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

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https://hdl.handle.net/11693/13886

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Open Access
Minimizing schedule length on identical parallel machines: an exact algorithm
(Bilkent University, 1991) Akyel, H. Cemal; Benli, Ömer S.
The primary concern of this study is to investigate the combinatorial aspects of the single-stage identical parallel machine scheduling problem and to develop a computationally feasible branch and bound algorithm for its exact solution. Although there is a substantial amount of literature on this problem, most of the work in this area is on the development and performance analysis of approximation algorithms. The few optimizing algorithms proposed in the literature have major drawbacks from the computer implementation point of view. Even though the single-stage scheduling problem is known to be unary A/’P-hard, there is still a need to develop a computationally feasible optimizing algorithm that solves the problem in a reasonable time. Development of such an algorithm is necessary for solving the multi-stage parallel machine scheduling problems which are currently an almost untouched issue in the deterministic scheduling theory. In this study, a branch and bound algorithm for the single-stage identical parallel machine scheduling problem is proposed. Promising results were obtained in the empirical analysis of the performance of this algorithm. Furthermore, the procedure that is developed to determine tight bounds at a node of the enumeration tree, is an approximation algorithm that solves a special class of identical parallel machine scheduling problems of practical interest. This algorithm delivers a solution that is arbitrarily close to 4/3 times the optimum. To our knowledge this is the best result obtained for this problem so far.
Open Access
Order quantity and pricing decisions in linear cost inventory systems
(Bilkent University, 1992) Polatoglu, Lutfi Hakan; Dinçer, Cemal
The primary concern of this study is to reveal the fundamental characteristics of the linear cost inventory model where price is a decision variable in addition to procurement quantity. In this context, the optimal solution must not only strike a balance between leftovers and shortages, but also simultaneously search for the best pricing alternative within the low price high demand and high price low demand tradeoff. To some extent, this problem has been studied in the literature. However, it seems that, there is a need to improve the model in order to understand the decision process better. To this end, optimal decisions must be characterised under a more general problem setting than it has been assumed in the existing models. In this study, we employ such a general model. The overall decision problem can be formulated under a dynamic programming structure. It follows that, the single period model is the basis of this periodic decision model. For this reason, we concentrate first on this problem. Having characterised the optimal solution to this basic model we extend the decision model to account for the multi-period setting. It is established with the results of this study that the decision problem in question is understood better. It is found that the characteristics of the optimal decision under the proposed model can be substantially different from the properties of the optimal solution of the corresponding classical model where there is no pricing decision. The primary reason for this is the fact that when there is a shortage in any period, the price that is set in this period could affect the future revenue which must be accounted in the overall decision problem. That is in a general model, price is an information which has an economic value that is transferred from one period to another just like transfering inventories or backlogs to future periods.
Open Access
Single machine scheduling problems: early-tardy penalties
(Bilkent University, 1993) Oguz, Ceyda; Dinçer, Cemal
The primary concern of this dissertation is to analyze single machine total earliness and tardiness scheduling problems with different due dates and to develop both a dynamic programming formulation for its exact solution and heuristic algorithms for its approximate solution within acceptable limits. The analyses of previous works on the single machine earliness and tardiness scheduling problems reveal that the research mainly focused on a restricted problem type in which no idle time insertion is allowed in the schedule. This study deals with the general case where idle time insertion is allowed whenever necessary. Even though this problem is known to be A'P-hard in the ordinary sense, there is still a need to develop an optimizing algorithm through dynamic programming formulation. Development of such an algorithm is necessary for further identifying an approximation scheme for the problem which is an untouched issue in the earliness and tardiness scheduling theory. Furthermore, the developed dynamic programming formulation is extended to an incomplete dynamic programming which forms the core of one of the heuristic procedure proposed.A second aspect of this study is to investigate two special structures for the different due dates, namely Equal-Slack and Total-Work-Content rules, and to discuss computational complexity of the problem with these special structures. Consequently, solution procedures which bear on the characteristics of the special due date structures are proposed. This research shows that the total earliness and tardiness scheduling problem with Equal-Slack rule is A/’P-hard but can be solvable in polynomial time in certain cases. Moreover, a very efficient heuristic algorithm is proposed for the problem with the other due date structure and the results of this part leads to another heuristic algorithm for the general due date structure. Finally, a lower bound procedure is presented which is motivated from the structure of the optimal solution of the problem. This lower bound is compared with another lower bound from the literature and it is shown that it performs well on randomly generated problems.
