A branch, price, and cut approach to solving the maximum weighted independent set problem

The maximum weight-independent set problem (MWISP) is one of the most well-known and well-studied NP-hard problems in the field of combinatorial optimization. In the first part of the dissertation, I explore efficient branch-and-price (B&P) approaches to solve MWISP exactly. B&P is a useful integer-programming tool for solving NP-hard optimization problems. Specifically, I look at vertex- and edge-disjoint decompositions of the underlying graph. MWISPâÂÂs on the resulting subgraphs are less challenging, on average, to solve. I use the B&P framework to solve MWISP on the original graph G using these specially constructed subproblems to generate columns. I demonstrate that vertex-disjoint partitioning scheme gives an effective approach for relatively sparse graphs. I also show that the edge-disjoint approach is less effective than the vertex-disjoint scheme because the associated DWD reformulation of the latter entails a slow rate of convergence. In the second part of the dissertation, I address convergence properties associated with Dantzig-Wolfe Decomposition (DWD). I discuss prevalent methods for improving the rate of convergence of DWD. I also implement specific methods in application to the edge-disjoint B&P scheme and show that these methods improve the rate of convergence. In the third part of the dissertation, I focus on identifying new cut-generation methods within the B&P framework. Such methods have not been explored in the literature. I present two new methodologies for generating generic cutting planes within the B&P framework. These techniques are not limited to MWISP and can be used in general applications of B&P. The first methodology generates cuts by identifying faces (facets) of subproblem polytopes and lifting associated inequalities; the second methodology computes Lift-and-Project (L&P) cuts within B&P. I successfully demonstrate the feasibility of both approaches and present preliminary computational tests of each

A branch, price, and cut approach to solving the maximum weighted independent set problem

The maximum weight-independent set problem (MWISP) is one of the most well-known and well-studied NP-hard problems in the field of combinatorial optimization. In the first part of the dissertation, I explore efficient branch-and-price (B&P) approaches to solve MWISP exactly. B&P is a useful integer-programming tool for solving NP-hard optimization problems. Specifically, I look at vertex- and edge-disjoint decompositions of the underlying graph. MWISPâÂÂs on the resulting subgraphs are less challenging, on average, to solve. I use the B&P framework to solve MWISP on the original graph G using these specially constructed subproblems to generate columns. I demonstrate that vertex-disjoint partitioning scheme gives an effective approach for relatively sparse graphs. I also show that the edge-disjoint approach is less effective than the vertex-disjoint scheme because the associated DWD reformulation of the latter entails a slow rate of convergence. In the second part of the dissertation, I address convergence properties associated with Dantzig-Wolfe Decomposition (DWD). I discuss prevalent methods for improving the rate of convergence of DWD. I also implement specific methods in application to the edge-disjoint B&P scheme and show that these methods improve the rate of convergence. In the third part of the dissertation, I focus on identifying new cut-generation methods within the B&P framework. Such methods have not been explored in the literature. I present two new methodologies for generating generic cutting planes within the B&P framework. These techniques are not limited to MWISP and can be used in general applications of B&P. The first methodology generates cuts by identifying faces (facets) of subproblem polytopes and lifting associated inequalities; the second methodology computes Lift-and-Project (L&P) cuts within B&P. I successfully demonstrate the feasibility of both approaches and present preliminary computational tests of each

A nested branch and price approach to designing the circuit card assembly factory

Due to the character of the original source materials and the nature of batch digitization, quality control issues may be present in this document. Please report any quality issues you encounter to [email protected], referencing the URI of the item.Includes bibliographical references (leaves 42-43).Issued also on microfiche from Lange Micrographics.Industrial competition has placed a premium on prescribing the optimal design of a circuit card assembly factory. This problem is to prescribe the number of lines of each type, the line type to which each circuit card type is to be assigned and the machine that should place each component type that populates it. The primary objective is to minimize total cost. This thesis achieves five research objectives. It presents a realistic model of this design problem. It prescribes an optimal design using a nested branch-and-price approach. It then presents an extension of the model to address workload balancing. The thesis then develops an efficient solution technique to minimize the computational effort needed to balance workloads. Finally, it extends the deterministic models to address uncertainties related to workload and availability using chance constraints

A Branch-and-Price Approach for the Maximum Weight Independent Set Problem

The maximum weight independent set problem (MWISP) is one of the most well-known and well-studied problems in combinatorial optimization. This paper presents a novel approach to solve MWISP exactly by decomposing the original graph into vertex-induced sub-graphs. The approach solves MWISP for the original graph by solving MWISP on the sub-graphs in order to generate columns for a branch-and-price framework. The authors investigate different implementation techniques that can be associated with the approach and offer computational results to identify the strengths and weaknesses of each implementation technique

Design of international assembly systems and their supply chains under NAFTA

The purpose of this paper is to provide a decision support aid for the strategic design of an assembly system in the international business environment created by NAFTA. The strategic design problem is to prescribe a set of facilities, including their locations, technologies, and capacities, as well as strategic aspects of the supply chain, selecting suppliers; locating distribution centers; planning transportation modes; and allocating target levels (i.e., amounts) for production, assembly, and distribution. The objective is to maximize after-tax profits. This paper presents a mixed integer programming model that represents the complexities of the international design problem as well as relevant enterprise-wide decisions in the US-Mexico business environment under NAFTA. It deals with a broad set of design issues (e.g., bill-of-material restrictions, international financial considerations, and material flow through the entire supply chain) using effective modeling devices (e.g., linearizing non-linearities that arise in modeling transfer prices and allocating transportation charges). Examples demonstrate how managers might use the model as a decision support aid.Designing international assembly systems Designing international supply chains Strategic planning under NAFTA Modeling international business considerations Mixed integer programming

Current Perspectives on Treatment of Gram-Positive Infections in India: What Is the Way Forward?

The emerging antimicrobial resistance leading to gram-positive infections (GPIs) is one of the major public health threats worldwide. GPIs caused by multidrug resistant bacteria can result in increased morbidity and mortality rates along with escalated treatment cost and hospitalisation stay. In India, GPIs, particularly methicillin-resistant Staphylococcus aureus (MRSA) prevalence among invasive S. aureus isolates, have been reported to increase exponentially from 29% in 2009 to 47% in 2014. Apart from MRSA, rising prevalence of vancomycin-resistant enterococci (VRE), which ranges from 1 to 9% in India, has raised concerns. Moreover, the overall mortality rate among patients with multidrug resistant GPIs in India is reported to be 10.8% and in ICU settings, the mortality rate is as high as 16%. Another challenge is the spectrum of adverse effects related to the safety and tolerability profile of the currently available drugs used against GPIs which further makes the management and treatment of these multidrug resistant organisms a complex task. Judicious prescription of antimicrobial agents, implementation of antibiotic stewardship programmes, and antibiotic policies in hospitals are essential to reduce the problem of drug-resistant infections in India. The most important step is development of newer antimicrobial agents with novel mechanisms of action and favourable pharmacokinetic profile. This review provides a synopsis about the current burden, treatment options, and the challenges faced by the clinicians in the management of GPIs such as MRSA, Quinolone-resistant Staphylococcus, VRE, and drug-resistant pneumococcus in India