Organizational Unit:

H. Milton Stewart School of Industrial and Systems Engineering

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https://hdl.handle.net/1853/70758

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Organizational Unit

College of Engineering

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Organizational Unit

William M. Keck Virtual Factory Lab (VFL)

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https://finding-aids.library.gatech.edu/agents/corporate_entities/1032

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Publication Search Results

Now showing 1 - 10 of 25

Distributed integer programming

(Georgia Institute of Technology, 2017-08-15) Karabulut, Ezgi

In this thesis, we study distributed integer programming problems that involve multiple players with integer programming problems linked together with a common resource constraint. Our goal is to design decentralized algorithms that do not require a central processor to allocate the resource across the players to solve the overall problem. The algorithms that we design have optimality guarantees when applied to problems for which the marginal value of each additional resource is non-increasing. For problems that do not have this step-wise concave structure, we propose approximation algorithms and provide error bounds. We also perform experiments to evaluate the algorithms' average performance on problems without the desired structure. Finally, we consider the same problem in an online setting. We show that there exists no deterministic online algorithms for our problem that has the state of the art error bound. Therefore we propose a randomized decentralized online algorithm for our problem whose error bound matches the results in the literature.
Track layout accommodating dynamic routing in automated material handling systems

(Georgia Institute of Technology, 2016-05-10) Lee, Junho

Modern semiconductor fabrication facilities depend on automated material handling systems (AMHSs) to manage the processes and variations in time required to produce advanced semiconductor products. Unified AMHSs, which operate overhead hoist transport vehicles, support direct tool-to-tool transfers between different bays. AMHSs continue to use static routing, but dynamic routing schemes have been studied to improve traffic conditions. In this dissertation, we propose an approach integrating optimization and simulation to design a track layout of an AMHS employing dynamic routing. We present a network design problem accommodating alternative paths. Our formulation is based on a multi-commodity network design problem, and we add secondary flow variables to represent rerouted vehicles. The problem requires input data, especially a base graph and commodities, reflecting realistic traffic conditions. We use simulation to validate the design from the optimization problem and provide its input data. We obtain a solution design using a heuristic that combines optimization and simulation. Our computational results illustrate that the parameter that controls the uniqueness of alternative paths has a significant impact on the routing performance of vehicles.
Robust optimization with applications in maritime inventory routing

(Georgia Institute of Technology, 2015-02-20) Zhang, Chengliang

In recent years, the importance of incorporating uncertainty into planning models for logistics and transportation systems has been widely recognized in the Operations Research and transportation science communities. Maritime transportation, as a major mode of transport in the world, is subject to a wide range of disruptions at the strategic, tactical and operational levels. This thesis is mainly concerned with the development of robustness planning strategies that can mitigate the effects of some major types of disruptions for an important class of optimization problems in the shipping industry. Such problems arise in the creation and negotiation of long-term delivery contracts with customers who require on-time deliveries of high-value goods throughout the year. In this thesis, we consider the disruptions that can increase travel times between ports and ultimately affect one or more scheduled deliveries to the customers. Computational results show that our integrated solution procedure and robustness planning strategies can generate delivery plans that are both economical as well as robust against uncertain disruptions.
Congestion-aware dynamic routing in automated material handling systems

(Georgia Institute of Technology, 2014-08-20) Bartlett, Kelly K.

In semiconductor manufacturing, automated material handling systems (AMHSs) transport wafers through a complex re-entrant manufacturing process. In some systems, Overhead Hoist Transport (OHT) vehicles move throughout the facility on a ceiling-mounted track system, delivering wafers to machines and storage locations. To improve efficiency in such systems, this thesis proposes an adaptive dynamic routing approach that allows the system to self-regulate, reducing steady-state travel times by 4-6% and avoiding excessive congestion and deadlock. Our approach allows vehicles to be rerouted while in progress in response to changes in the location and severity of congestion as measured by edge traversal time estimates updated via exponential smoothing. Our proposed method is efficient enough to be used in a large system where several routing decisions are made each second. We also consider how the effectiveness of a AMHS layout differs between static and dynamic routing. We demonstrate that dynamic routing significantly reduces sensitivity to shortcut placement and allows an eight-fold increase in the number of shortcuts along the center loop. This reduces travel times by an additional 24%. To demonstrate the effectiveness of our proposed routing approach, we use a high-fidelity simulation of vehicle movement. To test the impact of routing methods on layout effectiveness, we developed an associated Excel-based automated layout generation tool that allows the efficient generation of thousands of candidate layouts. The user selects from among a set of modular templates to create a design and all simulation files are generated with the click of a button.
Topics in discrete optimization: models, complexity and algorithms