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
Polyhedral Approaches to Hypergraph Partitioning and Cell Formation
(Bilkent University, 1994) Kandiller, Levent; Akgül, Mustafa
Hypergraphs are generalizations of graphs in the sense that each hyperedge can connect more than two vertices. Hypergraphs are used to describe manufacturing environments and electrical circuits. Hypergraph partitioning in manufacturing models cell formation in Cellular Manufacturing systems. Moreover, hypergraph partitioning in VTSI design case is necessary to simplify the layout problem. There are various heuristic techniques for obtaining non-optimal hypergraph partitionings reported in the literature. In this dissertation research, optimal seeking hypergraph partitioning approaches are attacked from polyhedral combinatorics viewpoint. There are two polytopes defined on r-uniform hypergraphs in which every hyperedge has exactly r end points, in order to analyze partitioning related problems. Their dimensions, valid inequality families, facet defining inequalities are investigated, and experimented via random test problems. Cell formation is the first stage in designing Cellular Manufacturing systems. There are two new cell formation techniques based on combinatorial optimization principles. One uses graph approximation, creation of a flow equivalent tree by successively solving maximum flow problems and a search routine. The other uses the polynomially solvable special case of the one of the previously discussed polytopes. These new techniques are compared to six well-known cell formation algorithms in terms of different efficiency measures according to randomly generated problems. The results are analyzed statistically.
Open Access
Modelling and analysis of pull production systems
(Bilkent University, 1995) Kırkavak, Nureddin; Dinçer, Cemal
A variety of production systems appearing in the literature are reviewed in order to develop a classification scheme for production systems. A number of pull production systems appearing in the classification are found to be equivalent to a tandem queue so that accurate tandem queue decomposition methods can be used to find the performance of such systems. The primary concern of this dissertation is to model and analyze non-tandem queue equivalent periodic pull production systems. In this research, an exact performance evaluation model is developed for a singleitem periodic pull production system. The processing and demand interarrival times are assumed to be Markovian. For large systems, which are difficult to evaluate exactly because of large state spaces involved, an approximate decomposition method is proposed. A typical approximate decomposition procedure takes individual stages or pairs of stages in isolation to analyze the system and then it aggregates the results to obtain an approximate performance for the whole system. An experiment is designed in order to investigate the general behavior of the decomposition. The results are worth attention. A second aspect of this study is to investigate an allocation methodology to achieve the maximum throughput rate with providing two sets of allocation parameters regarding the number of kanbans and the workload at each stage of the system. Together with some structural properties, the experimental results provide some insight into the behavior of pull production systems and also provide a basis for the proposed allocation methodology. Finally, we conclude our findings together with some directions for future research.
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
Modeling and analysis of issues in hub location problem
(Bilkent University, 1999) Kara, Bahar Yetiş; Tansel, Barbaros Ç.
The hub location problem has been around for more than 10 years. The first mathematical model was formulated by O’Kelly (1986) which is a quadratic integer program. Since then, nearly all of the researchers in this area have concentrated on developing ’good’ linearizations. However, there are many aspects of the problem that need to be analyzed. In this dissertation, we investigate some of these issues. We first study the application areas of the hub location problem and clarify the underlying assumptions of the real world problems which lead to the customarily defined hub location problem. We identify a certain problem characteristic of cargo delivery systems, which is one of the major application areas of the hub location problem, which is not satisfactorily modeled by means of the customarily defined hub location models. We propose a new hub location model that captures the specific requirements that are particular to cargo delivery systems. Another issue that we concentrate on is the identification, modeling and analysis of the hub location problem under different performance measures, namely minimax and covering criteria. We propose new integer programming models for the hub location problem under minimax and covering objectives. Both of the new models are the result of a different way of approaching the problem and their computational performance is far more superior than the performance of the various linearizations of the basic models proposed for these problems in the literature.
