Dept. of Industrial Engineering - Ph.D. / Sc.D.

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Open Access
Age and lifetime based policies for perishable items
(Bilkent University, 2018-10) Poormoaied, Saeed; Gürler, Ülkü
Many inventory systems hold items which perish after a specific time. Upon perishing, the inventory level falls down to zero which may incur irreparable costs to the system. Therefore, developing a genius control policy for managing such inventories is a crucial task. Since the lifetime of items are now affecting the inventory level, applying the traditional inventory policies which are based only on the stock level causes some shortcomings. The traditional inventory policies lack the information regarding the lifetime of items. On the other hand, the optimal policy for perishable items is known to be a periodic review policy keeping the complete information regarding the remaining lead times of orders, inventory onhand, and lifetimes of items. Optimal control policy class for continuous review is still an open question. In this regard, we attempt to contribute the remaining lifetime of items into the inventory policy for perishable items with positive lead time and fixed lifetime under a continuous review with a service level constraint. We develop a class of hybrid control policies which utilize the remaining lifetimes of items in addition to stock levels. We study a stochastic single item inventory system where demand follows a Poisson process and unmet demand is lost. The aging process of a new batch starts when it joins the inventories. We provide an exact analytic model by using an embedded Markov chain process to derive the stationary distribution of the effective lifetimes in the presence of both one and more than one outstanding orders assumptions. Operating characteristics of the system are derived using the renewal reward theorem. Additionally, we propose some control policies based on only the remaining lifetime of items. Our results reveal that the hybrid policies consistently outperform the stock level and remaining lifetime-based polices, especially when demand during the lifetime is sufficiently small and unit perishing cost is high. It is observed that the dominance relations among these two policy classes depend on the particular parameter setting. In particular, when the lifetime of items is long enough, the stock level based policy performs very well. Finally, we present our methodology for finding the optimal solution thorough a heuristic algorithm derived by considering the structure of the objective function and service level constraint, and a sensitivity analysis is performed to evaluate the impact of the key input parameters.
Open Access
Algorithms for linear and convex feasibility problems: A brief study of iterative projection, localization and subgradient methods
(Bilkent University, 1998) Özaktaş, Hakan; Akgül, Mustafa
Several algorithms for the feasibility problem are investigated. For linear systems, a number of different block projections approaches have been implemented and compared. The parallel algorithm of Yang and Murty is observed to be much slower than its sequential counterpart. Modification of the step size has allowed us to obtain a much better algorithm, exhibiting considerable speedup when compared to the sequential algorithm. For the convex feasibility problem an approach combining rectangular cutting planes and subgradients is developed. Theoretical convergence results are established for both ca^es. Two broad classes of image recovery problems are formulated as linear feasibility problems and successfully solved with the algorithms developed.
Open Access
Centralized and decentralized management of water resources with multiple users
(Bilkent University, 2011) Saleh, Yahya; Berk, Emre
In this study, we investigate two water inventory management schemes with multiple users in a dynamic game-theoretic structure over a two-period planning horizon. We first investigate the groundwater inventory management problem (i) under the decentralized management scheme, where each user is allowed to pump water from a common aquifer making usage decisions individually in a noncooperative fashion, and (ii) under the centralized management scheme, where users are allowed to pump water from a common aquifer with the supervision of a social planner. We consider the case of n non-identical users distributed over a common aquifer region. Furthermore, we consider different geometric configurations overlying the aquifer, namely, the strip, ring, double-layer ring, multi-layer ring and grid configurations. In each configuration, general analytical results of the optimal groundwater usage are obtained and numerical examples are discussed. We then consider the surface and groundwater conjunctive use management problem with two non-identical users in a dynamic game-theoretic structure over a planning horizon of two periods. Optimal water allocation and usage policies are obtained for each user in each period under the decentralized and centralized settings. Some pertinent hypothetical numerical examples are also provided.
Open Access
Concepts and analysis in facility location under uncertainty : applications to 1-median problem
(Bilkent University, 2001-08) Demir, Muhittin Hakan; Tansel, Barbaros Ç.
