A New Mixed Integer Linear Programming Formulation for Dynamic Facility Layout Problem

Abstract

The literature has established that the Dynamic facility layout problem (DFLP) is an NP-hard problem and very complex to solve optimally. Therefore, heuristics and metaheuristics are widely used in literature to solve DFLP. However, heuristics and metaheuristics do not give optimal solutions most of the time. Currently, the dynamic programming (DP) approach is used in literature to solve DFLP optimally. No other technique than DP is available in the literature to solve DFLP optimally. Therefore, this paper presents a linearized formulation of DFLP, a mixed-integer linear programming (MILP) model, to solve it optimally. From the author's knowledge, no such prior attempt has been made in the literature so far—two test problems of size five and periods three generated and solved in Lingo 10 software using the proposed model. The comparison of Lingo solutions with lower bounds of both problems shows that deviation is minimal (around 0.09%), suggesting MILP solutions are optimal solutions.