This paper presents integer programming models for the determination of(a) optimal sequences of wastewater treatment processes, and (b) minimum cost, energy efficient composite wall and roof structures. The first mode...
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This paper presents integer programming models for the determination of(a) optimal sequences of wastewater treatment processes, and (b) minimum cost, energy efficient composite wall and roof structures. The first model has been used to determine optimal sequences of wastewater treatment processes for a combined industrial and sanitary wastewater facility in Kuwait. The second model was used to assist design engineers in meeting government standards for the thermal resistance of building structures. Remarkably, the two models have essentially the same structure: a shortest path model with additional linear side constraints. The two practical applications are described and solved, and computational experience is discussed. (C) 1997 Elsevier Science B.V.
We consider the multiple bottleneck assignment problem which subsumes the well known min-sum and bottleneck assignment problems. The problem arises in the context of flexible manufacturing systems, where the objective...
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We consider the multiple bottleneck assignment problem which subsumes the well known min-sum and bottleneck assignment problems. The problem arises in the context of flexible manufacturing systems, where the objective is to maximize the throughput of a production system with several how shops, running in parallel, to produce a product. The problem is known to be strongly NP-hard. We propose a new algorithm for obtaining sharp lower bounds to the optimal objective value. Computational experiments are conducted to show the improvement over existing methods. (C) 1999 Elsevier Science B.V. All rights reserved.
In this paper we work on a multi-level network optimization problem that integrates into the same model important aspects of: (i) discrete facility location, (ii) topological network design, and (iii) network dimensio...
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In this paper we work on a multi-level network optimization problem that integrates into the same model important aspects of: (i) discrete facility location, (ii) topological network design, and (iii) network dimensioning. Potential applications for the model are discussed, stressing its growing importance. The multi-level network optimization problem treated is defined and a mathematical programming formulation is presented. We make use of a branch-and-bound algorithm based on Lagrangean relaxation lower bounds to introduce some new powerful auxiliary algorithms to exactly solve the problem. We conduct a set of computational experiments that indicate the quality of the proposed approach. (C) 1999 Elsevier Science B.V. All rights reserved.
In several resource allocation problems, one encounters transportation networks which may or may not be feasible, and which may also be accompanied by side constraints. In such contexts, one typically constructs some ...
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In several resource allocation problems, one encounters transportation networks which may or may not be feasible, and which may also be accompanied by side constraints. In such contexts, one typically constructs some dummy transportation arcs with associated penalties, which either serve the role of facilitating a convenient starting solution, or seeking a solution to an infeasible problem which minimizes the total flow on the dummy arcs. In either case, particularly when the original transportation problem is infeasible, one would like to know a preferably small lower bound on the dummy arc penalties which could be validly employed. This paper derives such a bound. Extensions to more general networks are also addressed. [ABSTRACT FROM AUTHOR]
This paper introduces the maximum benefit Chinese postman problem (MBCPP) and the maximum benefit traveling salesman problem (MBTSP). For the MBCPP a benefit is realized each time a link of a directed graph is travers...
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This paper introduces the maximum benefit Chinese postman problem (MBCPP) and the maximum benefit traveling salesman problem (MBTSP). For the MBCPP a benefit is realized each time a link of a directed graph is traversed. The MBCPP relaxes the constraint of the Chinese postman problem that each link be traversed at least once and finds a tour of maximum total net benefit. For the MBTSP a benefit is derived when a node is visited and a cost is incurred when a link is traversed. The MBTSP relaxes the constraint of the traveling salesman problem that each node be visited exactly (or at least) once and finds a tour of maximum total net benefit. Both problems are formulated as linear integer programming problems. A solution algorithm is given that repeatedly solves a relaxation of the formulation as a minimum cost flow problem using a branch-and-bound procedure. Computational examples are presented.
In t]his paper we model building evacuations by network flows with side constraints. Side constraints come from variable are capacities on some ares which are functions of flows in incident ares. In this context we st...
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In t]his paper we model building evacuations by network flows with side constraints. Side constraints come from variable are capacities on some ares which are functions of flows in incident ares. In this context we study maximum flow, minimum cost, and minimax objectives. For some special structured networks we propose 'greedy' algorithms for solving these problems. For more general network structures, solution procedures are recommended which take advantage of the network structures of the problems. [ABSTRACT FROM AUTHOR]
This paper describes the results of research, development and implementation of the Dynamic Interactive network Analysis System (DINAS) which enables the solution of various multi-objective transshipment problems with...
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This paper describes the results of research, development and implementation of the Dynamic Interactive network Analysis System (DINAS) which enables the solution of various multi-objective transshipment problems with facility location. DINAS utilizes an extension of the classical reference-point approach to handling multiple objectives. In this approach, the decision-maker (DM) forms his requirements in terms of aspiration and reservation levels, i.e., he specifies acceptable and required values for given objectives. For providing DINAS with solutions to single-objective problems, a special TRANSLOC solver was developed. It is based on the branch-and-bound scheme with a pioneering implementation of the simplex special ordered network (SON) algorithm with implicit representation of the VUB and SUB (variable and simple upper bound, respectively) constraints. A pilot version of the system is implemented on an IBM PC/XT microcomputer. DINAS is prepared as a menu-driven and easy-to-use system armed with a special network editor. [ABSTRACT FROM AUTHOR]
An algorithm is presented for determining the K best paths that may contain cycles in a directed network. The basic concept underlying the algorithm is quite simple: once the best path has been determined, it is excl...
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An algorithm is presented for determining the K best paths that may contain cycles in a directed network. The basic concept underlying the algorithm is quite simple: once the best path has been determined, it is excluded from the network in such a fashion that no new path is created and no more paths are excluded. This step leads to a larger network where all the paths except the best one can be determined. The method is repeated until the desired paths have been calculated. Computational results are presented, along with comparisons with other approaches for the classical problem. The proposed algorithm can be used not only for the classical K shortest paths problem, but also for ranking paths under a nonlinear objective function, as long as an algorithm for determining the best path exists.
Optimal transportation theory is an area of mathematics with real-world applications in fields ranging from economics to optimal control to machine learning. We propose a new algorithm for solving discrete transport (...
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Optimal transportation theory is an area of mathematics with real-world applications in fields ranging from economics to optimal control to machine learning. We propose a new algorithm for solving discrete transport (network flow) problems, based on classical auction methods. Auction methods were originally developed as an alternative to the Hungarian method for the assignment problem, so the classic auction-based algorithms solve integer-valued optimal transport by converting such problems into assignment problems. The general transport auction method we propose works directly on real-valued transport problems. Our results prove termination, bound the transport error, and relate our algorithm to the classic algorithms of Bertsekas and Castanon.
In this paper, we present an alternative multi-stage generalized upper bounds (GUB) based approach for detecting an embedded pure network structure in an LP problem. In order to identify a GUB structure, we use two di...
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In this paper, we present an alternative multi-stage generalized upper bounds (GUB) based approach for detecting an embedded pure network structure in an LP problem. In order to identify a GUB structure, we use two different approaches;the first is based on the notion of Markowitz merit count and the second exploits independent sets in the corresponding graphs. Our computational experiments show that the multi-stage GUB algorithm based on these approaches performs favourably when compared with other well known algorithms.
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