A robust single row facility layout problem with fuzzy random variables

The facility layout problem is the optimal arrangement of facilities in the plant area. Based on layout configurations, there are several types of the facility layout problem. The single row facility layout problem (SRFLP) is one them in which facilities have to be placed along a line. Although there are exact approaches, based on the integer programming model for solving SRFLP, a huge number of variables and constraints should be used in this model. This paper presents a new exact method to SRFLP based on a new class of variables and an extended branch and bound method (B&B). First, the SRFLP is formulated by new decision variables. To solve it, a new branching scheme for B&B algorithm is presented. Subsequently, we introduce a fuzzy robust single row facility layout problem (FRSRFLP) and solve it by a real expected value method and a fuzzy stochastic chance-constrained programming based on possibility and necessity measures together with an extended B&B method. Furthermore, the proposed methods are applied for solving some benchmark problems to show their efficiency.