A robust model for multi-floor layout problem

• We model a new multi-floor layout problem.
• The places for locating departments are restricted.
• We used a robust approach for modeling, with consideration of material demand uncertainty.
• Solving instances shows the robust model efficiency.

Multi-floor layout problem (MFLP) can be categorized as one of the most crucial basic problems in the real world especially in the field of plant layout design. Specially, the aim of this problem is to find the locations of each department, storage, and elevator in the floors of a multi-floor building and without overlapping to minimize the total material handling cost. In order to consider practical issues in theory and presenting an applicable problem, for the first time in the published literature for MFLP, we develop a robust mathematical model indiscrete and uncertain environment in which some parameters can be changed in predetermined intervals. In fact, one of the most considerable factors is material flow among departments and storages which is assumed to have uncertain values rather than fixed amounts. In this study, we develop a Mixed Integer Programming (MIP) robust model for a new form of MFLP, we called MFDLP where the cellar is considered to contain main storages and upper floors in which departments will be located in predetermined locations. Moreover, there is an elevator set for transferring materials between floors and should be located without overlapping with departments and storages. Finally, the presented model is tested and assessed on some problems and its efficiency is shown.