The National Collegiate Athletic Association Men’s Basketball Tournament is a 65-team championship in American college basketball, in which a single team is eliminated in a play-in game, followed by a six-round, sing...
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This paper concerns roundwood transport on gravel roads. The forest sector in Sweden has identified the road quality as a major problem, in particular in the spring, when the ground is thawing. The model simultaneousl...
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This paper concerns roundwood transport on gravel roads. The forest sector in Sweden has identified the road quality as a major problem, in particular in the spring, when the ground is thawing. The model simultaneously optimizes roundwood transport and road investments on gravel roads. The model is a mixed-integer programming model, since the road accessibility variables need to be binary. Investments in surface roads, maintenance and construction of new roads are not included in the model. We test the model with a sample problem using a small area. With a simple heuristic method 'near to optimal' solutions are obtained in reasonable time. In the last section we make some concluding remarks and discuss future use of the model. Heuristics and aggregation are two different ways to solve the problem in reasonable time. (c) 2004 Elsevier B.V. All rights reserved.
T he current airline practice in conducting fleet assignments is to begin assigning aircraft capacity to scheduled flights well in advance of departures. However, the accuracy of the passenger demand forecast improves...
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T he current airline practice in conducting fleet assignments is to begin assigning aircraft capacity to scheduled flights well in advance of departures. However, the accuracy of the passenger demand forecast improves markedly over time, and revisions to the initial fleet assignment become naturally pertinent when the observed demand differs considerably from the assigned aircraft capacities. The demand-driven refleeting (DDR) approach proposed in this paper offers a dynamic reassignment of aircraft capacities to the flight network, when improved demand forecasts become available, so as to maximize the total revenue. Because of the need to preserve the initial crew schedule, this reassignment approach is limited within a single family of aircraft types and to the flights assigned to this particular family. This restriction makes it computationally tractable to include more relevant path-level demand information into the DDR model. Accordingly, we construct a mixed-integer programming model for this enhanced problem context and study its polyhedral structure to explore ways for tightening its representation and for deriving certain classes of valid inequalities. Various schemes for implementing such reformulation techniques are investigated and tested using a set of simulated and real instances obtained from United Airlines.
The generalized vertex packing problem seeks to identify a largest subset of nodes from an undirected graph, such that the subgraph induced by this subset of nodes contains no more than some threshold number of edges....
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The generalized vertex packing problem seeks to identify a largest subset of nodes from an undirected graph, such that the subgraph induced by this subset of nodes contains no more than some threshold number of edges. This paper derives a class of valid inequalities based on certain special subgraphs called webs, which are general structures that subsume cliques, matchings, odd holes, and odd anti-holes. We also provide a set of conditions for this class of valid inequalities to be facet-inducing for the web subgraph polytope. Finally, we prescribe a web subgraph identification procedure. and test the computational benefits obtained by solving generalized vertex packing instances with formulations augmented by these web-based valid inequalities. (C) 2004 Elsevier B.V. All rights reserved.
This paper presents a decision support system for efficient service location design for an agency in the State of Michigan. We consider a total of 169 branch offices of the agency located in 79 counties that process a...
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This paper presents a decision support system for efficient service location design for an agency in the State of Michigan. We consider a total of 169 branch offices of the agency located in 79 counties that process a variety of transactions and provide services including automobile registrations, issuance of driver licenses, recreational vehicle registration, and personal identification registry. The proposed methodology and decision support system incorporate a number of factors such as branch office efficiencies based on multiple measures, budget restrictions, capacity limitations for processing transactions, and demand requirements in designing an efficient service system. Our approach employs data envelopment analysis (DEA) and mixed-integer programming (MIP) models. A series of experiments are conducted with the proposed model by varying, the levels of system-wide efficiency, resource reallocation, and budget in generating a set of decisions that executive management of the agency can implement. In addition, we investigate service channel management issues that the agency is currently facing in providing the services by web, phone, facsimile, and mail in addition to branch offices. We discuss how the branch closures influence channel management decisions. (C) 2004 Elsevier B.V. All rights reserved.