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
Essays on scheduling with controllable processing times in flexible manufacturing systems
(Bilkent University, 2003) Türkcan, Ayten
Open Access
Parameter estimation in switching stochastic models
(Bilkent University, 2004) Güleryüz, Güldal; Gürler, Ülkü
In this thesis, we suggest an approach to statistical parameter estimation when an estimator is constructed by the trajectory observations of a stochastic system and apply the approach to reliability models. We analyze the asymptotic properties of the estimators constructed by the trajectory observations using moments method, maximum likelihood method and least squares method. Using limit theorems for Switching Processes and the results for parameter estimation by trajectory observations, we study the behavior of moments method estimators which are constructed by the observations of a trajectory of a switching process and prove the consistency and asymptotic normality of such estimators. We consider four different reliability models with large number of devices. For each of the models, we represent the system process as a Switching Process and prove that the system process converges to the solution of a differential equation. We also prove the consistency of the moments method estimators for each model. Simulation results are also provided to support asymptotic results and to indicate the applicability of the approach to finite sample case for reliability models.
Open Access
Stochastic joint replenishment problem : a new policy and analysis for single location and two eclehon inventory systems
(Bilkent University, 2005) Yüksel Özkaya, Banu; Gürler, Ülkü
In this study we examine replenishment coordination strategies for multiple item or multiple location inventory systems In particular we propose a new parsimonious control policy for the stochastic joint replenishment problem We rst study the single location setting with multiple items under this policy An extensive numerical study indicates that the proposed policy achieves signi cant cost improvements in comparison with the existing policies The single location model also represents a two echelon supply chain for a single item with multiple locations where the upper echelon employs cross docking We then extend our model to incorporate multi location settings where the upper echelon also holds inventory Our modeling methodology based on the development of the ordering process by the lower echelon provides an analytical tool to investigate various joint replenishment policies An extensive numerical study is conducted to determine the performance of the system and identify regions of dominance across policies Keywords S
Open Access
Optimization of transportation requirements in the deployment of military units
(Bilkent University, 2005) Akgün, İbrahim; Tansel, Barbaros Ç.
We study the deployment planning problem (DPP) that may roughly be defined as the problem of the planning of the physical movement of military units, stationed at geographically dispersed locations, from their home bases to their designated destinations while obeying constraints on scheduling and routing issues as well as on the availability and use of various types of transportation assets that operate on a multimodal transportation network. The DPP is a large-scale real-world problem for which no analytical models are existent. In this study, we define the problem in detail and analyze it with respect to the academic literature. We propose three mixed integer programming models with the objectives of cost, lateness (the difference between the arrival time of a unit and its earliest allowable arrival time at its destination), and tardiness (the difference between the arrival time of a unit and its latest arrival time at its destination) minimization to solve the problem. The cost-minimization model minimizes total transportation cost of a deployment and is of use for investment decisions in transportation resources during peacetime and for deployment planning in cases where the operation is not imminent and there is enough time to do deliberate planning that takes costs into account. The lateness and tardiness minimization models are of min-max type and are of use when quick deployment is of utmost concern. The lateness minimization model is for cases when the given fleet of transportation assets is sufficient to deploy units within their allowable time windows and the tardiness minimization model is for cases when the given fleet is not sufficient. We propose a solution methodology for solving all three models. The solution methodology involves an effective use of relaxation and restriction that significantly speeds up a CPLEX-based branchand-bound. The solution times for intermediate sized problems are around one hour at maximum for cost and lateness minimization models and around two hours for the tardiness minimization model. Producing a suboptimal feasible solution based on trial and error methods for a problem of the same size takes about a week in the current practice in the Turkish Armed Forces. We also propose a heuristic that is essentially based on solving the models incrementally rather than at one step. Computational results show that the heuristic can be used to find good feasible solutions for the models. We conclude the study with comments on how to use the models in the realworld.
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
Quadratic assignment problem : linearizations and polynomial time solvable cases
(Bilkent University, 2006) Erdoğan, Güneş; Tansel, Barbaros Ç.
The Quadratic Assignment Problem (QAP) is one of the hardest combinatorial optimization problems known. Exact solution attempts proposed for instances of size larger than 15 have been generally unsuccessful even though successful implementations have been reported on some test problems from the QAPLIB up to size 36. In this dissertation, we analyze the binary structure of the QAP and present new IP formulations. We focus on “flow-based” formulations, strengthen the formulations with valid inequalities, and report computational experience with a branch-and-cut algorithm. Next, we present new classes of instances of the QAP that can be completely or partially reduced to the Linear Assignment Problem and give procedures to check whether or not an instance is an element of one of these classes. We also identify classes of instances of the Koopmans-Beckmann form of the QAP that are solvable in polynomial time. Lastly, we present a strong lower bound based on Bender’s decomposition.