Open Access
Continuous time control of make-to-stock production systems
(Bilkent University, 2010) Bulut, Önder; Fadıloğlu, M. Murat
We consider the problem of production control and stock rationing in a make-tostock production system with multiple servers –parallel production channels--, and several customer classes that generate independent Poisson demands. At decision epochs, in conjunction with the stock allocation decision, the control specifies whether to increase the number of operational servers or not. Previously placed production orders cannot be cancelled. We both study the cases of exponential and Erlangian processing times and model the respective systems as M /M /s and M /Ek /s make-to-stock queues. We characterize properties of the optimal cost function, and of the optimal production and rationing policies. We show that the optimal production policy is a state-dependent base-stock policy, and the optimal rationing policy is of state-dependent threshold type. For the M /M /s model, we also prove that the optimal ordering policy transforms into a bang-bang type policy when we relax the model by allowing order cancellations. Another model with partial ordercancellation flexibility is provided to fill the gap between the no-flexibility and the full-flexibility models. Furthermore, we propose a dynamic rationing policy for the systems with uncapacitated replenishment channels, i.e., exogenous supply systems. Such systems can be modeled by letting s --the number of replenishment channels-- go to infinity. The proposed policy utilizes the information on the status of the outstanding replenishment orders. This work constitutes a significant extension of the literature in the area of control of make-to-stock queues, which considers only a single server. We consider an arbitrary number of servers that makes it possible to cover the spectrum of the cases from the single server to the infinite servers. Hence, our work achieves to analyze both the exogenous and endogenous supply leadtimes.
Open Access
Designing intervention strategy for public-interest goods
(Bilkent University, 2016-09) Demirci, Ece Zeliha; Erkip, Nesim K.
Public-interest goods, which are also referred as goods with positive externalities, create benefits to individual consumers as well as non-paying third parties. Some significant examples include health related products such as vaccines and products with less carbon emissions. When positive externalities exist, the good may be under-produced or under-supplied due to incorrect pricing policies or failing to value external benefits and that is why a need for intervention arises. A central authority such as government or social planner intervenes into the system of these goods so that their adoption levels are increased towards socially desirable levels. The central authority seeks to design and finance an intervention strategy that will impact the decisions of the channel in line with the good of the society, specified as social welfare. A key issue in designing an intervention mechanism is choosing the intervention tools to incorporate. The intervention tools can target the supply or demand of the good. One option for the intervention tool is investment in demand-increasing strategies, which affects the level of stochastic demand in the market. Second option is investment in strategies that will improve supply of the good. Alternatives for this option include registering rebates or subsidies and investment in yield-improving strategies when production process faces imperfect yield. As several real life cases indicate, central authority operates under a limited budget in this environment. Thus, we introduce and analyze social welfare maximization models with the emphasis on optimal budget allocation. We model the lower level problem, which represents the channel as a newsvendor problem. We then utilize bilevel programming for modeling the environment incorporating the role of central authority. After obtaining single level equivalent formulations of the problems, we analyze and solve them as non-linear programs. Our first problem is to analyze an intervention strategy, which uses only subsidy issued per unit order quantity. We explore the subsidy design problem for single retailer and n retailers cases. We show that all of the budget will be used under mild conditions and present structural results. Also, we analyze subsidy design problem for two echelon setting, where the central authority gives subsidy both to retailer and manufacturer. We consider centralized and manufacturer-driven problems and present numerical results. In the remaining part of the thesis, we focus on joint intervention mechanisms in which two intervention tools are applied simultaneously. First, we study a joint mechanism composed of demand-increasing strategy and rebate. We present two models and associated structural properties. First model aims to find optimal budget and allocation of it among intervention tools. We deduce that rebate amount may be independent of investment made in demand-increasing strategies and improvement pattern of demand. Second model decides on the optimal allocation of a given budget between intervention tools. We show that central authority will allocate all budget under mild conditions. Furthermore, we use real-life data and information of California electric vehicle market in order to verify the proposed models and show benefits of taking such an approach. We also explore the application of the joint mechanism under a given budget for exponentially distributed demand family and fully characterize the optimal solution. The analysis of the solution reveals that designing an intervention scheme without considering an explicit budget constraint will result in budget deficit and excess money transfers to the retailer. As the second modeling environment we consider a joint mechanism consisting of demand-increasing strategy and yield-improving strategy in a setting where yield uncertainty exists. We introduce lognormal demand and yield models that take into account the investments made for improving them. We test the suggested model with a case study relying on the available estimates of US influenza market. The results indicate that addressing both demand and yield issues by the proposed mechanism will increase vaccination percentages remarkably.