We propose an effective supplier selection method to maintain a continuous supply-relationship with suppliers. Costs have been sharply increasing and profit decreasing as the global competition among companies has inc...
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We propose an effective supplier selection method to maintain a continuous supply-relationship with suppliers. Costs have been sharply increasing and profit decreasing as the global competition among companies has increased and customer demands have diversified in the current business environment. Many other functions are now outsourced globally to strengthen competition. As a result, one of the issues is how to select good suppliers which can maintain a continuous supply-relationship. We suggest a mathematical programming model that considers the change in suppliers' supply capabilities and customer needs over a period in time. We design a model which not only maximizes revenue but also satisfies customer needs. The suggested model is applied to supplier selection and management of the agriculture industry in Korea. (c) 2005 Elsevier Ltd. All rights reserved.
mixed-integer Gomory cuts have become an integral part of state-of-the-art software for solving mixed-integer linear programming problems. Therefore, improvements in the performance of these cutting planes can be of g...
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mixed-integer Gomory cuts have become an integral part of state-of-the-art software for solving mixed-integer linear programming problems. Therefore, improvements in the performance of these cutting planes can be of great practical value. In this paper, we present a simple and fast heuristic for improving the coefficients on the continuous variables in the mixed-integer Gomory cuts. This is motivated by the fact that in a mixed-integer Gomory cut, the coefficient of an integer variable lies between 0 and 1, whereas for a continuous variable, there is no upper bound. The heuristic tries to reduce the coefficients of the continuous variables. We call the resulting cuts reduce-and-split cuts. We found that on several test problems, reduce-and-split cuts can substantially enhance the performance of a branch-and-bound algorithm.
This paper presents a review of advances in the mathematical programming approach to discrete/continuous optimization problems. We first present a brief review of MILP and MINLP for the case when these problems are mo...
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This paper presents a review of advances in the mathematical programming approach to discrete/continuous optimization problems. We first present a brief review of MILP and MINLP for the case when these problems are modeled with algebraic equations and inequalities. Since algebraic representations have some limitations such as difficulty of formulation and numerical singularities for the nonlinear case, we consider logic-based modeling as an alternative approach, particularly Generalized Disjunctive programming (GDP), which the authors have extensively investigated over the last few years. Solution strategies for GDP models are reviewed, including the continuous relaxation of the disjunctive constraints. Also, we briefly review a hybrid model that integrates disjunctive programming and mixed-integer programming. Finally, the global optimization of nonconvex GDP problems is discussed through a two-level branch and bound procedure.
This paper has as a major objective to present a unified overview and derivation of mixed-integer nonlinear programming (MINLP) techniques, Branch and Bound, Outer-Approximation, Generalized Benders and Extended Cutti...
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This paper has as a major objective to present a unified overview and derivation of mixed-integer nonlinear programming (MINLP) techniques, Branch and Bound, Outer-Approximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems that are expressed in algebraic form. The solution of MINLP problems with convex functions is presented first, followed by a brief discussion on extensions for the nonconvex case. The solution of logic based representations, known as generalized disjunctive programs, is also described. Theoretical properties are presented, and numerical comparisons on a small process network problem.
This paper presents a hybrid refinery scheduling system combining mathematical programming model and expert system. mixed-integer linear programming models for crude oil movement between units are merged into the expe...
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This paper presents a hybrid refinery scheduling system combining mathematical programming model and expert system. mixed-integer linear programming models for crude oil movement between units are merged into the expert system that is for qualitative issues concerning crude vessel unloading operations. The target problem ranging from the crude unloading to the crude charging to distillation towers is decomposed into several module problems for efficiency. Compared with existing scheduling approaches for oil movement, the proposed hybrid refinery scheduling system is very effective in dealing with timing decisions involving vessel unloading operations due to the advantages of an expert system. Since the proposed scheduling system can generate solutions so fast, it is expected to play a key role in the real processes.
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