Open Access
Scheduling in flexible robotic manufacturing cells
(Bilkent University, 2006) Gültekin, Hakan; Aktürk, M. Selim
The focus of this thesis is the scheduling problems arising in robotic cells which consist of a number of machines and a material handling robot. The machines used in such systems for metal cutting industries are highly flexible CNC machines. Although flexibility is the key term that affects the performance of these systems, the current literature ignores this. As a consequence, the problems considered in the current literature are either too limiting or the provided solutions are suboptimal for the flexible systems. This thesis analyzes different robotic cell configurations with different sources of flexibility. This study is the first one to consider operation allocation problems and controllable processing times as well as some design problems and bicriteria models in the context of robotic cell scheduling. Also, a new class of robot move cycles is defined, which is overlooked in the existing literature. Optimal solutions are provided for solvable cases, whereas complexity analyses and efficient heuristic algorithms are provided for the remaining problems.
Open Access
Robust network design under polyhedral traffic uncertainty
(Bilkent University, 2007) Altın, Ayşegül; Pınar, Mustafa Ç.
In this thesis, we study the design of networks robust to changes in demand estimates. We consider the case where the set of feasible demands is defined by an arbitrary polyhedron. Our motivation is to determine link capacity or routing configurations, which remain feasible for any realization in the corresponding demand polyhedron. We consider three well-known problems under polyhedral demand uncertainty all of which are posed as semi-infinite mixed integer programming problems. We develop explicit, compact formulations for all three problems as well as alternative formulations and exact solution methods. The first problem arises in the Virtual Private Network (VPN) design field. We present compact linear mixed-integer programming formulations for the problem with the classical hose traffic model and for a new, less conservative, robust variant relying on accessible traffic statistics. Although we can solve these formulations for medium-to-large instances in reasonable times using off-the-shelf MIP solvers, we develop a combined branch-and-price and cutting plane algorithm to handle larger instances. We also provide an extensive discussion of our numerical results. Next, we study the Open Shortest Path First (OSPF) routing enhanced with traffic engineering tools under general demand uncertainty with the motivation to discuss if OSPF could be made comparable to the general unconstrained routing (MPLS) when it is provided with a less restrictive operating environment. To the best of our knowledge, these two routing mechanisms are compared for the first time under such a general setting. We provide compact formulations for both routing types and show that MPLS routing for polyhedral demands can be computed in polynomial time. Moreover, we present a specialized branchand-price algorithm strengthened with the inclusion of cuts as an exact solution tool. Subsequently, we compare the new and more flexible OSPF routing with MPLS as well as the traditional OSPF on several network instances. We observe that the management tools we use in OSPF make it significantly better than the generic OSPF. Moreover, we show that OSPF performance can get closer to that of MPLS in some cases. Finally, we consider the Network Loading Problem (NLP) under a polyhedral uncertainty description of traffic demands. After giving a compact multicommodity formulation of the problem, we prove an unexpected decomposition property obtained from projecting out the flow variables, considerably simplifying the resulting polyhedral analysis and computations by doing away with metric inequalities, an attendant feature of most successful algorithms on NLP. Under the hose model of feasible demands, we study the polyhedral aspects of NLP, used as the basis of an efficient branch-and-cut algorithm supported by a simple heuristic for generating upper bounds. We provide the results of extensive computational experiments on well-known network design instances.
