TY - JOUR

T1 - Mathematical optimization approach for facility layout on several rows

AU - Anjos, Miguel F.

AU - Vieira, Manuel V. C.

N1 - info:eu-repo/grantAgreement/FCT/5876/147204/PT#

PY - 2021/2

Y1 - 2021/2

N2 - 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.

AB - 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.

KW - Continuous optimization

KW - Facilities planning and design

KW - Mixed integer linear programming

KW - Row layout

KW - Unequal-areas facility layout

UR - http://www.scopus.com/inward/record.url?scp=85088585194&partnerID=8YFLogxK

U2 - 10.1007/s11590-020-01621-z

DO - 10.1007/s11590-020-01621-z

M3 - Article

AN - SCOPUS:85088585194

SN - 1862-4472

VL - 15

SP - 9

EP - 23

JO - Optimization Letters

JF - Optimization Letters

IS - 1

ER -