An improved mixed-integer programming model for the double row layout of facilities

Secchin, Leonardo D.; Amaral, André Renato Sales

doi:10.1007/s11590-018-1263-9

Cited by 27 publications

(12 citation statements)

References 17 publications

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“…For each combination of expected value interval and variance interval, 30 problem instances are randomly generated. Then, for each problem instance, randomly generate 10,000 layouts (solutions) and calculate their real objective function value (MHC) by Equation (1), the objective function value based on Naslund's approximation method (MHC ) by Equation ( 14), the value of square root term F 1 by Equation ( 13) and linear Manhattan distance F 2 by Equation (15). The top 8000 layouts are used as the training set and the remaining 2000 layouts as the test set.…”

Section: Experimental Results and Analysismentioning

confidence: 99%

“…This can provide a solution for the DRLP with up to 12 machines. Later, Secchin and Amaral [15] modified the mixed integer programming model in [14] and proposed a tighter model. This modified model can be utilized to solve the DRLP with up to 15 machines.…”

Section: Related Literaturementioning

confidence: 99%

“…This modified model can be utilized to solve the DRLP with up to 15 machines. Chae and Reganb [16] proposed a model for DRLP, which is modified from the model in [15]. The model greatly reduces the calculation time and solves DRLP with 16 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%

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

2021

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“…Most of the subsequent mathematical optimization approaches in the literature use either mixed integer linear programming (MILP), see [2,12,36], or semidefinite programming (SDP) [24]. 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].…”

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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“…The proposed MIP was then compared with previous models by Chung and Tanchoco [4] and Amaral [5]. Further, Secchin and Amaral [6] updated the MIP model for more efficient computation.…”

Section: Introductionmentioning

confidence: 99%

A Genetic Algorithm for the Double Row Layout Problem

Rifai

Mara

Kusumastuti

et al. 2020

jti

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The double row layout problem (DRLP) is an NP-hard and has many applications in the industry. The problem concerns on arranging the position of machines on the two rows so that the material handling cost is minimized. Although several mathematical programming models and local heuristics have been previously proposed, there is still a requirement to develop an approach that can solve the problem efficiently. Here, a genetic algorithm is proposed, which is aimed to solve the DRLP in a reasonable and applicable time. The performances of the proposed method, both its obtained objective values and computational time, are evaluated by comparing it with the existing mathematical programming model. The results demonstrate that the proposed GA can find relatively high-quality solutions in much shorter time than the mathematical programming model, especially in the problem with large number of machines.

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An improved mixed-integer programming model for the double row layout of facilities

Cited by 27 publications

References 17 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

Mathematical optimization approach for facility layout on several rows

A Genetic Algorithm for the Double Row Layout Problem

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