Open Access
Deterministic and stochastic team formation problems
(Bilkent University, 2021-01) Berktaş, Nihal; Karaşan, Oya
In various organizations, physical or virtual teams are formed to perform jobs that require diﬀerent skills. The success of a team depends on the technical capabilities of the team members as well as the quality of communication among the team members. We study diﬀerent variants of the team formation problem where the goal is to build the best team with respect to given criteria. First, we study a deterministic team formation problem which aims to construct a capable team that can communicate and collaborate eﬀectively. To measure the quality of communication, we assume the candidates constitute a social network and we deﬁne a cost of communication using the proximity of people in the social network. We minimize the sum of all pairwise communication costs, and we impose an upper bound on the largest communication cost. This problem is formulated as a constrained quadratic set covering problem. Our experiments show that a general-purpose solver is capable of solving small and medium-sized instances to optimality. We propose a branch-and-bound algorithm to solve larger sizes: we reformulate the problem and relax it in such a way that it decomposes into a series of linear set covering problems, and we impose the relaxed constraints through branching. Our computational experiments show that the algorithm is capable of solving large-sized instances, which are intractable for the solver. Second, we consider a two-stage stochastic team formation problem where the objective is to minimize the expected communication cost of the team. We as-sume that for a subset of pairs the communication costs are uncertain but they have a known discrete distribution. The ﬁrst stage is a trial stage where the decision-maker chooses a limited number of pairs from this subset. The actual cost values of the chosen pairs are realized before the second stage. Hence, the uncertainty in this problem is decision-dependent, also called endogenous, be-cause the ﬁrst stage decisions determine for which parameters the uncertainty will resolve. For this problem, we give two formulations, the ﬁrst one contains a set of non-anticipativity constraints similar to the models in the related lit-erature. In the second, we are able to eliminate these constraints by changing the objective function into a quadratic one, which is linearized by a set of extra binary variables. We show that the size of instances we can solve with these for-mulations using a commercial solver is limited. Therefore, we develop a Benders’ decomposition-based branch-and-cut algorithm that exploits decision-dependent nature to partition scenarios and use tight linear relaxations to obtain strong cuts. We show the eﬃciency of the algorithm presenting results of experiments conducted with randomly generated instances. Finally, we study a multi-stage team formation problem where the objective is to minimize the monetary cost including hiring and outsourcing costs. In this problem, stages correspond to projects which are carried out consecutively. Each project consists of several tasks each of which requires a human resource. We assume that due to incomplete information there is uncertainty in people’s performances and consequently the time a person needs to complete a task is random for some person-task pairs. When a person is assigned to a task, we learn how long it takes for this person to ﬁnish the task. Hence, the uncertainty is again decision-dependent. If the duration of a task exceeds the allowable time for a project then the manager must hire an external resource to speed up the process. We present an integer programming formulation to this problem and explain that the size of the formulation strongly depends on the number of random parameters and scenarios. While this deterministic equivalent formulation can be solved with a commercial solver for small-sized instances, it easily becomes intractable when the number of random parameters increases by one. For such cases where exact methods are not promising, we investigate heuristic methods to obtain tight bounds and near-optimal solutions. In the related literature, diﬀerent Lagrangian decomposition methods are developed for such stochastic problems. In this study, we show that the convergence of existing methods is very slow, and we propose an alternative method where a relaxation of the formulation is solved by a decomposition-based branch-and-bound algorithm.
Open Access
Discrete location models for content distribution
(Bilkent University, 2005) Bektaş, Tolga; Oğuz, Osman
The advances in information and computer technology has tremendously eased the way to reach electronic information. This, however, also brought forth many problems regarding the distribution of electronic content. This is especially true in the Internet, where there is a phenomenal growth of demand for any kind of electronic information, placing a high burden on the underlying infrastructure. In this dissertation, we study problems arising in distribution of electronic content. The first problem studied here is related to Content Distribution Networks (CDNs), which have emerged as a new technology to overcome the problems arising on the Internet due to the fast growth of the web-related traffic, such as slow response times and heavy server loads. They aim at increasing the effectiveness of the network by locating identical or partial copies of the origin server(s) throughout the network, which are referred to as proxy servers. In order for such structures to run efficiently, the CDN must be designed such that system resource are properly managed. To this purpose, we develop integer programming models for the problem of designing CDNs and investigate exact and heuristic algorithms for their solution. The second problem considered in this dissertation is Video Placement and Routing, which is related to the so-called Video-on-Demand (VoD) services. Such services are used to deliver programs to the users on request and find many applications in education, entertainment and business. Although bearing similarities with the CDN phenomena, VoD services have special characteristics with respect to the structure of the network and the type of content distributed. We study the problem of Video Placement and Routing for such networks and offer an optimization based solution algorithm for the associated integer programming model. The third problem studied here is the problem of allocating databases in distributed computing systems. In this context, we specifically focus on the well-known multidimensional Knapsack Problem (mKP). The mKP arises as a subproblem in solving the database location problem. We concentrate on the well known cover inequalities that are known to be important for the solution of the mKP. We then propose a novel separation procedure to identify violated cover inequalities and utilize this procedure in a branch-and-cut framework devised for the solution of the mKP.
