Performance Analysis of Dynamic and Static Facility Layouts in a Stochastic Environment

In this paper, to cope with the stochastic dynamic (or multi-period) problem, two new quadratic assignment-based mathematical models corresponding to the dynamic and static approaches are developed. The product demands are presumed to be dependent uncertain variables with normal distribution having known expectation, variance, and covariance that change from one period to the next one, randomly. In the proposed models, time value of money and the decision maker’s attitude about uncertainty are also considered. The models are verified and validated by performing statistical, robustness and stability analyses carried out by using design of experiment and benchmark methods. In addition, the effect of dependency of product demands and interest rate on the total cost function of the proposed models has also been investigated. The dynamic programming algorithm, which is coded in Matlab, is used to solve the models. The main conclusions are as follows: (i) the dynamic layout behaves like static layout in the case of low facility rearrangement cost; (ii) unlike the static layout, the robustness and stability of the dynamic layout depend on the facility rearrangement cost; (iii) the decision maker’s attitude about uncertainty affects the robustness of each of the dynamic and static layouts; (iv) considering non-zero interest rate leads to increase in the total cost over the range of uncertainty; and (v) regarding both the dynamic and the static layouts, the effect of dependency of product demands on the total cost is a function of the decision maker’s defined percentile level.