsity constraint sets most of the coefficients to zero which makes interpretation of the linear transform easier. We present two approaches to the sparsity constrained Principal Component Analysis. Firstly, we develop computationally cheap heuristics that can be deployed in very high-dimensional problems. Our heuristics are justified with linear algebra approximations and theoretical guarantees. Furthermore, we strengthen our algorithms by deploying the necessary conditions for the optimization model. Secondly, we use a non-convex log-sum penalty in the semidefinite space. We show a connection to the cardinality function and develop an algorithm, PCA Sparsified, to solve the problem locally via solving a sequence of convex optimization problems. We analyze the theoretical properties of this algorithm and comment on the numerical implementation. Moreover, we derive a pre-processing method that can be used with previous approaches. Finally, our findings from the numerical experiments we conducted show that our greedy algorithms scale to high dimensional problems easily while being highly competitive in many problems with state-of-art algorithms and even beating them uniformly in some cases. Additionally, we illustrate the effectiveness of PCA Sparsified on small dimensional problems in terms of variance explained. Although it is computationally very demanding, it consistently outperforms local and greedy approaches.Item Open Access Algorithms for the integer multicommodity network design problem(Bilkent University, 2004) Kılınç, Mustafa RasimIn this thesis, we study the problem of logical network design in telecommunication networks. Given a set of nodes and a set of commodities, we aim to locate lightpaths(links) between nodes and route the commodities over these lightpaths. The cost to be minimized is the number of lightpaths used. The problem has capacity, degree and delay constraints. An important characteristic of our problem is that the commodities can not be split, therefore they must be routed on a single path. We present two integer programming formulations of the problem and consider four sets of valid inequalities. Additionally, a relaxation of the problem is presented to obtain a lower bound to the problem. Finally, we propose two algorithms of generating good feasible solutions to the problem. Our results prove to be close to the lower bounds.Item Open Access Algorithms for the survivable telecommunications network design problem under dedicated protection(Bilkent University, 2010) Damcı, PelinThis thesis presents algorithms to solve a survivable network design problem arising in telecommunications networks. As a design problem, we seek to find 2-edge disjoint paths between every potential origin destination pair such that the fixed costs of installing edges and the routing costs are jointly minimized. Despite the fact that the survivable network design literature is vast, the particular problem at hand incorporating fixed and variable edge costs as well as different cost structures on the two paths has not been studied. Initially, an IP model addressing the proposed problem is developed. In order to solve problems of higher dimensions, different heuristic algorithms are designed and results of a computational study on a large bed of problem instances are reported.Item Open Access Allocating vaccines under scarce supply(Bilkent University, 2023-08) Kılınç, OnurWe consider the vaccine allocation problem under scarce supply. We formulate the problem as a two stage stochastic programming model, considering the uncertain factors such as vaccine efficacy, disease spread dynamics and the amount of future supply. We discuss two variants of the model that could be used under different preferences. We demonstrate the usability of our formulations on two case study examples that are generated based on real-life data. The results demonstrate that incorporating the uncertainty in these factors into the decision making process would allow the policy makers to use more effective strategies with an adaptive nature. This is also indicated by the value of stochastic solution, which shows a significant enhancement in disease control gained by the stochastic programming solution compared to a plan based on expected figures.Item Open Access Analyses of serial production lines and assembly systems for throughput and inyerdeparture time variability(Bilkent University, 1998) Kök, Abdullah GürhanIn this thesis, we study three different but closely related production system design problems. First, we investigate the effects of various design factors such as number of stations, buffer capacity, allocation of bulfers and location of a bottleneck on the interdeparture time variability of serial production lines. In the second part, we study the effects of number of component stations, processing time distributions, buffers and buffer allocation schemes on throughput and interdeparture time variability of assembly systems. As an alternative to work transfer, we introduce variability transfer and assess its effectiveness. We analyze the anomaly displayed by optimal throughput for some processing time distributions and uncover the underlying details