Open Access
Energy management in plug-in hybrid electric vehicle penetrated networks
(Bilkent University, 2016-04) Arslan, Okan; Karaşan, Oya Ekin
With the introduction of electric vehicles (EVs) and plug-in hybrid electric vehicles (PHEVs) into the transportation system, a new line of research has emerged in the literature that reconsiders existing problems from the electrified transportation point of view. In this context, our objective is to understand the challenges that arise with the emergence of PHEV technology through a series of essays. Due to their ability to use electricity and gasoline as sources of energy with di↵erent cost structures and limitations, PHEVs stand as both a challenge and an opportunity for the existing transportation systems. They provide transportation cost reductions by utilizing less gasoline, which in turn contribute to the environmental benefits. In this context, we addressed a practically important problem: ‘finding the minimum cost path for PHEVs’. We formally present this problem, show that it is NP-Complete and propose exact and heuristic solution techniques. Using these techniques, we investigate impacts of battery characteristics, driver preferences and road network features on travel costs of a PHEV for long-distance trips. Through this analysis, the location of charging stations is identified as one of the critical factors a↵ecting the costs. In this regard, we introduce another practically important problem: ‘Hybrid charging station location’. Di↵erent than existing approaches to the charging station location problems, we also consider PHEVs when locating stations. We propose a Benders Decomposition algorithm as an exact solution methodology, and accelerate the implementation by generating nondominated cuts. Finally, we analyze the cost and emission impacts of PHEV penetration into electricity networks with widespread adoption of distributed energy resources. Approaching PHEVs from a long-distance point of view, we introduced new problems and solution approaches to the literature. Our results show that by establishing an adequate level of the intercity charging station infrastructure, wellstudied benefits of electrified transportation in urban regions can be extended to long-distance trips.
Open Access
Energy operations management for renewable power producers in electricity markets
(Bilkent University, 2023-05) Karakoyun, Ece Çiğdem; Kocaman, Ayşe Selin
Renewable energy generation has grown dramatically around the world in recent years, and policies targeted at reducing greenhouse gas emissions that cause global warming are expected to ensure a consistent expansion of renewable power generation in the electricity sector. With the increasing contribution of renewable sources to the overall energy supply, renewable power producers participate in electricity markets where they are imposed to make advance commitment decisions for energy delivery and purchase. Making advance commitments, however, is a complex task due to the inherent intermittency of renewable sources, increasingly volatile electricity prices, and penalties incurred for possible energy imbalances in electricity markets. Integrating renewable sources with energy storage units is among the most effective methods to address this challenging task. Motivated by the recent trends of paired renewable energy generators and storage units, we study the energy commitment, generation and storage problem of a wind power producer who owns a battery and participates in a spot market operating with hourly commitments and settlements. In each time period, the producer decides how much energy to commit to selling to or purchasing from the market in the next time period, how much energy to generate in the wind power plant, and how much energy to charge into or discharge from the battery. The existence of the battery not only helps smooth out imbalances caused by the fluctuating wind output but also enables the producer to respond to price changes in the market. We formulate the wind power producer's problem as a Markov decision process by taking into account the uncertainties in wind speed and electricity price. In the first part of this dissertation, we consider two different problem settings: In the first setting, the producer may choose to deviate from her commitments based on the latest available information, using the battery to support such deviations. In the second setting, the producer is required to fulfill her commitments, using the battery as a back-up source. We numerically examine the effects of system components, imbalance pricing parameters, and negative prices on the producer's profits, curtailment decisions, and imbalance tendencies in each problem setting. We provide managerial insights to renewable power producers in their assessment of energy storage adoption decisions and to power system operators in their understanding of the producers' behavior in the market with their storage capabilities. In the second part of this dissertation, we establish several multi-dimensional structural properties of the optimal profit function such as supermodularity and joint concavity. This enables us to prove the optimality of a state-dependent threshold policy for the storage and commitment decisions under the assumptions of a perfectly efficient system and positive electricity prices. Leveraging this policy structure, we construct two heuristic solution methods for solving the more general problem in which the battery and transmission line can be imperfectly efficient and the price can also be negative. Numerical experiments with data-calibrated instances have revealed the high efficiency and scalability of our solution procedure. In the third part of this dissertation, we characterize the optimal policy structure by taking into account the battery and transmission line efficiency losses and showing the joint concavity of the optimal profit function. In the last part of this dissertation, we consider an alternative problem setting that allows for real-time trading without making any advance commitment. We analytically compare the total cash flows of this setting to those of our original problem setting. We conclude with a numerical investigation of the effect of advance commitment decisions on the producer's energy storage and generation decisions.