(Georgia Institute of Technology, 2013-08-12) He, Qie

In this dissertation we examine several discrete optimization problems through the perspectives of modeling, complexity and algorithms. We first provide a probabilistic comparison of split and type 1 triangle cuts for mixed-integer programs with two rows and two integer variables in terms of cut coefficients and volume cutoff. Under a specific probabilistic model of the problem parameters, we show that for the above measure, the probability that a split cut is better than a type 1 triangle cut is higher than the probability that a type 1 triangle cut is better than a split cut. The analysis also suggests some guidelines on when type 1 triangle cuts are likely to be more effective than split cuts and vice versa. We next study a minimum concave cost network flow problem over a grid network. We give a polytime algorithm to solve this problem when the number of echelons is fixed. We show that the problem is NP-hard when the number of echelons is an input parameter. We also extend our result to grid networks with backward and upward arcs. Our result unifies the complexity results for several models in production planning and green recycling including the lot-sizing model, and gives the first polytime algorithm for some problems whose complexities were not known before. Finally, we examine how much complexity randomness will bring to a simple combinatorial optimization problem. We study a problem called the sell or hold problem (SHP). SHP is to sell k out of n indivisible assets over two stages, with known first-stage prices and random second-stage prices, to maximize the total expected revenue. Although the deterministic version of SHP is trivial to solve, we show that SHP is NP-hard when the second-stage prices are realized as a finite set of scenarios. We show that SHP is polynomially solvable when the number of scenarios in the second stage is constant. A max{1/2,k/n}-approximation algorithm is presented for the scenario-based SHP.
Lower bounds for integer programming problems

(Georgia Institute of Technology, 2013-05-13) Li, Yaxian

Solving real world problems with mixed integer programming (MIP) involves efforts in modeling and efficient algorithms. To solve a minimization MIP problem, a lower bound is needed in a branch-and-bound algorithm to evaluate the quality of a feasible solution and to improve the efficiency of the algorithm. This thesis develops a new MIP model and studies algorithms for obtaining lower bounds for MIP. The first part of the thesis is dedicated to a new production planning model with pricing decisions. To increase profit, a company can use pricing to influence its demand to increase revenue, decrease cost, or both. We present a model that uses pricing discounts to increase production and delivery flexibility, which helps to decrease costs. Although the revenue can be hurt by introducing pricing discounts, the total profit can be increased by properly choosing the discounts and production and delivery decisions. We further explore the idea with variations of the model and present the advantages of using flexibility to increase profit. The second part of the thesis focuses on solving integer programming(IP) problems by improving lower bounds. Specifically, we consider obtaining lower bounds for the multi- dimensional knapsack problem (MKP). Because MKP lacks special structures, it allows us to consider general methods for obtaining lower bounds for IP, which includes various relaxation algorithms. A problem relaxation is achieved by either enlarging the feasible region, or decreasing the value of the objective function on the feasible region. In addition, dual algorithms can also be used to obtain lower bounds, which work directly on solving the dual problems. We first present some characteristics of the value function of MKP and extend some properties from the knapsack problem to MKP. The properties of MKP allow some large scale problems to be reduced to smaller ones. In addition, the quality of corner relaxation bounds of MKP is considered. We explore conditions under which the corner relaxation is tight for MKP, such that relaxing some of the constraints does not affect the quality of the lower bounds. To evaluate the overall tightness of the corner relaxation, we also show the worst-case gap of the corner relaxation for MKP. To identify parameters that contribute the most to the hardness of MKP and further evaluate the quality of lower bounds obtained from various algorithms, we analyze the characteristics that impact the hardness of MKP with a series of computational tests and establish a testbed of instances for computational experiments in the thesis. Next, we examine the lower bounds obtained from various relaxation algorithms com- putationally. We study methods of choosing constraints for relaxations that produce high- quality lower bounds. We use information obtained from linear relaxations to choose con- straints to relax. However, for many hard instances, choosing the right constraints can be challenging, due to the inaccuracy of the LP information. We thus develop a dual heuristic algorithm that explores various constraints to be used in relaxations in the Branch-and- Bound algorithm. The algorithm uses lower bounds obtained from surrogate relaxations to improve the LP bounds, where the relaxed constraints may vary for different nodes. We also examine adaptively controlling the parameters of the algorithm to improve the performance. Finally, the thesis presents two problem-specific algorithms to obtain lower bounds for MKP: A subadditive lifting method is developed to construct subadditive dual solutions, which always provide valid lower bounds. In addition, since MKP can be reformulated as a shortest path problem, we present a shortest path algorithm that uses estimated distances by solving relaxations problems. The recursive structure of the graph is used to accelerate the algorithm. Computational results of the shortest path algorithm are given on the testbed instances.
Cutting planes in mixed integer programming: theory and algorithms