of this behavior. In the third part, we analyze serial production lines and assembly systems under constant workload condition. In addition to investigating the problem of determining the optimal system size, we examine the effects of other design factors such as buffers and material handling time on throughput, interdeparture time variability and cost related measures. Each part reveals several important findings. We also discuss the managerial implications of these findings to present guidelines for the practitioners.Item Open Access Analysis of a hospital call center(Bilkent University, 2012) Budak, Ezel EzgiIn this thesis, we study the call center operations of a particular hospital located in Ankara, namely Güven Hospital. The hospital call center takes role as a medical consulting and appointment center and also domestic call traffic flows over the call center. These three types of calls are classified as consulting, appointment and domestic calls. The arriving call rate to the call center vary depending on hours and each agent is capable of giving service to each type of calls.( i.e. Agents are multitasking). Different types of calls have different exponential service time distributions. Regardless of call type calls may abandon during their waiting time in the call center. Abandonment rate and arrival rates of the calls are assumed to be exponential. Call center directs some percent of appointment calls to a doctor who gives service in the call center and some percent of consulting calls to hospital units depending on customers’ requests. A domestic call only receives service from the call center. Some percent of these diverted calls to doctor and hospital units return to call center. This diverting and returning process among call center, doctor and hospital units constitutes the call center network of the hospital. The aim of this study is to model this call center network as to reflect the properties of the analyzed system. Accordingly, the system is modeled with queuing network and simulation approaches. Different models are developed with different divert and return rates and different number of agents being multi-tasking or dedicated to give service to a specific call type. These models are compared in terms of systems performance metrics and related numerical analyses are reported.Item Open Access Analysis of consignment contracts for spare parts inventory systems(Bilkent University, 2006) Latifoğlu, ÇağrıWe study a Vendor Managed Inventory (VMI) partnership between a manufacturer and a retailer. More specifically, we consider a consignment contract, under which the manufacturer assumes the ownership of the inventory in retailer’s premises until the goods are sold, the retailer pays an annual fee to the manufacturer and the manufacturer pays the retailer backorder penalties. The main motivation of this research is our experience with a capital equipment manufacturer that manages the spare parts (for its systems) inventory of its customers in their stock rooms. We consider three factors that may potentially improve the supply chain efficiency under such a partnership: i-) reduction in inventory ownership costs (per unit holding cost) ii-) reduction in replenishment lead time and iii-) joint replenishment of multiple retailer installations. We consider two cases. In the first case, there are no setup costs; the retailer (before the contract) and the manufacturer (after the contract) both manage the stock following an (S − 1, S) policy. In the second case, there are setup costs; the retailer manages its inventories independently following an (r, Q) policy before the contract, and the manufacturer manages inventories of multiple retailer installations jointly following a (Q, S) policy. Through an extensive numerical study, we investigate the impact of the physical improvements above and the backorder penalties charged by the retailer on the total cost and the efficiency of the supply chain.Item Open Access Analysis of Erlang transfer lines(Bilkent University, 1997) Dönmez, NebahatTransfer lines are widely used in the modeling and analysis of complex production systems. The literature is mostly devoted to the analysis of transfer lines with exponential processing times. However, most of the time a part is |)rocessed through stages(phases) of exponential processing times. It is possil)le to model such systems by means of processing times that are A,·—Erlang distributed. In the modeling and solution of these systems, significant difficulties arise due to the nature of the problem. In this thesis, we propose a -Markov model for transfer lines consisting of n reliable machines with A—Erlang processing times and finite buffers. The arrivals to the system is Poisson distributed. A program coded in C which is capable of solving the Markov model of a three machine transfer line is also developed. Besides the commonly used performance measures, such as utilization of the machines, mean throughput, mean WIP level, we calculate the variance of VVIP so that it is possible to construct confidence intervals.Item Open Access An analysis of FMS scheduling problem: a beam search based algorithm and comparison of scheduling schemes(Bilkent