Open Access
Essays on bilateral trade with discrete types
(Bilkent University, 2019-10) Mohammadinezhad, Kamyar Kargar; Pınar, Mustafa Çelebi
Bilateral trade is probably the most common market interaction problem and can be considered as the simplest form of two sided markets where a seller and a buyer bargain over an indivisible object subject to incomplete information on the reservation values of participants. We treat this problem as a combinatorial optimization problem and re-establish some results of economic theory that are well-known under continuous valuations assumptions for the case of discrete valuations using linear programming techniques. First, we propose mathematical formulation for the problem under dominant strategy incentive compatibility (DIC) and ex-post individual rationality (EIR) properties. Then we derive necessary and sufficient conditions under which ex-post efficiency can be obtained together with DIC and EIR. We also define a new property called Allocation Maximality and prove that the Posted Price mechanism is the only mechanism that satisfies DIC, EIR and allocation maximality. In the final part we consider ambiguity in the problem framework originating from different sets of priors for agents types and derive robust counterparts. Next, we study the bilateral trade problem with an intermediary who wants to maximize her expected gains. Using network programming we transform the initial linear program into one from which the structure of mechanism is transparent. We then relax the risk-neutrality assumption of the intermediary and consider the problem from the perspective of risk-averse intermediary. The effects of risk-averse approach are presented using computational experiments. Finally, we broaden the scope of the problem and discuss the case in which the seller is also a producer at the same time and consider benefit and cost functions for the respective parties. Starting by a non-convex optimization problem, we obtain an equivalent convex optimization problem from which the problem is solved easily. We also reconsider the same problem under dominant strategy incentive compatibility and ex-post individual rationality constraints to preserve the practicality of all obtained solutions.
Open Access
Essays on non-cooperative inventory games
(Bilkent University, 2012) Körpeoğlu, Evren; Şen, Alper
In this thesis we study different non–cooperative inventory games. In particular, we focus on joint replenishment games and newsvendor duopoly under asymmetric information. Chapter 1 contains introduction and motivation behind the research. Chapter 2 is a preliminary chapter which introduce basic concepts used in the thesis such as Nash equilibrium, Bayesian Nash equilibrium and mechanism design. In Chapter 3, we study a non-cooperative game for joint replenishment of multiple firms that operate under an EOQ–like setting. Each firm decides whether to replenish independently or to participate in joint replenishment, and how much to contribute to joint ordering costs in case of participation. Joint replenishment cycle time is set by an intermediary as the lowest cycle time that can be financed with the private contributions of participating firms. We consider two variants of the participation-contribution game: in the single–stage variant, participation and contribution decisions are made simultaneously, and, in the two-stage variant, participating firms become common knowledge at the contribution stage. We characterize the behavior and outcomes under undominated Nash equilibria for the one-stage game and subgame-perfect equilibrium for the two-stage game. In Chapter 4, we extend the private contributions game to an asymmetric information counterpart. We assume each firm only knows the probability distribution of the other firms’ adjusted demand rates (demand rate multiplied by inventory holding cost rate). We show the existence of a pure strategy Bayesian Nash equilibrium for the asymmetric information game and provide its characterization. Finally, we conduct some numerical study to examine the impact of information asymmetry on expected and interim values of total contributions, cycle times and total costs. quantities for all firm types except the type that has the highest possible unit cost, who orders the same quantity as he would as a monopolist newsboy. Consequently, competition leads to higher total inventory in the industry. A firm’s equilibrium order quantity increases with a stochastic increase in the total industry demand or with an increase in his initial allocation of the total industry demand. Finally, we provide full characterization of the equilibrium, corresponding payoffs and comparative statics for a parametric special case with uniform demand and linear market shares.
