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Maximum network flows with concave gains

MATHEMATICAL PROGRAMMING 2006年第3期107卷 439-459页

作者： Shigeno, M Univ Tsukuba Grad Sch Syst & Informat Engn Tsukuba Ibaraki 3058573 Japan

This paper deals with a generalized maximum flow problem with concave gains, which is a nonlinear network optimization problem. Optimality conditions and an algorithm for this problem are presented. The optimality conditions are extended from the corresponding results for the linear gain case. The algorithm is based on the scaled piecewise linear approximation and on the fat path algorithm described by Goldberg, Plotkin and Tardos for linear gain cases. The proposed algorithm solves a problem with piecewise linear concave gains faster than the naive solution by adding parallel arcs.

关键词： generalized networks flow algorithms nonlinear optimization

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Approximation algorithms for problems combining facility location and network design

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OPERATIONS RESEARCH 2006年第1期54卷 73-81页

作者： Ravi, R Sinha, A Carnegie Mellon Univ David A Tepper Sch Business Pittsburgh PA 15213 USA Univ Michigan Stephen M Ross Sch Business Ann Arbor MI 48109 USA

We present approximation algorithms for integrated logistics problems that combine elements of facility location and transport network design. We first study the problem where opening facilities incurs opening costs and transportation from the clients to the facilities incurs buy-at-bulk costs, and provide a combinatorial approximation algorithm. We also show that the integer-programming formulation of this problem has small integrality gap. We extend the model to the version when there is a bound on the number of facilities that may be opened.

关键词： facilities location discrete networks/graphs flow algorithms transportation models networks

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A multiperiod dynamic model of taxi services with endogenous service intensity

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OPERATIONS RESEARCH 2005年第3期53卷 501-515页

作者： Yang, H Ye, M Tang, WHC Wong, SC Hong Kong Univ Sci & Technol Dept Civil Engn Kowloon Hong Kong Peoples R China China Acad Urban Design & Planning Inst Beijing 100044 Peoples R China Univ Hong Kong Dept Civil Engn Hong Kong Hong Kong Peoples R China

This paper presents a spatially aggregated multiperiod taxi service model with endogenous service intensity. The whole day service period is divided into a number of subperiods;during each subperiod, taxi supply and customer demand characteristics are assumed to be uniform. Customer demand is period-specific and described as a function of waiting time and taxi fare. Taxi operating cost for each work shift consists of two components: one component a function of total service time and the other component period-dependent. Each taxi driver can work for one or more shifts each day and freely chooses the starting and ending time of each shift. Equilibrium of taxi services is obtained when taxi drivers cannot increase their individual profits by changing their individual working schedules. A novel clock network representation is proposed to characterize the multiperiod taxi service equilibrium problem. The problem of interest is formulated as a network equilibrium model with path-specific costs and arc-capacity constraints, which can be solved using conventional nonlinear network flow optimization methods. The proposed model can ascertain at equilibrium the service intensity and utilization rate of taxis and the level of service quality throughout the day. The information obtained is useful for the prediction of the effects of alternative government regulations on the equilibrium of demand and supply in the urban taxi industry.

关键词： transportation models taxis/limousines networks/graphs:applications flow algorithms

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A new algorithm for reoptimizing shortest paths when the arc costs change

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OPERATIONS RESEARCH LETTERS 2003年第2期31卷 149-160页

作者： Pallottino, S Scutellà, MG Univ Pisa Dipartimento Informat I-56125 Pisa Italy

We propose the first algorithmic. approach which reoptimizes the shortest paths when any subset of arcs of the input graph is affected by a change of the costs;which can be either lower or higher than the old ones. This situation is more general than the ones addressed in the literature so far. We analyze the worst case time. complexity of the algorithm as. a function of both the input size and the overall cost perturbation, and discuss cases for which the proposed reoptimization method theoretically outperforms the approach of,applying a standard shortest path algorithm-after the change of the arc costs. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： shortest paths reoptimization flow algorithms

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algorithms for source-to-all maximum cost-to-time ratio problem in acyclic networks

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NETWORKS 2003年第1期42卷 1-14页

作者： Makri, A Klabjan, D Univ Illinois Dept Mech & Ind Engn Urbana IL 61801 USA

The source-to-all maximum cost-to-time ratio problem is the problem of finding the maximum cost-to-time ratio path from a source node to every other node. The motivation comes from an application in large-scale linear programming. We present three algorithms for solving the problem. We give proofs of correctness and we analyze the running times. One of the algorithms is polynomial and the remaining two are pseudopolynomial. We present extensive computational results on several networks. (C) 2003 Wiley Periodicals, Inc.

