Solving the fixed charge problem with Lagrangian relaxation and cost allocation heuristics

Wright, Don D.; Lanzenauer, Christoph Haehling von

doi:10.1016/0377-2217(89)90441-4

Cited by 22 publications

(11 citation statements)

References 19 publications

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“…These methods take advantage of various strategies; some utilizing relaxation approaches (Wright et al, 1989 and1991) and others employing extreme point search techniques and embedded network procedures (Balinski, 1961;Kuhn and Baumol, 1961;Denzler, 1964;Dwyer, 1966;Cooper and Drebes, 1967;Cooper, 1975;Walker, 1976;Stienberg, 1970 andShetty, 1990;Diaby, 1991;Khang and Fujiwara, 1991;Sun and McKeown, 1993;Gottlieb and Eckert, 2002;Adlakha and Kowalski, 2003). A notable metaheuristic approach, a tabu search method by Sun et al (1998), has established itself as the best method for solving a collection of fixed-charge transportation network problems that constitutes the largest body of randomly generated problems in the literature.…”

Section: Fc-mip Minimize X O [Fc] = Cx + Fzmentioning

confidence: 99%

Parametric Ghost Image Processes for Fixed-Charge Problems: A Study of Transportation Networks

Glover

2005

J Heuristics

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We present a parametric approach for solving fixed-charge problems first sketched in Glover (1994). Our implementation is specialized to handle the most prominently occurring types of fixed-charge problems, which arise in the area of network applications. The network models treated by our method include the most general members of the network flow class, consisting of generalized networks that accommodate flows with gains and losses. Our new parametric method is evaluated by reference to transportation networks, which are the network structures most extensively examined, and for which the most thorough comparative testing has been performed. The test set of fixed-charge transportation problems used in our study constitutes the most comprehensive randomly generated collection available in the literature. Computational comparisons reveal that our approach performs exceedingly well. On a set of a dozen small problems we obtain ten solutions that match or beat solutions found by CPLEX 9.0 and that beat the solutions found by the previously best heuristic on 11 out of 12 problems. On a more challenging set of 120 larger problems we uniformly obtain solutions superior to those found by CPLEX 9.0 and, in 114 out of 120 instances, superior to those found by the previously best approach. At the same time, our method finds these solutions while on average consuming 100 to 250 times less CPU time than CPLEX 9.0 and a roughly equivalent amount of CPU time as taken by the previously best method.

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Section: Fc-mip Minimize X O [Fc] = Cx + Fzmentioning

confidence: 99%

Parametric Ghost Image Processes for Fixed-Charge Problems: A Study of Transportation Networks

Glover

2005

J Heuristics

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“…Nemhauser and Wolsey (1988) and Bienstock and Günlük (1996)) may also be used to solve the FCTP. Wright and Haehling von Lanzenauer (1989) develop a Lagrangian heuristic for the FCTP which is based on relaxing the variable upper bound constraints Xij < Uijyij. It can be proved that an optimal Solution to the FCTP is an extreme point of the convex region defined by constraints (4b)-(4d) (see Hirsch and Dantzig (1968)).…”

Section: Fixed-charge Transportation Problemmentioning

confidence: 99%

Combinatorial Optimisation Problems of the Assignment Type and a Partitioning Approach

Klose

Drexl

2002

Lecture Notes in Economics and Mathematical Systems

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract Assignment type problems consist in optimally assigning or allocating a given set of "activities" to a given set of "resources". Optimisation problems of the assignment type have numerous applications in production planning and logistics. A populär approach to solve such problems or to compute lower b ounds on the optimal Solution value (in case of a minimisation problem) is to employ column generation. By means of co nsidering subsets of "activities" which can feasibly be assigned to a Single resource, the problem is reformulated as some kind of set-partitioning problem. Column generation is then used in order to solve the linear relaxation of the reformulation. The lower bound obtainable from this approach may, however, be improved by partitioning the set of resources into subsets and by considering subsets of activities which can feasibly be assigned to subsets of resources. This paper outlines the application of this partitioning method to a number of important combinatorial optimisation problems of the assignment type. Terms of use: Documents in EconStor may

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“…Other heuristic methods that must be emphasized are the Lagrangean heuristic method of Wright et al (1989Wright et al ( , 1991, the tabu search heuristic procedure (TS) of Sun et al (1998) and the recently proposed parametric ghost image processes (GIP) of Glover et al (2005).…”

Section: Introductionmentioning

confidence: 99%

Fixed Charge Transportation Problems: a new heuristic approach based on Lagrangean relaxation and the solving of core problems

Aguado

2008

Ann Oper Res

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In this paper the Fixed Charge Transportation Problem is considered. A new heuristic approach is proposed, based on the intensive use of Lagrangean relaxation techniques. The more novel aspects of this approach are new Lagrangean relaxation and decomposition methods, the consideration of several core problems, defined from the previously computed Lagrangean reduced costs, the heuristic selection of the most promising core problem and the final resort to enumeration by applying a branch and cut algorithm to the selected core problem. For problems with a small ratio of the average fixed cost to the average variable cost (lower than or equal to 25), the proposed method can obtain similar or better solutions than the state-of-art algorithms, such as the tabu search procedure and the parametric ghost image processes. For larger ratios (between 50 and 180), the quality of the obtained solutions could be considered to be halfway between both methods.

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Solving the fixed charge problem with Lagrangian relaxation and cost allocation heuristics

Cited by 22 publications

References 19 publications

Parametric Ghost Image Processes for Fixed-Charge Problems: A Study of Transportation Networks

Parametric Ghost Image Processes for Fixed-Charge Problems: A Study of Transportation Networks

Combinatorial Optimisation Problems of the Assignment Type and a Partitioning Approach

Fixed Charge Transportation Problems: a new heuristic approach based on Lagrangean relaxation and the solving of core problems

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