A genetic algorithm for the two‐dimensional knapsack problem with rectangular pieces

Bortfeldt, Andreas; Winter, Tobias

doi:10.1111/j.1475-3995.2009.00701.x

Cited by 24 publications

(12 citation statements)

References 41 publications

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“…In our case, the rectangle r represents not the item i itself but its facings

k_{i}

and the corresponding width dimension

W_{i}

, depth dimension

d_{i}

, as well as its profit value

π_{i}

. Selected rectangles need to be orthogonally placed in the container and are not allowed to overlap the container limits (Bortfeldt and Winter ). Different constraints are applicable to this problem.…”

Section: Development Of the Decision Modelmentioning

confidence: 99%

Maximizing Profit via Assortment and Shelf‐Space Optimization for Two‐Dimensional Shelves

Hübner

Schäfer

Schaal

2020

Production and Operations Management

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Product proliferation and changes in demand require that retailers regularly determine how items should be allocated to retail shelves. The existing shelf‐space literature mainly deals with regular retail shelves onto which customers only have a frontal perspective. This study provides a modeling and solution approach for two‐dimensional shelves, e.g., for meat, bread, fish, cheese, or clothes. These are categories that are kept on tilted shelves. Customers have a total perspective on these shelves and can observe units of one particular item horizontally and vertically instead of just seeing the foremost unit of an item, as is the case of regular shelves. We develop a decision model that optimizes the two‐dimensional shelf‐space assignment of items to a restricted, tilted shelf. We contribute to current literature by integrating the assortment decision and accounting for stochastic demand, space elasticity and substitution effects in the setting of such self types. To solve the model, we implement a specialized heuristic that is based on a genetic algorithm (GA). By comparing it to an exact approach and other benchmarks, we prove its efficiency and demonstrate that results are near‐optimal with an average solution quality of above 99% in terms of profit. Based on a numerical study with data from one of Germany’s largest retailers, we were able to show within the scope of a case study that our approach can lead to an increase in profits of up to 15%. We demonstrate with further simulated data that integration of stochastic demand, substitution, and space elasticity results in up to 80% higher profits.

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“…In our case, the rectangle r represents not the item i itself but its facings

k_{i}

and the corresponding width dimension

W_{i}

, depth dimension

d_{i}

, as well as its profit value

π_{i}

Section: Development Of the Decision Modelmentioning

confidence: 99%

Maximizing Profit via Assortment and Shelf‐Space Optimization for Two‐Dimensional Shelves

Hübner

Schäfer

Schaal

2020

Production and Operations Management

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“…Among the metaheuristics, Alvarez‐Valdés et al. (, ) proposed a Greedy Randomized Adaptive Search Procedure (GRASP) and a tabu‐search algorithm, whereas Bortfeldt and Winter () designed a genetic algorithm and Polyakovsky and M'Hallah () exploited an agent‐based approach. Recently, Borgulya () proposed an Estimation of Distribution Algorithm (EDA) approach.…”

Section: C2dc Solving Approaches and Literature Reviewmentioning

confidence: 99%

Constrained two‐dimensional guillotine cutting problem: upper‐bound review and categorization

Russo¹,

Boccia

Sforza³

et al. 2019

Int Trans Operational Res

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In the two‐dimensional (2D) cutting (2DC) problem, a large rectangular sheet has to be dissected into smaller rectangular pieces with the aim of maximizing the total profit associated with the extracted pieces. When the number of copies of each piece to be extracted is bounded, it is referred to as constrained 2DC (C2DC) problem. The C2DC has been widely studied by the operations research community for its applications and theoretical issues. In this work, we recall the best exact and heuristic solving approaches for the C2DC and we provide a review and a categorization of the available upper bounds. We also discuss improvements and combinations of these upper bounds and give directions for their effective exploitation. Finally, we demonstrate the loss of accuracy of several exact methods present in literature because of the effect of the used antiredundancy strategies on the implemented bounding criteria. This work, based on more than 90 contributions, has a twofold target. For researchers working in C2DC, it provides a useful insight on the topic. For expert practitioners, it represents a systematic collection of the main findings and achievements, posing also the basis for future research.

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“…The knapsack problem aims to find a set of objects that have high value and low weight compared to the capacity of the knapsack (Taskiran, 2012). The solutions of the knapsack problem are presented in a binary encoding where the selected objects are represented by '1' and the abandoned ones are represented by '0' (Bortfeldt & Winter, 2012). Genetic algorithms are designed to find a local maximum solution for the problem, since generating the best solution will require a long period of time to find.…”

Section: Genetic Algorithmsmentioning

confidence: 99%

Genetic Algorithm Solution of the Knapsack Problem Used in Finding Full Issues in the Holy Quran Based on the Number (19)

Najadat¹,

Kanaan²,

Kanaan³

et al. 2013

CIS

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The Holy Quran is the biggest Miracle of Muslims everywhere and at every time; therefore, it is valid for every time and place. Actually, researches and studies into the Holy Quran that aim to uncover new miracles within are considered as a kind of worship for Muslims researchers since it facilitates the Islamic mission and clarifies the vague picture of Islam throughout the world. From this perspective, the researchers have selected the vague miracle of the number 19 in the Holy Quran to examine through this study.In this study, the researchers describe a special algorithm that facilitates the retrieval process of the full-issues according to the conditions of number 19 miracle in the Holy Quran. This algorithm is derived from the genetic algorithm that is used to solve the knapsack problem, since it is so similar to the case of this study. However, in the results of this study many full-issues have appeared that insure the truth of the number 19 miracle in the Holy Quran and thus support the miracle of the whole Holy Quran.

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A genetic algorithm for the two‐dimensional knapsack problem with rectangular pieces

Cited by 24 publications

References 41 publications

Maximizing Profit via Assortment and Shelf‐Space Optimization for Two‐Dimensional Shelves

Maximizing Profit via Assortment and Shelf‐Space Optimization for Two‐Dimensional Shelves

Constrained two‐dimensional guillotine cutting problem: upper‐bound review and categorization

Genetic Algorithm Solution of the Knapsack Problem Used in Finding Full Issues in the Holy Quran Based on the Number (19)

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