关键词： networks graphs flow algorithms

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Solving inverse spanning tree problems through network flow techniques

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OPERATIONS RESEARCH 1999年第2期47卷 291-298页

作者： Sokkalingam, PT Ahuja, RK Orlin, JB CISCO CDC Ctr HCL Chennai India Univ Florida Gainesville FL 32611 USA MIT Cambridge MA 02139 USA

Given a solution x* and an a priori estimated cost vector c, the inverse optimization problem is to identify another cost vector d so that x* is optimal with respect to the cost vector d and its deviation from c is minimum. In this paper, we consider the inverse spanning tree problem on an undirected graph G = (N, A) with n nodes and m arcs, and where the deviation between c and d is defined by the rectilinear distance between the two vectors, that is, L-1 norm. We show that the inverse spanning tree problem can be formulated as the dual of an assignment problem on a bipartite network G(0) = (N-0, A(0)) with N-0 = N-1 boolean OR N-2 and A(0) subset of or equal to N-1 x N-2. The bipartite network satisfies the property that \N-1\ = (n - 1), \N-2\ = (m - n + 1), and \A(0)\ = O(nm). In general, \N-1\ much less than \N-2\. Using this special structure of the assignment problem, we develop a specific implementation of the successive shortest path algorithm that runs in O(n(3)) time. We also consider the weighted version of the inverse spanning tree problem in which the objective function is to minimize the sum of the weighted deviations of arcs. The weighted inverse spanning tree can be formulated as the dual of the transportation problem. Using a cost scaling algorithm, this transportation problem can be solved in O(n(2) mlog(nC)) time, where C denotes the largest are cost in the data. Finally, we consider a minimax version of the inverse spanning tree problem and show that it can be solved in O(n(2)) time.

关键词： networks/graphs flow algorithms minimum cost flow problem networks/graphs tree algorithms inverse spanning tree problem programming linear application of duality theory

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A tabu search heuristic procedure for the fixed charge transportation problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1998年第2-3期106卷 441-456页

作者： Sun, M Aronson, JE McKeown, PG Drinka, D Univ Texas Coll Business Div Management & Mkt San Antonio TX 78249 USA Univ Georgia Terry Coll Business Dept Management Athens GA 30602 USA Univ Alaska Anchorage Coll Business & Publ Policy Dept Comp Informat & Off Syst Anchorage AK 99508 USA

We develop a tabu search approach for the fixed charge transportation (FCT) problem using recency based and frequency based memories, together with two strategies for each of the intermediate and long term memory processes, making use of a network based implementation of the simplex method as the local search method. Our approach is evaluated computationally on randomly generated problems of different sizes and of different ranges of magnitude of fixed costs relative to variable costs. Comparisons are made with two leading methods previously proposed, one in the category of exact methods and one in the category of heuristic methods. Our tabu search procedure obtains optimal or near-optimal solutions more than a thousand times faster than the exact solution algorithm for simple problems and thoroughly dominates the exact algorithm on all dimensions for more complex problems. Compared to the heuristic approach, on very small and easy test problems the tabu search procedure required about the same amount of solution time and found solutions at least as good. However, for larger problems and for problems with higher fixed to variable costs, the tabu search procedure was 3-4 times faster than the competing heuristic, and found significantly better solutions in all cases. (C) 1998 Elsevier Science B.V. All rights reserved.

关键词： networks/graphs flow algorithms programming integer algorithms integer heuristic fixed charge transportation problem tabu search

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Proportional equity flow problem for terminal arcs

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OPERATIONS RESEARCH 1997年第4期45卷 521-535页

作者： Betts, LM Brown, JR KENT STATE UNIV KENTOH 44242 USA

The proportional equity dow problem extends a class of problems referred to as equity flow problems whose objective is to equitably distribute dow among the arcs in a how circulation network. The proportionally bounded dow circulation problem places lower and upper bounds on each are flow that are nondecreasing continuous functions of the flow through one special are, and the objective is to maximize the flow through the special arc. The proportional equity dow problem for terminal arcs (Problem TA) is then defined as a special case where all the proportional arcs enter a sink vertex. Applications of both the general problem and Problem TA are given. Two optimality conditions for Problem TA are developed, as well as an algorithm that is polynomially bounded for many types of nondecreasing, continuous, proportional bounding functions. Specifically, the algorithm is shown to be polynomially bounded if the largest root of an equation can be found in polynomial time.

关键词： networks/graphs flow algorithms proportional equity flow problems

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THE NETWORK SYNTHESIS PROBLEM IN A CYCLE

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OPERATIONS RESEARCH LETTERS 1995年第5期17卷 231-236页

作者： HOJATI, M College of Commerce University of Saskatchewan Saskatoon Sask. Canada S7N 0W0

The network synthesis problem is to design an undirected network with a minimum total construction cost which non-simultaneously satisfies given flow requirements between pairs of nodes. This well-known problem was introduced by Gomory and Hu (1961) who formulated it as a very large linear program and solved it by a method similar to column generation. We provide an efficient algorithm for this problem when the underlying graph is a cycle.

关键词： NETWORKS flow algorithms MULTITERMINAL DESIGN

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FIXED JOB SCHEDULING WITH 2 TYPES OF PROCESSORS

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OPERATIONS RESEARCH 1992年第1期40卷 S76-S85页

作者： DONDETI, VR EMMONS, H CASE WESTERN RESERVE UNIV CLEVELANDOH 44106

We consider a scheduling problem that involves two types of processors, but three types of jobs. Each job has a fixed start time and a fixed completion time, and falls into one of three types. Jobs of type 1 can be done only by type-1 processors, type-2 jobs only by type-2 processors, and type-0 jobs by either type of processors. We present a polynomial algorithm for finding the minimal cost combination of the two types of processors required to complete all jobs. The steps of the algorithm consist of constructing a job schedule network, transforming it into a single-commodity flow problem and finding the maximal flow through it.

关键词： networks/graphs flow algorithms flows and arc-disjoint paths of networks production/scheduling sequencing assigning two types of processors to three types

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