Open Access
Service time optimization of flow shop systems
(Bilkent University, 2008) Selvi, Ömer; Gökbayrak, Kağan
One of the key questions that engineers face in áow shop systems is the service time control, i.e., how long jobs should be processed at each machine. This is an important question because processing times can have great impacts on the cost e¢ ciency of the áow shop systems. In order to meet job completion deadlines and to decrease inventory costs, one may set the service times as small as possible; however, this usually comes at the expense of reduced tool life increasing service costs. In this thesis, we study the áow shop systems under such trade-o§s. We consider the service time optimization of deterministic áow shop systems processing identical jobs that arrive at the system at known times and are processed in the order they arrive within deadlines. The cost function to be minimized consists of service costs at machines and regular completion-time costs of jobs. The decision variables are the service times that are controllable within constraints. We Örst consider the Öxed service time áow shop systems formed of initially controllable machines, where the service times are set only once at the start up time and cannot be altered between processes, and uncontrollable machines, where the service times are Öxed and known in advance. For such systems, we formulate a non-convex and non-di§erentiable optimization problem with a standard solution procedure based on the linearization of the constraints allowing for a convex optimization problem with high memory requirements. Regardless of the cost function, we present a set of waiting and completion time characteristics in such áow shop systems and employ them to derive a simpler equivalent convex optimization problem which improves solution times and alleviates the memory requirements enabling solutions for larger systems. However, the resulting simpliÖed convex optimization problem still needs the use of a convex optimization solver which may not be available at some of the manufacturing companies. To overcome such need, we introduce another equivalent convex optimization problem along with its subgradient algorithm yielding substantial improvements in solution times and solvable system sizes. We also consider a speciÖc nonlinear decreasing service cost structure allowing us to introduce a new search algorithm much faster than the subgradient solution algorithm. Building on the results for Öxed service time áow shop systems, we also consider the mixed line áow shop systems formed of fully controllable machines, where the service times are adjustable for each process, initially controllable machines, and uncontrollable machines. Similarly, we formulate a non-convex and non-di§erentiable optimization problem for such systems and, as a standard way of solving the formulated problem, we apply the method of linearization on the constraints to present a convex optimization problem with high memory requirements. Then, we present a set of optimal waiting characteristics in such áow shop systems and employ them to derive simpler equivalent convex optimization problems. A "forward in time" algorithm is also proposed to decompose the resulting simpliÖed equivalent convex optimization problem into smaller convex optimization problems for the áow shop systems formed of only fully controllable and uncontrollable machines. The computational results demonstrate that the simpliÖcations and the decomposition not only improve the solution times considerably but also allow us to solve larger problems by alleviating memory constraints.
Open Access
Time/cost trade-offs in machine scheduling with controllable processing times
(Bilkent University, 2008) Gürel, Sinan; Aktürk, M. Selim
Processing time controllability is a critical aspect in scheduling decisions since most of the scheduling practice in industry allows controlling processing times. A very well known example is the computer numerically controlled (CNC) machines in flexible manufacturing systems. Selected processing times for a given set of jobs determine the manufacturing cost of the jobs and strongly affect their scheduling performance. Hence, when making processing time and scheduling decisions at the same time, one must consider both the manufacturing cost and the scheduling performance objectives. In this thesis, we have studied such bicriteria scheduling problems in various scheduling environments including single, parallel and non-identical parallel machine environments. We have included some regular scheduling performance measures such as total weighted completion time and makespan. We have considered the convex manufacturing cost function of CNC turning operation. We have provided alternative methods to find efficient solutions in each problem. We have particularly focused on the single objective problems to get efficient solutions, called the -constraint approach. We have provided efficient formulations for the problems and shown useful properties which led us to develop fast heuristics to generate set of efficient solutions. In this thesis, taking another point of view, we have also studied a conic quadratic reformulation of a machine-job assignment problem with controllable processing times. We have considered a convex compression cost function for each job and solved a profit maximization problem. The convexity of cost functions is a major source of difficulty in finding optimal integer solutions in this problem, but our strengthened conic reformulation has eliminated this difficulty. Our reformulation approach is sufficiently general so that it can also be applied to other mixed 0-1 optimization problems with separable convex cost functions.Our computational results demonstrate that the proposed conic reformulation is very effective for solving the machine-job assignment problem with controllable processing times to optimality. Finally, in this thesis, we have considered rescheduling with controllable processing times. In particular, we show that in contrast to fixed processing times, if we have the flexibility to control the processing times of the jobs, we can generate alternative reactive schedules in response to a disruption such as machine breakdown. We consider a non-identical parallel machining environment where processing times of the jobs are compressible at a certain cost which is a convex function of the compression on the processing time. When rescheduling, it is critical to catch up the initial schedule as soon as possible by reassigning the jobs to the machines and changing their processing times. On the other hand, one must keep the total cost of the jobs at minimum. We present alternative match-up scheduling problems dealing with this trade-off. We use the strong conic reformulation approach in solving these problems. We further provide fast heuristic algorithms.
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.