Mathematical models and routing algorithms for economical cutting tool paths

Makarovskikh, Tatiana; Panyukov, Anatoly V.; Savitskiy, E. A.

doi:10.1080/00207543.2017.1401746

Cited by 14 publications

(6 citation statements)

References 10 publications

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“…OE-Cycle) [19], [21] O(|E| • log 2 |E|) OE-Postman Route (alg. CPP OE) [17] O(|E| • |V |) OE-Router [1] O(|E| • log 2 |E|) Optimal OE-Router [1] O(|V | 2 ) MultiComponent (OE-Cover for Disconnected graph [18]) O(|E| • log 2 |E|) DoubleBridging (OE-Cover for Disconnected graph [18])…”

Section: Route Typementioning

confidence: 99%

“…The recent advances are given in our later papers [3,5,18]. In [3] we consider the algorithm that transforms the initial plane Eulerian graph to a plane 4-regular graph for which the routing problem can be solved in polynomial time by constructing an AOE-chain, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…This trail is to be the NOE-chain (non-intersecting OE-chain) for the initial graph after absorbing all the fictive edges and vertices obtained while splitting vertices of the initial graph. Some relevant algorithms and proofs are discussed in [5,18].…”

Section: Introductionmentioning

confidence: 99%

“…To solve the routing problem, the cutting plan may be represented as a plane graph as following [18].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The estimation of the number of OE-chains and realizable OE-routes for cutting plans with combined contours

Makarovskikh

Savitsky

2020

YUGOSLAV J OPERATION

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Cuts combination of plane details leads to optimization of material use and shortening of cutting time. However, the problem of cutting plan realization arises. This plan has to satisfy the following restrictions: (1) part cut off a sheet does not require further cuts (constructing of OE-route); (2) there are some restrictions on placement of pierce points (constructing of PPOE-cover). In this paper we consider the problem of enumeration the OE-chains for cutting plan with combined cuts and necessary conditions of realizable cutting.

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Section: Route Typementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…To solve the routing problem, the cutting plan may be represented as a plane graph as following [18].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The estimation of the number of OE-chains and realizable OE-routes for cutting plans with combined contours

Makarovskikh

Savitsky

2020

YUGOSLAV J OPERATION

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“…A model based on graph theory is presented in Makarovskikh et al. (2017) to solve the ICP and the ECP; the authors use a group of algorithms to find the cutting pattern. Finally, in Kandasamy and Udhayakumar (2019), the problem of cutting the sheet metal parts is solved by introducing the concept of microjoints.…”

Section: Introductionmentioning

confidence: 99%

Modeling and solving the endpoint cutting problem

Cuellar‐Usaquén

Palacio

Ospina

et al. 2021

Int Trans Operational Res

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The material cutting process consists of two NP-hard problems: first, it is necessary to find the optimal cutting pattern to minimize the waste area. Second, it is necessary to find the cutting sequence over the plate to extract the pieces in the shortest possible time. The structure of the cutting path problem can vary according to the technology used in the process. In industries where material can be considered a commodity, the cutting path is decisive due to the need to operate economically and efficiently. These types of minimization demand exact models that use nonconventional formulation techniques in search of computational efficiency and for heuristic processes to be specialized so that a good solution is guaranteed. In this paper, three different approaches were proposed. First, a novel and accurate formulation was presented based on a network flow structure. Second, a reactive GRASP algorithm with solution filtering was designed, using seven operators executed under two randomly selected local search philosophies. Finally, four warm-start variants were designed hybridizing the GRASP algorithm subprocedures with the exact model. The approaches are compared through benchmarking; for this, a set of instances composed of cutting patterns taken from the solution of classical instances of the two-dimensional cutting problem was created and made available. The obtained results show that all three approaches solve the problem successfully. Additionally, the computing time is analyzed, illustrating the pros and cons of each approach. Given the cutting path, including the quality of the pieces is left as a future work proposal.

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