The block layout problem for a multi-floor facility is an important sub class of the facility layout problem with practical applications when the price of land is high or when a compact building allows for more efficient environmental control. Several alternative formulations for the block layout problem of a multi-floor facility are presented, where the material handling transportation between floors is executed through elevators. Both elevator types that either service all floors or a limited subset of the floors are considered. The department and floors are modeled as rectangular shapes. The floors may have different dimensions provided the floor projections on the ground floor are nested starting from the ground floor to the top floor. The formulations yield large mixed-integer programming problems. We will report on the results of the numerical experiments to solve these problems with a MIP solver for the base formulation and using various acceleration techniques such as symmetry-breaking constraints and valid inequalities. Insights on the relative difficulty of the problems based on the numerical experiment will also be shared.
Georgia Institute of Technology, Feb-2007.