University, 1994) Karabük, SüleymanFMS scheduling procedures in the literature can be classified into on-line and off-line schemes according to the number of scheduling decisions made at a point in time. Online scheduling attempts to schedule operations one at a time when it is needed and off-line scheduling refers to scheduling operations of available jobs for the entire scheduling period. In the literature there is no unified argument for or against either of these scheduling schemes. This research has two main objectives: development of a new scheduling scheme called quasi on-line that makes a trade-off between on-line and off-line schemes and comparison of the proposed scheme with others under various experimental conditions. A new algorithm is proposed on which the quasi online scheme is based. The proposed algorithm is a heuristic and utilizes a beam search technique. It considers finite buffer capacity, routing and sequence flexibilities and generates machine and AGV schedules for a given scheduling period. A simulation model is also developed to implement and test scheduling schemes.Item Open Access Analysis of locations of existing fire stations in Ankara in comparison to optimized locations(Bilkent University, 2012) Balcı, PelinThis thesis aims to evaluate the locations of the existing fire stations in the city of Ankara. Vertex restricted p-center problem is solved via set covering problem and optimal locations of fire stations are found. We evaluate the fire stations in two ways. The first study aims to locate the same number of fire stations with the existing case. We use an algorithm proposed by Tansel (2011) which solves a finite series of set covering problems to reach the optimal solution of the p-center problem. We use three approaches for the p-center solution which constitutes our first study. In the first approach, we optimally locate the fire stations while keeping their allocation sets the same as those of the existing stations.In the second approach, we locate the fire stations to minimize the maximum of the distances between demand nodes and their closest stations. In the last approach, we take the population of the nodes into account and solve a weighted p-center problem where the weights of demand nodes are defined by their composite populations. We also give a methodology to compute the composite population counts for nodes. In the second study, we locate a minimum number of fire stations while ensuring that each demand node is covered within a pre-determined upper bound on the service time (distance). The bounds are taken to be 4 minutes and 8 minutes in accordance with the internationally accepted norms. Optimally located fire stations are found for both time restrictions. There are two subcases for this study; one of them aims to locate the fire stations without considering the existing fire stations while the other one locates the new fire stations in addition to the existing fire stations. Optimal solutions for all the cases explained above are compared with the existing fire stations with regard to the maximum distances, populations, and covered regions. Assessments are made on existing fire stations by benchmarking their performances against optimal solutions obtained via pcenter or covering solutions as outlined above. Geographical information systems are used for obtaining the demographic data and presenting visual analysis.Item Open Access Analysis of multimedian problems on time dependent networks(Bilkent University, 1994) Salman, F SibelTime dependency arises in transportation and computer-communication networks due to factors such as time varying demand, traffic intensity, and road conditions. This necessitates a locational decision to be based on an analysis involving a time horizon. In this study, we analyze multi-median problems with linear demand functions on both tree and cyclic networks in a continuous time domain. The trajectory of the optimal solution is a piecewise linear concave function. We develop an algorithm that constructs the trajectory by solving 0{q) static problems, where q is the number of linear pieces in the trajectory. The properties of the optimal solution over the time horizon are also analyzed for various randomly generated problem instances.Item Open Access An analysis of order review(Bilkent University, 1995) Karapınar, H YavuzOrder Review/Release (ORR) activities have mostly been ignored in past job shop research. In the majority of these studies, arriving jobs are immediately released to the shop floor without considering any information about the job and the system status. In practice, however, jobs arriving at the shop are first collected in a pool and then released periodically according to some release criterion. Although practitioners use ORR mechanisms to improve shop floor performance, researchers have found limited supports for the use of these input regulation policies. In this thesis, we reexamine the problem in a capacitated system. Specifically, we compare the performances of the ORR policies in a job shop with finite buffer capacities and material handling considerations. A new ORR mechanism is also proposed and compared with other methods.