Open Access
Essays on scheduling with controllable processing times in flexible manufacturing systems
(Bilkent University, 2003) Türkcan, Ayten
Open Access
Exact solution approaches for non-Hamiltonian vehicle routing problems
(Bilkent University, 2017-07) Özbaygın, Amine Gizem; Paternotte, Hande Yaman
In this thesis, we study di erent non-Hamiltonian vehicle routing problem variants and concentrate on developing e cient optimization algorithms to solve them. First, we consider the split delivery vehicle routing problem (SDVRP).We provide a vehicle-indexed ow formulation for the problem, and then, a relaxation obtained by aggregating the vehicle-indexed variables over all vehicles. This relaxation may have optimal solutions where several vehicles exchange loads at some customers. We cut-o such solutions either by extending the formulation locally with vehicle-indexed variables or by node splitting. We compare these approaches using instances from the literature and new randomly generated instances. Additionally, we introduce two new extensions of the SDVRP by restricting the number of splits and by relaxing the depot return requirement, and modify our algorithms to handle these extensions. Second, we focus on a problem unifying the notion of coverage and routing. In some real-life applications, it may not be viable to visit every single customer separately due to resource limitations or e ciency concerns. In such cases, utilizing the notion of coverage; i.e., satisfying the demand of multiple customers by visiting a single customer location, may be advantageous. With this motivation, we study the time constrained maximal covering salesman problem (TCMCSP) in which the aim is to nd a tour visiting a subset of customers so that the amount of demand covered within a limited time is maximized. We provide ow and cut formulations and derive valid inequalities. Since the connectivity constraints and the proposed valid inequalities are exponential in the size of the problem, we devise di erent branch-and-cut schemes. Computational experiments performed on a set of problem instances demonstrate the e ectiveness of the proposed valid inequalities in terms of strengthening the linear relaxation bounds as well as speeding up the solution procedure. Moreover, the results indicate the superiority of using a branch-and-cut methodology over a ow-based formulation. Finally, we discuss the relation between the problem parameters and the structure of optimal solutions based on the results of our experiments. Third, we study the vehicle routing problem with roaming delivery locations (VRPRDL) in which a customer order has to be delivered to the trunk of the customer's car during the time that the car is parked at one of the locations in the (known) customer's travel itinerary. We formulate the problem as a set covering problem and develop a branch-and-price algorithm for its solution. The algorithm can also be used for solving a more general variant in which a hybrid delivery strategy is considered that allows a delivery to either a customer's home or to the trunk of the customer's car. We evaluate the e ectiveness of the many algorithmic features incorporated in the algorithm in an extensive computational study and analyze the bene ts of these innovative delivery strategies. The computational results show that employing the hybrid delivery strategy results in average cost savings of nearly 20% for the instances in our test set.Finally, we consider the dynamic version of the VRPRDL in which customer itineraries may change during the execution of the planned delivery schedule, which can become infeasible or suboptimal as a result. We refer to this problem as the dynamic VRPRDL (D-VRPRDL) and propose an iterative solution framework in which the previously planned vehicle routes are re-optimized whenever an itinerary update is revealed. We use the branch-and-price algorithm developed for the static VRPRDL both for solving the planning problem (to obtain an initial delivery schedule) and for solving the re-optimization problems. Since many re-optimization problems may have to be solved during the execution stage, it is critical to produce solutions to these problems quickly. To this end, we devise heuristic procedures through which the columns generated during the previous branch-and-price executions can be utilized when solving a re-optimization problem. In this way, we may be able to save time that would otherwise be spent in generating columns which have already been (partially) generated when solving the previous problems, and nd optimal solutions or at least solutions of good quality reasonably quickly. We perform preliminary computational experiments and report the results.
Open Access
Exact solution methodologies for the p-center problem under single and multiple allocation strategies
(Bilkent University, 2013) Çalık, Hatice; Karaşan, Oya Ekin
The p-center problem is a relatively well known facility location problem that involves locating p identical facilities on a network to minimize the maximum distance between demand nodes and their closest facilities. The focus of the problem is on the minimization of the worst case service time. This sort of objective is more meaningful than total cost objectives for problems with a time sensitive service structure. A majority of applications arises in emergency service locations such as determining optimal locations of ambulances, fire stations and police stations where the human life is at stake. There is also an increased interest in p-center location and related location covering problems in the contexts of terror fighting, natural disasters and human-caused disasters. The p-center problem is NP-hard even if the network is planar with unit vertex weights, unit edge lengths and with the maximum vertex degree of 3. If the locations of the facilities are restricted to the vertices of the network, the problem is called the vertex restricted p-center problem; if the facilities can be placed anywhere on the network, it is called the absolute p-center problem. The p-center problem with capacity restrictions on the facilities is referred to as the capacitated p-center problem and in this problem, the demand nodes can be assigned to facilities with single or multiple allocation strategies. In this thesis, the capacitated p-center problem under the multiple allocation strategy is studied for the first time in the literature. The main focus of this thesis is a modelling and algorithmic perspective in the exact solution of absolute, vertex restricted and capacitated p-center problems. The existing literature is enhanced by the development of mathematical formulations that can solve typical dimensions through the use of off the-shelf commercial solvers. By using the structural properties of the proposed formulations, exact algorithms are developed. In order to increase the efficiency of the proposed formulations and algorithms in solving higher dimensional problems, new lower and upper bounds are provided and these bounds are utilized during the experimental studies. The dimensions of problems solved in this thesis are the highest reported in the literature.
