A robust mathematical model and ACO solution for multi-floor discrete layout problem with uncertain locations and demands

• We model a new multi-floor layout problem.
• Unequal-area departments should have no overlapping with each other and the elevator in a discrete environment.
• We used two robust approaches for modeling, with consideration of uncertain locations, demands and material flows.
• An ACO is developed for solving large-size instances.

The Multi-Floor Layout Problem (MFLP) is the problem of finding the position of each department in a plant floor in a multi-floor building without any overlapping between departments in order to optimize a particular objective function, more commonly the sum of the material handling costs. In this paper, a special class of MFLP, called Uncertain Multi-Floor Discrete Layout Problem (UMFDLP), is defined. In this problem, a multi-floor building is considered in which an underground store is utilized to contain main storages, and different departments can be located in the other floors in potential pre-determined locations. Furthermore, all material flows are not constant. Moreover, the locations for departments can be chosen from intervals, where no overlaps are allowed.We develop a Mixed Integer Programming (MIP) model to generate a robust solution for UMFDLP. Furthermore, the lower bound of objective function is obtained. Moreover, an ACO algorithm is designed for solving large instances. Then, a set of problems is generated and tested by the proposed algorithm. The results show the efficiency of our model and algorithm.