A hierarchical approach for one-dimensional cutting stock problems in the steel industry that maximizes yield and minimizes overgrading

Vasko, Francis J.; Newhart, Dennis D.; Stott, Kenneth L.

doi:10.1016/s0377-2217(98)00035-6

Cited by 19 publications

(7 citation statements)

References 7 publications

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“…In the traditional multipleknapsack models in the steel industry, the decision problem is to allocate orders directly to the existing stock materials while maximizing the allocated profits (order weights). Vasko et al [17], Kalagnanam et al [18], Dawande et al [19], and Forrest et al [20] studied the allocation problem of coil products in the steel industry and proposed heuristics including matching and bin packing. The inventory allocation problem we tackle is different because of the dimension transformations from slabs to mother plates.…”

Section: Inventory Allocationmentioning

confidence: 99%

Production design for plate products in the steel industry

et al. 2007

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We describe an optimization tool for a multistage production process for rectangular steel plates. The problem we solve yields a production design (or plan) for rectangular plate products in a steel plant, i.e., a detailed list of operational steps and intermediate products on the way to producing steel plates. We decompose this problem into subproblems that correspond to the production stages, where one subproblem requires the design of casts by sequencing slabs which, in turn, have to be designed from mother plates. The design of mother plates consists of a two-dimensional packing problem. We develop a solution approach which combines mathematical programming models with search techniques from artificial intelligence. The use of these tools provides two types of benefits: improvements in the productivity of the plant and an approach to making the key business performance indicators, such as available-to-promise at a production level, operational.

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Section: Inventory Allocationmentioning

confidence: 99%

Production design for plate products in the steel industry

et al. 2007

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“…Also, there are many cutting stock problems that can be formulated as MKSPs. An example from the steel industry is given in [5]. Specifically, cutting customer orders for structural products from long steel beams can be formulated as a MKSP where the long steel beams are the knapsacks.…”

Section: Introductionmentioning

confidence: 99%

Using general-purpose integer programming software to generate bounded solutions for the multiple knapsack problem: a guide for or practitioners

Shively-Ertas

Lu²,

Song³

et al. 2023

Int. J. Ind. Optim.

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An NP-Hard combinatorial optimization problem that has significant industrial applications is the Multiple Knapsack Problem. If approximate solution approaches are used to solve the Multiple Knapsack Problem there are no guarantees on solution quality and exact solution approaches can be intricate and challenging to implement. This article demonstrates the iterative use of general-purpose integer programming software (Gurobi) to generate solutions for test problems that are available in the literature. Using the software package Gurobi on a standard PC, we generate in a relatively straightforward manner solutions to these problems in an average of less than a minute that are guaranteed to be within 0.16% of the optimum. This algorithm, called the Simple Sequential Increasing Tolerance (SSIT) algorithm, iteratively increases tolerances in Gurobi to generate a solution that is guaranteed to be close to the optimum in a short time. This solution strategy generates bounded solutions in a timely manner without requiring the coding of a problem-specific algorithm. This approach is attractive to management for solving industrial problems because it is both cost and time effective and guarantees the quality of the generated solutions. Finally, comparing SSIT results for 480 large multiple knapsack problem instances to results using published multiple knapsack problem algorithms demonstrates that SSIT outperforms these specialized algorithms.

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“…At each step of this multi-step procedure, if the goal yield is achieved, then the procedure is terminated. Finally, in Vasko et al (1999), a sequence of one-dimensional cutting stock problems is defined that progressively shifts the trade-off between maximizing yield and minimizing overgrading. Again, the procedure is terminated as soon as a goal yield is achieved.…”

Section: Introductionmentioning

confidence: 99%

Simple strategies that generate bounded solutions for the multiple‐choice multi‐dimensional knapsack problem: a guide for OR practitioners

Dellinger

Song

et al. 2022

Int Trans Operational Res

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The multiple‐choice multi‐dimensional knapsack problem (MMKP) is an NP‐hard generalization of the classic 0–1 knapsack problem. The MMKP has a variety of important industrial and business applications. Approximate solution approaches characteristically give no guarantees on solution quality. Exact solution approaches usually generate solutions that are guaranteed to be close to the optimum but typically take excessive computation times—one to several hours have been recorded in the literature. In this article, we use both simple single‐step and multiple step strategies to demonstrate how a commercial software package (Gurobi in this case) can easily be used to generate guaranteed tightly bounded solutions for 293 MMKP instances commonly tested in the literature. These four simple strategies that require no problem‐specific algorithms are shown to perform competitively with the five best published algorithms for the MMKP. Since no problem‐specific coding is required, these simple strategies are easy for operations research practitioners to use.

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A hierarchical approach for one-dimensional cutting stock problems in the steel industry that maximizes yield and minimizes overgrading

Cited by 19 publications

References 7 publications

Production design for plate products in the steel industry

Production design for plate products in the steel industry

Using general-purpose integer programming software to generate bounded solutions for the multiple knapsack problem: a guide for or practitioners

Simple strategies that generate bounded solutions for the multiple‐choice multi‐dimensional knapsack problem: a guide for OR practitioners

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