A simple heuristic for solving small fixed-charge transportation problems

Adlakha, Veena; Kowalski, Krzysztof

doi:10.1016/s0305-0483(03)00025-2

Cited by 97 publications

(54 citation statements)

References 16 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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“…Syarif et al (2002) presented spanning tree-based GA using Prufer number representation to study the choice of facilities to be opened and the distribution network designed to satisfy the customer demand with minimum cost. Adlakha and Kowalski (2003) proposed a simple heuristic algorithm for solving small FCTP. However, it is stated that the proposed method is more time consuming than the algorithms for solving a regular transportation problem.…”

Section: Literature Reviewmentioning

confidence: 99%

Glowworm swarm optimisation algorithm for nonlinear fixed charge transportation problem in a single stage supply chain network

Manimaran¹,

Selladurai²

2014

IJLEG

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Abstract:In this paper, Glowworm swarm optimisation (GSO) is proposed to solve nonlinear fixed charge transportation problem (NLFCTP) in a single stage supply chain network. In a fixed charge transportation problem, fixed cost is incurred for every route, along with the variable cost that is proportional to the amount shipped. In some cases, the variable cost is associated with quadratic variables in which the cost function will be nonlinear. This problem is more difficult to solve due to presence of the fixed costs that result in discontinuities in the objective function. The objective of this paper is to determine the least cost transportation plan that minimises the total variable and fixed costs while satisfying the supply and demand requirements of each plant and customer. The performance of GSO is compared in terms of total distribution cost with a spanning tree-based genetic algorithm. The comparison reveals that GSO provides better solutions.Keywords: distribution problem; glowworm swarm optimisation; GSO; fixed cost; NP-hard; supply chain.Reference to this paper should be made as follows: Manimaran, P. and Selladurai, V. (2014) 'Glowworm swarm optimisation algorithm for nonlinear fixed charge transportation problem in a single stage supply chain network', Int.

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“…(10)(11) Sun et al (12) proposed a Tabu search method. Whereas Palekar et al (13) attempted to provide exact algorithms based on the branch-and-bound method, Adlakha, V. and K. Kowalski (14) presents a simple algorithm for the solution of small, fixed-charge problems. Ever since the genetic algorithms (GAs) was introduced by Holland (15) to tackle linear and nonlinear optimization problems, it has emerged as one of the most efficient stochastic solution search procedures for solving various network design problems in supply chains and other fields (16) .…”

Section: Introductionmentioning

confidence: 99%

Case Study on Optimal Routing in Logistics Network by Priority-based Genetic Algorithm

et al. 2007

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The definition of logistics adopted by the Council of Logistics Management is "the process of planning, implementing, and controlling the efficient, effective flow and storage of goods, services, and related information from point of origin to point of consumption for the purpose of conforming to customer requirements". Recently, the research on logistics caught more and more attention, and numerous theoretical models have been developed.However, most of the problems are much more practically intricate than that in theory. Since logistics includes almost all of the activities involved in securing, the right type of material, in the right quantity, to the right locations, at the right time, and at the right cost, also delivered with the right tailored services required by the buyer organization. It needs the expertises and experiences in business, management science, mathematics, information science and other thchoniques for defferent industries to overcome kinds of diffculties and to succeed in logistical practices for that reason. Due to the diversity and complexity of the practical problems, the existing models are usually not very satisfying to find the solutions efficiently and convinently.In the domain of logistics, the transportation problem (TP) is a well-known basic network problem. In general it is concerned with distributing commodities from the group of sources to the group of destinations, in such a way as to minize the total distribution cost. In practices, fixed cost, independent of the amount transported, is very common in TP. Involving the fixed cost, TP converts to fixed charged transportation problem (fcTP). Hultberg and Cardoso had proved that an equivalent formulation for a special case of fcTP is NP-hard. An optimal solution may occur at an extreme point of the constraint set and, for a non-degenerate fcTP with all positive fixed costs, every extreme point of the feasible region is a local minimum. Because of the complexity involved in examining and escaping from many local minima of objective functions, it requires excessssive computational effort to solve fcTP, and the existing analytical algorithms for solving fcTPs are useful only for small problems.Earlier attempts have been made to solve this problem consisted of finding an approximate solution. Balinski observed that there exists an optimal solution to the relaxed version of fcTP formed by ignoring the integer restriction, i.e. the value of the fcTP follows closely the value of its corresponding reduced TP (rTP). Other well-known heuristic approaches are the ones by Cooper and Drebes, and Diaby, while some others have offered techniques based on ranking the extreme points. Sun et al. proposed a Tabu search method. Gray has attempted to provide an exact solution to this problem by decomposing it into a master integer program and a series of transportation sub-programs. Whereas Palekar et al. attempted to provide exact algorithms based on the branch-and-bound method for the solutions of small, fxed-charge problems.Genetic algorithm (GA)...

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A simple heuristic for solving small fixed-charge transportation problems

Cited by 97 publications

References 16 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

Glowworm swarm optimisation algorithm for nonlinear fixed charge transportation problem in a single stage supply chain network

Case Study on Optimal Routing in Logistics Network by Priority-based Genetic Algorithm

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