(Georgia Institute of Technology, 2013-02-19) Tyber, Steven Jay

Recent developments in mixed integer programming have highlighted the need for multi-row cuts. To this day, the performance of such cuts has typically fallen short of the single-row Gomory mixed integer cut. This disparity between the theoretical need and the practical shortcomings of multi-row cuts motivates the study of both the mixed integer cut and multi-row cuts. In this thesis, we build on the theoretical foundations of the mixed integer cut and develop techniques to derive multi-row cuts. The first chapter introduces the mixed integer programming problem. In this chapter, we review the terminology and cover some basic results that find application throughout this thesis. Furthermore, we describe the practical solution of mixed integer programs, and in particular, we discuss the role of cutting planes and our contributions to this theory. In Chapter 2, we investigate the Gomory mixed integer cut from the perspective of group polyhedra. In this setting, the mixed integer cut appears as a facet of the master cyclic group polyhedron. Our chief contribution is a characterization of the adjacent facets and the extreme points of the mixed integer cut. This provides insight into the families of cuts that may work well in conjunction with the mixed integer cut. We further provide extensions of these results under mappings between group polyhedra. For the remainder of this thesis we explore a framework for deriving multi-row cuts. For this purpose, we favor the method of superadditive lifting. This technique is largely driven by our ability to construct superadditive under-approximations of a special value function known as the lifting function. We devote our effort to precisely this task. Chapter 3 reviews the theory behind superadditive lifting and returns to the classical problem of lifted flow cover inequalities. For this specific example, the lifting function we wish to approximate is quite complicated. We overcome this difficulty by adopting an indirect method for proving the validity of a superadditive approximation. Finally, we adapt the idea to high-dimensional lifting problems, where evaluating the exact lifting function often poses an immense challenge. Thus we open entirely unexplored problems to the powerful technique of lifting. Next, in Chapter 4, we consider the computational aspects of constructing strong superadditive approximations. Our primary contribution is a finite algorithm that constructs non-dominated superadditive approximations. This can be used to build superadditive approximations on-the-fly to strengthen cuts derived during computation. Alternately, it can be used offline to guide the search for strong superadditive approximations through numerical examples. We follow up in Chapter 5 by applying the ideas of Chapters 3 and 4 to high-dimensional lifting problems. By working out explicit examples, we are able to identify non-dominated superadditive approximations for high-dimensional lifting functions. These approximations strengthen existing families of cuts obtained from single-row relaxations. Lastly, we show via the stable set problem how the derivation of the lifting function and its superadditive approximation can be entirely embedded in the computation of cuts. Finally, we conclude by identifying future avenues of research that arise as natural extensions of the work in this thesis.
Optimization in maritime inventory routing

