Two-staged guillotine cut, two-dimensional bin packing optimisation with flexible bin size for steel mother plate design

Wy, Juyoung; Kim, Byung‐In

doi:10.1080/00207540903317523

Cited by 16 publications

(5 citation statements)

References 20 publications

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“…Constraints (8) shows that the spatial locations of subplate i and subplate j must not overlap. Constraints (9) states that each subplate must fit inside the motherboard. Constraints (10) confirms whether the motherboard is being used; Constraints (11) specifies the range of values for the length and width of the motherboard.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Step 2 Constraints are arranged so that there is a one-to-one correspondence between the slab and the motherboard based on Equations (7)(8)(9)(10)(11)(12)(13).…”

Section: Algorithm Flowchartmentioning

confidence: 99%

“…One‐dimensional cutting problems are modelled in a simpler way that is not applicable to the two‐dimensional motherboard design problem. Furthermore, the objective function is not sufficiently considered, for example, only the number of motherboards used is calculated, while space utilisation is ignored [9]. The constraints can be reasonably redefined to better meet the actual production process, including spatial position constraints between sub‐plates, correspondence between sub‐plates, motherboards and slabs, as well as splicing losses between different steel grades.…”

Section: Introductionmentioning

confidence: 99%

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A two‐stage solution method for the design problem of medium‐thick plates in steel plants

Peng,

Zhang,

Jiang

2024

IET Collab Intel Manufact

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The medium‐thick plate is an important type of steel product widely used in construction and engineering machinery. The orders are usually characterised by multiple specifications and small quantities. The plate design is an important part in the production process of medium‐thick plate, which includes the combination of sub‐plates and the size design of the motherboard. A multi‐objective model for medium‐thick plate design is proposed based on the 2D bin packing model, comprehensively considering spatial and size constraints of the plate production. A two‐stage genetic algorithm (TSGA) is developed to solve the proposed model. In the first stage, an improved GA is used to optimise the corresponding relationship between the sub‐plates and the slab, as well as the size of the motherboard. In the second stage, an exact algorithm based on the integer programming model is applied to calculate the order layout to minimise the surplus materials. To validate the proposed method, computational experiments are conducted based on actual production data from a steel plant. The experimental results show the effectiveness of the TSGA algorithm in solving the plate design problem.

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Section: Mathematical Modelmentioning

confidence: 99%

“…Step 2 Constraints are arranged so that there is a one-to-one correspondence between the slab and the motherboard based on Equations (7)(8)(9)(10)(11)(12)(13).…”

Section: Algorithm Flowchartmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A two‐stage solution method for the design problem of medium‐thick plates in steel plants

Peng,

Zhang,

Jiang

2024

IET Collab Intel Manufact

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“…The stochastic optimisation approach includes simulated annealing in Portmann and Rohr (1995) and Lin and Ying (2009), evolutionary algorithm in Tanev et al (2004) and Kumar et al (2006a), and tabu search in Ruiz et al (2008). As a deterministic optimisation approach, linear programming models, including Integer Programming (IP) and Mixed Integer Programming (MIP), have been recently used in Kumar et al (2006b), Missbauer et al (2009), Li et al (2011), and Wy and Kim (2010. A study employing the Lagrangian relaxation approach to address the steelmaking process scheduling is also presented in Tang et al (2002).…”

Section: Introductionmentioning

confidence: 99%

Scheduling of die casting operations including high-mix low-volume and line-type production

Park

Yang

2013

International Journal of Production Research

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This article addresses the scheduling problem of a real die casting shop. The problem is of practical importance and yet complicated, especially for a modern casting environment where a variety of cast products made of different alloys are simultaneously manufactured in relatively small lot sizes. As a simple and robust scheduling methodology, a Linear Programming (LP) model is proposed so as to determine the quantity of each product in a casting shift. The solution of the LP model maximises the average efficiency of melting furnaces, i.e., the percentage use of molten alloys throughout the shifts. Our model can represent a most general casting environment to the extent that some die casting machines carry out frequent in-process die exchanges for flexible manufacturing. At the same time, we employ line-type casting as well as a combination die with multi-cavities which can cast dissimilar shapes concurrently. In the high-mix low-volume manufacturing world, the proposed LP model can assist the die casting industry to strengthen its competence by providing an optimal schedule that satisfies practical constraints on casting processes.

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“…Recently, many studies have focused on special classes of cutting patterns, such as the p-group, T-shaped, or p-staged, due to the impractical computational time and particular characteristics of certain cutting machines (Yanasse and Morabito 2008, Cui and Yang 2011, Wy and Kim 2011. However, far fewer studies have considered exact algorithms for non-staged CTDC because non-staged CTDC is more difficult to solve than any other type of TDC (i.e., it is more difficult than UTDC or staged TDC).…”

Section: Introductionmentioning

confidence: 99%

An improved best-first branch-and-bound algorithm for constrained two-dimensional guillotine cutting problems

Yoon

Ahn

Kang

2013

International Journal of Production Research

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The constrained two-dimensional cutting problem involves maximising the sum of the profits obtained from small rectangular pieces cut from a large rectangular plate where the number of each type of cut piece cannot exceed a prescribed quantity. This paper proposes a best-first branch-and-bound algorithm to find the optimal solution to the problem. The proposed algorithm uses an efficient method to remove the duplicate patterns, and it improves the existing upper bounds. It also prevents the construction of dominated patterns and introduces a new bounding strategy that can prune more than one node at a time. Computational results are compared with a well-known exact algorithm to demonstrate the efficiency of the proposed algorithm. The proposed algorithm is as fast as or faster than the existing algorithm and reduces the average computing time by up to 99% for benchmark problems. For some problems, it can also find optimal solutions that existing algorithms are not able to find.

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Two-staged guillotine cut, two-dimensional bin packing optimisation with flexible bin size for steel mother plate design

Cited by 16 publications

References 20 publications

A two‐stage solution method for the design problem of medium‐thick plates in steel plants

A two‐stage solution method for the design problem of medium‐thick plates in steel plants

Scheduling of die casting operations including high-mix low-volume and line-type production

An improved best-first branch-and-bound algorithm for constrained two-dimensional guillotine cutting problems

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