Decorous combinatorial lower bounds for row layout problems

Dahlbeck, Mirko; Fischer, Anja; Fischer, Frank

doi:10.1016/j.ejor.2020.04.010

Cited by 14 publications

(4 citation statements)

References 63 publications

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“…Using a and b (the surrogate model), the fitting objective function values (MHC ) of each element in the test set are calculated by Equation (17). Based on the test set, the mean absolute percentage error (MAPE) [37] of Naslund's approximation and surrogate model are calculated by Equation (18). The average MAPE value of all the 30 problem instances is shown in Figure 5.…”

Section: Experimental Results and Analysismentioning

confidence: 99%

“…The model is more intuitive for handling qualitative inputs. Dahlbeck [18] presented combinatorial lower bounds for DRLP, and combined these lower bounds with a new distance-based mixed integer linear programming model to improve the lower bounds. Amaral [19] established a mixed integer programming model for DRLP based on a linear extension of a partial order on the set of machines.…”

Section: Related Literaturementioning

confidence: 99%

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A Surrogate Model-Based Hybrid Approach for Stochastic Robust Double Row Layout Problem

2021

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The double row layout problem is to arrange a number of machines on both sides of a straight aisle so as to minimize the total material handling cost. Aiming at the random distribution of product demands, we study a stochastic robust double row layout problem (SR-DRLP). A mixed integer programming (MIP) model is established for SR-DRLP. A surrogate model is used to linearize the nonlinear term in the MIP to achieve a mixed integer linear programming model, which can be readily solved by an exact method to yield high-quality solutions (layouts) for small-scale SR-DRLPs. Furthermore, we propose a hybrid approach combining a local search and an exact approach (LS-EA) to solve large-scale SR-DRLPs. Firstly, a local search is designed to optimize the machine sequences on two rows and the clearance from the most left machine on row 1 to the left boundary. Then, the exact location of each machine is further optimized by an exact approach. The LS-EA is applied to six problem instances ranging from 8 to 50 machines. Experimental results show that the surrogate model is effective and LS-EA outperforms the comparison approaches.

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Section: Experimental Results and Analysismentioning

confidence: 99%

Section: Related Literaturementioning

confidence: 99%

A Surrogate Model-Based Hybrid Approach for Stochastic Robust Double Row Layout Problem

2021

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“…We have adapted these benchmark instances for the BLLP by using the lengths of facilities as distances between adjacent machine locations (the set consists of 20 instances with n = 64, 72, 81, 100). The sko dataset is well known and is used as a benchmark to test algorithms in the facility layout literature [32,45,[50][51][52]; (b) a series of randomly generated larger-scale BLLP instances ranging in size from 110 to 300 machines. The off-diagonal entries of the flow cost matrix and the distances between adjacent locations in these instances are integer numbers drawn uniformly at random from the intervals [0, 10] and [1, 10], respectively; (c) instances introduced by Anjos et al [53] and adapted for the TIP by Ghosh [4].…”

Section: Methodsmentioning

confidence: 99%

An Approach Integrating Simulated Annealing and Variable Neighborhood Search for the Bidirectional Loop Layout Problem

Palubeckis

2020

Mathematics

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In the bidirectional loop layout problem (BLLP), we are given a set of machines, a set of locations arranged in a loop configuration, and a flow cost matrix. The problem asks to assign machines to locations so as to minimize the sum of the products of the flow costs and distances between machines. The distance between two locations is calculated either in the clockwise or in the counterclockwise direction, whichever path is shorter. We propose a hybrid approach for the BLLP which combines the simulated annealing (SA) technique with the variable neighborhood search (VNS) method. The VNS algorithm uses an innovative local search technique which is based on a fast insertion neighborhood exploration procedure. The computational complexity of this procedure is commensurate with the size of the neighborhood, that is, it performs O(1) operations per move. Computational results are reported for BLLP instances with up to 300 machines. They show that the SA and VNS hybrid algorithm is superior to both SA and VNS used stand-alone. Additionally, we tested our algorithm on two sets of benchmark tool indexing problem instances. The results demonstrate that our hybrid technique outperforms the harmony search (HS) heuristic which is the state-of-the-art algorithm for this problem. In particular, for the 4 Anjos instances and 4 sko instances, new best solutions were found. The proposed algorithm provided better average solutions than HS for all 24 Anjos and sko instances. It has shown robust performance on these benchmarks. For 20 instances, the best known solution was obtained in more than 50% of the runs. The average time per run was below 10 s. The source code implementing our algorithm is made publicly available as a benchmark for future comparisons.

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“…Among the most recent publications on the DRFLP are [3], [11,32] that present MILP models for DRFLP; we note that [32] makes use of the concept of betweenness from [1]. New combinatorial lower bounds for the DRFLP that can be computed very fast are presented in [13]. Problems related to the DRFLP that are also the focus of current research are the corridor allocation problem, see [17,35], and the parallel row ordering problem [34].…”

Section: Literature Reviewmentioning

confidence: 99%

Mathematical optimization approach for facility layout on several rows

Anjos

Vieira

2020

Optim Lett

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The facility layout problem is concerned with finding an arrangement of non-overlapping indivisible departments within a facility so as to minimize the total expected flow cost. In this paper we consider the special case of multi-row layout in which all the departments are to be placed in three or more rows, and our focus is on, for the first time, solutions for large instances. We first propose a new mixed integer linear programming formulation that uses continuous variables to represent the departments’ location in both x and y coordinates, where x represents the position of a department within a row and y represents the row assigned to the department. We prove that this formulation always achieves an optimal solution with integer values of y, but it is limited to solving instances with up to 13 departments. This limitation motivates the application of a two-stage optimization algorithm that combines two mathematical optimization models by taking the output of the first-stage model as the input of the second-stage model. This algorithm is, to the best of our knowledge, the first one in the literature reporting solutions for instances with up to 100 departments.

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Decorous combinatorial lower bounds for row layout problems

Cited by 14 publications

References 63 publications

A Surrogate Model-Based Hybrid Approach for Stochastic Robust Double Row Layout Problem

A Surrogate Model-Based Hybrid Approach for Stochastic Robust Double Row Layout Problem

An Approach Integrating Simulated Annealing and Variable Neighborhood Search for the Bidirectional Loop Layout Problem

Mathematical optimization approach for facility layout on several rows

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