(Georgia Institute of Technology, 2012-11-13) Papageorgiou, Dimitri Jason

The primary aim of this thesis is to develop effective solution techniques for large-scale maritime inventory routing problems that possess a core substructure common in many real-world applications. We use the term “large-scale” to refer to problems whose standard mixed-integer linear programming (MIP) formulations involve tens of thousands of binary decision variables and tens of thousands of constraints and require days to solve on a personal computer. Although a large body of literature already exists for problems combining vehicle routing and inventory control for road-based applications, relatively little work has been published in the realm of maritime logistics. A major contribution of this research is in the advancement of novel methods for tackling problems orders of magnitude larger than most of those considered in the literature. Coordinating the movement of massive vessels all around the globe to deliver large quantities of high value products is a challenging and important problem within the maritime transportation industry. After introducing a core maritime inventory routing model to aid decision-makers with their coordination efforts, we make three main contributions. First, we present a two-stage algorithm that exploits aggregation and decomposition to produce provably good solutions to complex instances with a 60-period (two-month) planning horizon. Not only is our solution approach different from previous methods discussed in the maritime transportation literature, but computational experience shows that our approach is promising. Second, building on the recent successes of approximate dynamic programming (ADP) for road-based applications, we present an ADP procedure to quickly generate good solutions to maritime inventory routing problems with a long planning horizon of up to 365 periods. For instances with many ports (customers) and many vessels, leading MIP solvers often require hours to produce good solutions even when the planning horizon is limited to 90 periods. Our approach requires minutes. Our algorithm operates by solving many small subproblems and, in so doing, collecting and learning information about how to produce better solutions. Our final research contribution is a polyhedral study of an optimization problem that was motivated by maritime inventory routing, but is applicable to a more general class of problems. Numerous planning models within the chemical, petroleum, and process industries involve coordinating the movement of raw materials in a distribution network so that they can be blended into final products. The uncapacitated fixed-charge transportation problem with blending (FCTPwB) that we study captures a core structure encountered in many of these environments. We model the FCTPwB as a mixed-integer linear program and derive two classes of facets, both exponential in size, for the convex hull of solutions for the problem with a single consumer and show that they can be separated in polynomial time. Finally, a computational study demonstrates that these classes of facets are effective in reducing the integrality gap and solution time for more general instances of the FCTPwB.
Optimization of automated float glass lines

(Georgia Institute of Technology, 2010-12-20) Na, Byungsoo

Motivated by operational issues in real-world glass manufacturing, this thesis addresses a problem of laying out and sequencing the orders so as to minimize wasted glass, called scrap. This optimization problem combines aspects of traditional cutting problems and traditional scheduling and sequencing problems. In so far as we know, the combination of cutting and scheduling has not been modeled, or solved. We propose a two-phase approach: snap construction and constructing cutting and offload schedules. Regarding the second phase problem, we introduce FGSP (float glass scheduling problem), and provide its solution structure, called coveys. We analyze simple sub-models of FGSP considering the main elements: time, unit, and width. For each model, we provide either a polynomial time algorithm or a proof of NP-completeness. Since FGSP is NP-complete, we propose a heuristic algorithm, Longest Unit First (LUF), and analyze the worst case performance of the algorithm in terms of the quality of solutions; the worst case performance bound is {1+(m-1)/m}+{1/3-1/(3m)} where m is the number of machines. It is 5/3 when m=2. For the real-world problem, we propose two different methods for snap construction, and we apply two main approaches to solve cutting and offloading schedules: an MIP approach and a heuristic approach. Our solution approach produces manufacturing yields greater than 99%; current practice is about 95%. This is a significant improvement and these high-yield solutions can save millions of dollars.
Time decomposition of multi-period supply chain models

(Georgia Institute of Technology, 2010-08-04) Toriello, Alejandro

Many supply chain problems involve discrete decisions in a dynamic environment. The inventory routing problem is an example that combines the dynamic control of inventory at various facilities in a supply chain with the discrete routing decisions of a fleet of vehicles that moves product between the facilities. We study these problems modeled as mixed-integer programs and propose a time decomposition based on approximate inventory valuation. We generate the approximate value function with an algorithm that combines data fitting, discrete optimization and dynamic programming methodology. Our framework allows the user to specify a class of piecewise linear, concave functions from which the algorithm chooses the value function. The use of piecewise linear concave functions is motivated by intuition, theory and practice. Intuitively, concavity reflects the notion that inventory is marginally more valuable the closer one is to a stock-out. Theoretically, piecewise linear concave functions have certain structural properties that also hold for finite mixed-integer program value functions. (Whether the same properties hold in the infinite case is an open question, to our knowledge.) Practically, piecewise linear concave functions are easily embedded in the objective function of a maximization mixed-integer or linear program, with only a few additional auxiliary continuous variables. We evaluate the solutions generated by our value functions in a case study using maritime inventory routing instances inspired by the petrochemical industry. The thesis also includes two other contributions. First, we review various data fitting optimization models related to piecewise linear concave functions, and introduce new mixed-integer programming formulations for some cases. The formulations may be of independent interest, with applications in engineering, mixed-integer non-linear programming, and other areas. Second, we study a discounted, infinite-horizon version of the canonical single-item lot-sizing problem and characterize its value function, proving that it inherits all properties of interest from its finite counterpart. We then compare its optimal policies to our algorithm's solutions as a proof of concept.