Approximate algorithms for the travelling purchaser problem

Ong, H. L.

doi:10.1016/0167-6377(82)90041-4

Cited by 47 publications

(19 citation statements)

References 5 publications

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“…Pearn and Chien [12] improved on the two previous works of Golden et al [5] and Ong [11] . They suggested three heuristic methods: the PS-GSH (parameter selection GSH), the TS-GSH (tie selection GSH), and the CAH (commodity adding heuristic).…”

Section: Literature Reviewmentioning

confidence: 93%

The Multiple Traveling Purchaser Problem for Minimizing the Maximal Acquisition Completion Time in Wartime

Choi¹,

Moon²,

Choi³

2011

Journal of the Korea Institute of Military Science and Technolo

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In war time, minimizing the logistics response time for supporting military operations is strongly needed. In this paper, i propose the mathematical formulation for minimizing the maximal acquisition completion time in wartime or during a state of emergency. The main structure of this formulation is based on the traveling purchaser problem (TPP), which is a generalized form of the well-known traveling salesman problem (TSP). In the case of the general TPP, an objective function is to minimize the sum of the traveling cost and the purchase cost. However, in this study, the objective function is to minimize the traveling cost only. That's why it's more important to minimize the traveling cost (time or distance) than the purchase cost in wartime or in a state of emergency. I generate a specific instance and find out the optimal solution of this instance by using ILOG OPL STUDIO (CPLEX version 11.1).

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Section: Literature Reviewmentioning

confidence: 93%

The Multiple Traveling Purchaser Problem for Minimizing the Maximal Acquisition Completion Time in Wartime

Choi¹,

Moon²,

Choi³

2011

Journal of the Korea Institute of Military Science and Technolo

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“…Regarding approximate algorithms, Pearn and Chien [122] derive a heuristic from the lexicographic method of Ramesh [131], present improved versions of previous heuristics by Golden et al [66] and Ong [119], and propose a new one called commodity adding heuristic. These methods apply to the UTPP and are basically constructive greedy procedures, based on add and drop movements.…”

Section: The Profitable Tour Problemmentioning

confidence: 99%

Locating a cycle in a transportation or a telecommunications network

Laporte

Rodríguez-Martín

2007

Networks

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Several problems arising in transportation and telecommunications can be cast in terms of optimally locating a cycle in a graph. This paper proposes a classification of cycle location problems under two main headings. In Hamiltonian problems, all vertices of the graph must belong to the cycle. The most important cases are the traveling salesman problem (TSP), the TSP with precedence constraints, the clustered TSP, the TSP with backhauls, the TSP with time windows, several classes of pickup and delivery problems, and stochastic TSPs. In non-Hamiltonian problems, only a subset of vertices must be visited. These problems include the generalized TSP, the covering tour problem, the median cycle and ring star problems, and several cycle location problems with revenues. These problems are modeled within a unified framework and algorithmic strategies are provided, together with computational results. Several applications are also described.

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“…For the covering sa]esman problem, Current and Schilling [7] give an integer programming formulation anda simple heuristic method. Two heuristic algorithm~ axe proposed to the traveling purchaser problem; Golden, Levy and Dahl propose a generalized version of the Clark and Wright saving method [3], and Ong develops a tour reduction method [36].…”

Section: Related Workmentioning

confidence: 99%

On symmetric subtour problems

Kubo

Kasugai

1992

Japan J. Indust. Appl. Math.

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Recently several practical variants of the classical traveling salesman problem &re proposed. These variants include the traveling purchaser problem, the prize collecting traveling salesman problem, the orienteering problem, the median shortest path problem, and the covering 8ale~man problem. The most important common chaxacteristic of these problems is that the salesman travels the subset of customers, i.e., the tottr doos not necessarily visit all nodes as in the traveling salesman problem. We call this class of problems the subtour problem. In this paper, we derive several valid inequalities and show some of them axe facets of the polytope of the subtour problem. Further we preBent several integer or mixed integer programming formulations of the subtour problem and compare these formulations in terms of bounds obtained by linear programming relaxations.Key word~, subtour problem, valid inequality, integer programming formulation, traveling salesman problem IntroductionThe traveling sa[esman problem (TSP) is the problem of finding a miniraum cost (distance) tour which visits a[1 cities (nodes) in a graph, and has wide apphcations in many practica[ areas such as vehicle routing and schednling, machine scheduling and sequencing, VLSI network design, and clustering data array, etc. Many researchers have investigated the TSP, and have derived efficient solution methods; some are approximate a[gorithm.% the others are opt]miTation a[gorithms. Resent progress of such solution methods includes 1. heuristics with the worst-case guarantees, 2. heuristics with the probabilistic guarantees, and 3. exact schemes based on the polyhedra[ computation.The results of these progresses &re snmmarized in a recently published book [29]. The most impressive exact a[gorithm is a combination procedure of the cutting plane and branch-and-bound methods in which polyhedra[ theory plays a centra[ role to compute tight lower bounds. The TSP with severa[ thousands of nodes can be solved based on this approach [37]. In contrast to it, the variants of the TSP cannot be solved when the problem size is relatively large; this indicates that polyhedra[ ana[ysis is necessary for the exact methods for the variants of the TSP.In this paper, we ana[yze the polyhedra[ aspects of a variant of the TSP termed the subtour problem.In the subtour problem, the salesman travels the subset of cities, i.e., the tour does not necessarily visit a[1 nodes as in the TSP. This variant includes the traveling purchaser problem, the prize collecting travehng sa[esman problem, the orienteering

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Approximate algorithms for the travelling purchaser problem

Cited by 47 publications

References 5 publications

The Multiple Traveling Purchaser Problem for Minimizing the Maximal Acquisition Completion Time in Wartime

The Multiple Traveling Purchaser Problem for Minimizing the Maximal Acquisition Completion Time in Wartime

Locating a cycle in a transportation or a telecommunications network

On symmetric subtour problems

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