Open Access
Facility location, capacity acquisition and technology selection models for manufacturing strategy planning
(Bilkent University, 1993) Verter, Vedat; Dinçer, Cemal
The primary aim of this dissertation research is to contribute to the manufacturing strategy planning process. The firm is perceived as a value chain which can be represented by a production-distribution network. Structural decisions regarding the value chain of a firm are the means to implement the firm’s manufacturing strategy. Thus, development of analytical methods to aid the design of production-distribution sytems constitutes the essence of this study. The differentiating features of the manufacturing strategy planning process within the multinational companies are especially taken into account due to the significance of the globalization in product, factor, and capital markets. A review of the state-of-the-art in production-distribution system design reveals that although the evaluation of strategy alternatives received much attention, the existing analytical methods are lacking the capability to produce manufacturing strategy options. Further, it is shown that the facility location, capacity acquisition, and technology selection decisions have been dealt with separately in the literature. Whereas, the interdependencies among these structural decisions are pronounced within the international context, and hence global manufacturing strategy planning requires their simultaneous optimization. Thus, an analytical method is developed for the integration of the facility location and sizing decisions in producing a single commodity. Then, presence of product-dedicated technology alternatives in acquiring the required production capacity at each facility is incorporated. The analytical method is further extended to the multicommodity problem where product- flexible technology is also available as a technology alternative. Not only the arising models facilitate analysis of the trade-offs associated with the scale and scope economies in capacity/technology acquisition on the basis of alternative facility locations, but they also provide valuable insights regarding the presence of some dominance properties in manufacturing strategy design.
Open Access
Generating robust and stable machine schedules from a proactive standpoint
(Bilkent University, 2009) Gören, Selçuk; Sabuncuoğlu, İhsan
In practice, scheduling systems are subject to considerable uncertainty in highly dynamic operating environments. The ability to cope with uncertainty in the scheduling process is becoming an increasingly important issue. In this thesis we take a proactive approach to generate robust and stable schedules for the environments with two sources of uncertainty: processing time variability and machine breakdowns. The information about the uncertainty is modeled using cumulative distribution functions and probability theory is utilized to derive inferences. We first focus on the single machine environment. We define two robustness (expected total flow time and expected total tardiness) and three stability (the sum of the squared and absolute differences of the job completion times and the sum of the variances of the realized completion times) measures. We identify special cases for which the measures can be optimized without much difficulty. We develop a dominance rule and two lower bounds for one of the robustness measures, which are employed in a branch-and-bound algorithm to solve the problem exactly. We also propose a beam-search heuristic to solve large problems for all five measures. We provide extensive discussion of our numerical results. Next, we study the problem of optimizing both robustness and stability simultaneously. We generate the set of all Pareto optimal points via -constraint method. We formulate the sub-problems required by the method and establish their computational complexity status. Two variants of the method that works with only a single type of sub-problem are also considered. A dominance rule and alternative ways to enforce the rule to strengthen one of these versions are discussed. The performance of the proposed technique is evaluated with an experimental study. An approach to limit the total number of generated points while keeping their spread uniform is also proposed. Finally, we consider the problem of generating stable schedules in a job shop environment with processing time variability and random machine breakdowns. The stability measure under consideration is the sum of the variances of the realized completion times. We show that the problem is not in the class NP. Hence, a surrogate stability measure is developed to manage the problem. This version of the problem is proven to be NP-hard even without machine breakdowns. Two branchand-bound algorithms are developed for this case. A beam-search and a tabu-search based two heuristic algorithms are developed to handle realistic size problems with machine breakdowns. The results of extensive computational experiments are also provided.
