Dynamic facility layout problem (DFLP) considers flow over multiple time periods in an environment where material flow between departments changes over time. These changes render the current facility layout inefficient and could increase material handling costs, which results in a need for dynamic layout models. But a key factor ignored for simplicity in the DFLP literature, is considering the effects of non-cooperating internal and external competitions on the mentioned changes in facility layout over time that sometimes results in main conflict of objectives/goals for these distinct decision makers. To the best our knowledge, the existing special literature did not cover this important assumption. Ignoring this main assumption resulted in the existing monopolistic models for DFLP that cannot satisfy the new needs in the nowadays competitive environments. Therefore, in this paper, a duopoly Bertrand non-cooperative game model is presented to consider the impacts of all conflicting factors on a DFLP for each period and three meta-heuristic algorithms are proposed to obtain Nash equilibrium for this model. The results obtained from solving some numerical examples with these algorithms show that the proposed simulated annealing algorithm is more effective than the others for the competitive dynamic facility layout problem.
