The multi-commodity one-to-one pickup-and-delivery traveling salesman problem

Hernández-Pérez, Hipólito; Salazar-González, Juan-José

doi:10.1016/j.ejor.2008.05.009

Cited by 61 publications

(33 citation statements)

References 43 publications

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“…As mentioned in the introduction, the CSOP was introduced in [13]. In the CSOP, the vehicle has a (positive integer) capacity Q and each precedence relation (p, q) ∈ B is associated with a commodity that has a weight of d pq and needs to be collected at p and delivered at q.…”

Section: The Csopmentioning

confidence: 99%

“…Many formulations and algorithms have been proposed for the SOP (e.g., [1,2,3,4,6,7,11,13]). The standard integer programming formulation [1,3,7] uses one binary variable x a for each arc a ∈ A, taking the value 1 if and only if arc a is traversed in the solution.…”

Section: The Sequential Ordering Problemmentioning

confidence: 99%

“…The following MCF formulation of the CSOP was presented in [13]. For each a ∈ A and each b ∈ B, define the binary variable f b a , taking the value 1 if and only if commodity b is carried across arc a.…”

Section: The Csopmentioning

confidence: 99%

“…For this formulation, many classes of strong valid linear inequalities have been discovered, which have formed the basis of successful exact algorithms for the SOP (e.g., [1,2,3,7]). There are also a few papers that discuss alternative formulations that use additional variables, together with appropriate linking constraints [11,12,13].…”

Section: Introductionmentioning

confidence: 99%

“…• Hernández & Salazar [13] presented a multi-commodity flow (MCF) formulation for the SOP, and also for a capacitated version of the SOP, called the multi-commodity one-to-one pickup-and-delivery traveling salesman problem. (For brevity, we just call it the CSOP.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Stronger multi-commodity flow formulations of the (capacitated) sequential ordering problem

Letchford

Salazar-González

2016

European Journal of Operational Research

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The sequential ordering problem (SOP) is the generalisation of the asymmetric travelling salesman problem in which there are precedence relations between pairs of nodes. Hernández & Salazar introduced a multi-commodity flow (MCF) formulation for a generalisation of the SOP in which the vehicle has a limited capacity. We strengthen this MCF formulation by fixing variables and adding valid equations. We then use polyhedral projection, together with some known results on flows, cuts and metrics, to derive new families of strong valid inequalities for both problems. Finally, we give computational results, which show that our findings yield good lower bounds in practice.

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Section: The Csopmentioning

confidence: 99%

Section: The Sequential Ordering Problemmentioning

confidence: 99%

Section: The Csopmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stronger multi-commodity flow formulations of the (capacitated) sequential ordering problem

Letchford

Salazar-González

2016

European Journal of Operational Research

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The multi‐commodity pickup‐and‐delivery traveling salesman problem

Hernández-Pérez

Salazar-González

2013

Networks

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The "multi-commodity Pickup-and-Delivery Traveling Salesman Problem" (m-PDTSP) is a generalization of the well-known "Traveling Salesman Problem" in which cities correspond to customers providing or requiring known amounts of m different products, and the vehicle has a known capacity. Each customer must be visited exactly once by the vehicle serving the demands of the different products while minimizing the total travel distance. It is assumed that a unit of a product collected from a customer can be supplied to any other customer that requires this product. We introduce a mixed integer linear programming model for the m-PDTSP, discuss a classical decomposition technique, describe valid inequalities to strengthen the linear programming relaxation of the model, and detail separation procedures to develop a branch-and-cut procedure. Computational experiments on randomly generated instances with up to 30 customers, three products, and small vehicle capacities are analyzed.A better model than (1)-(8) can be given by tightening the bounds on the continuous variables, projecting out these variables, and introducing new valid inequalities exploiting the nature of the m-PDTSP solutions.

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An improved approximation algorithm for the capacitated TSP with pickup and delivery on a tree

Lai

Lim

et al. 2013

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In this research, we study the capacitated traveling salesman problem with pickup and delivery (CTSPPD) on a tree, which aims to determine the best route for a vehicle with a finite capacity to transport amounts of a product from pickup points to delivery points on a tree network, such that the vehicle's total travel distance is kept to a minimum. It has several applications in logistics and is known to be NP‐hard. We develop a 2‐approximation algorithm that is a significant improvement over the best constant approximation ratio of 5 derived from existing CTSPPD literature. Computational results show that the proposed algorithm also achieves good average performance over randomly generated instances. © 2013 Wiley Periodicals, Inc. NETWORKS, Vol. 63(2), 179–195 2014

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The multi-commodity one-to-one pickup-and-delivery traveling salesman problem

Cited by 61 publications

References 43 publications

Stronger multi-commodity flow formulations of the (capacitated) sequential ordering problem

Stronger multi-commodity flow formulations of the (capacitated) sequential ordering problem

The multi‐commodity pickup‐and‐delivery traveling salesman problem

An improved approximation algorithm for the capacitated TSP with pickup and delivery on a tree

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