Open Access
Green location and routing problems with conventional vehicles and drones
(Bilkent University, 2019-05) Dükkancı, Okan; Yetiş, Bahar
Green Location and Routing Problems extend the network design problems that consider location and routing decisions by explicitly accounting environmental impacts such as CO2 emissions caused by fuel or energy consumption of delivery vehicles. These environmental impacts estimated by fuel or energy consumption models are a ected by several factors including payload and speed of delivery vehicles. We present four new green location and routing problems where we consider these factors while calculating the environmental impacts. We rst introduce the Green Location-Routing Problem, in which vehicle payload and speed decisions are incorporated to a location-routing problem and the fuel consumption of trucks is estimated and minimized. Second, we study the Green Hub Location Problem, where we minimize the fuel consumption by optimizing truck payload and speed decisions on a hub network. Third, we present a freight transportation problem called the Drone Delivery Problem, where the integration of trucks and drones is used to make deliveries. Drone speed is considered as a decision of the problem in order to minimize energy consumption of drones while not exceeding the drone range. Fourth, we study an extension of the Drone Delivery Problem, called the Stochastic Drone Delivery Problem, where uncertainty of wind speed and its impact on the drone speed are considered.
Open Access
Hub & regenerator location and survivable network design
(Bilkent University, 2010) Özkök, Onur; Karaşan, Oya Ekin
With the vast development of the Internet, telecommunication networks are employed in numerous different outlets. In addition to voice transmission, which is a traditional utilization, telecommunication networks are now used for transmission of different types of data. As the amount of data transmitted through the network increases, issues such as the survivability and the capacity of the network become more imperative. In this dissertation, we deal with both design and routing problems in telecommunications networks. Our first problem is a two level survivable network design problem. The topmost layer of this network consists of a backbone component where the access equipments that enable the communication of the local access networks are interconnected. The second layer connects the users on the local access network to the access equipments, and consequently to the backbone network. To achieve a survivable network, one that stays operational even under minor breakdowns, the backbone network is assumed to be 2-edge connected while local access networks are to have the star connectivity. Within the literature, such a network is referred to as a 2-edge connected/star network. Since the survivability requirements of networks may change based on the purposes they are utilized for, a variation of this problem in which local access networks are also required to be survivable is also analyzed. The survivability of the local access networks is ensured by providing two connections for every component of the local access networks to the backbone network. This architecture is known as dual homing in the literature. In this dissertation, the polyhedral analysis of the two versions of the two level survivable network design problem is presented; separation problems are analyzed; and branch-and-cut algorithms are developed to find exact solutions. The increased traffic on the telecommunications networks requires the use of high capacity components. Optical networks, composed of fiber optical cables, offer solutions with their higher bandwidths and higher transmission speeds. This makes the optical networks a good alternative to handle the rapid increase in the data traffic. However, due to signal degradation which makes signal regeneration necessary introduces the regenerator placement problem as signal regeneration is a costly process in optical networks. In the regenerator placement problem, we study a location and routing problem together on the backbone component of a given telecommunications network. Survivability is also considered in this problem simultaneously. Exact solution methodologies are developed for this problem: mathematical models and some valid inequalities are proposed; separation problems for the valid inequalities are analyzed and a branch-and-cut algorithm is devised.
Open Access
Hub location and Hub network design
(Bilkent University, 2009) Alumur, Sibel Alev; Kara, Bahar Y.
he hub location problem deals with finding the location of hub facilities and allocating the demand nodes to these hub facilities so as to effectively route the demand between origin–destination pairs. Hub location problems arise in various application settings in telecommunication and transportation. In the extensive literature on the hub location problem, it has widely been assumed that the subgraph induced by the hub nodes is complete. Throughout this thesis we relax the complete hub network assumption in hub location problems and focus on designing hub networks that are not necessarily complete. We approach to hub location problems from a network design perspective. In addition to the location and allocation decisions, we also study the decision on how the hub network must be designed. We focus on the single allocation version of the problems where each demand center is allocated to a single hub node. We start with introducing the 3-stop hub covering network design problem. In this problem, we aim to design hub networks so that all origin– destination pairs receive service by visiting at most three hubs on a route. Then, we include hub network design decisions in the classical hub location problems introduced in the literature. We introduce the single allocation incomplete p-hub median, hub location with fixed costs, hub covering, and p-hub center network design problems to the literature. Lastly, we introduce the multimodal hub location and hub network design problem. We include the possibility of using different hub links, and allow for different transportation modes between hubs, and for different types of service time promises between origin–destination pairs, while designing the hub network in the multimodal problem. In this problem, we jointly consider transportation costs and travel times, which are studied separately in hub location problems presented in the literature. Computational analyses with all of the proposed models are presented on the various instances of the CAB data set and on the Turkish network.