Dynamic Facility Layout Problem: A New Bilevel Formulation and Some Metaheuristic Solution Methods

The dynamic facility layout problem considers flow over multiple time periods in an environment where the material flow between departments changes over time. If this complex problem is combined with the other system problems, such as material handling system designing, this results in a more complicated problem. In most recently proposed approaches for these two synchronized problems, the integrated formulations have been used where the objective function is a weighted sum of some conflicting objectives that may belong to either one or different decision makers. In the former case, the poor practicability of such an approach is due to the difficulty of normalizing these functions and of quantifying the weights. In addition to these problems, in multiagent systems with a strong cooperation, there is another important problem in incorporating the conflicting objectives of conflicting decision makers that is not considered in the existing researches. By these descriptions, developing some other solution strategies, such as iterative or hierarchical methods, are necessary for these cases. In this paper, a bilevel model is developed. The experimental results reveal significant enhancements with respect to more classical approaches (i.e., integrated formulation and Pareto optimal solutions) based on the proposed bilevel model and algorithms.

Nomenclature

Flow of materials between facilities and in period .

Number of types of material handling devices (MHDs).

Number of production facilities.

Number of periods.

Average percentage working time of MHD with load.

Average loading and offloading time of MHD that is moving at a medium speed (in min).

Average speed of MHD in meters per minute.

All costs, such as cost of working force, maintenance, energy, etc., due to working MHD per minute.

Time for handling a unit of material from facility to facility by MHD (min) in period .

Variable handling cost for per unit of material from facility to facility by MHD in per unit of distance in period .

Distance between the locations of the facilities and (decision variable).

Binary quantity that is equal to 1 if we use MHD g for handling material from facility to facility at the beginning of period else it is equal to 0 (decision variable).

Number of the MHD needed thorough the period (decision variable).

Number of the MHD purchased at the beginning of period (decision variable).

Number of the MHD is useless thorough period .

Invested value on the per unit MHD purchased at the beginning of the period .

Cost of being useless the per unit MHD thorough period .

Binary quantity that is equal to 1 if facility settles in the location at the beginning of period else it is equal to 0 (decision variable).

Coordinate of the location .

Cost of shifting department from location to in period .

Binary quantity that is equal to 1 if department is shifted from location to at the beginning of period , else it is equal to 0 (decision variable).

Number of materials that can be transported from facility to facility by MHD per trip or the capacity of the device g between facilities i and j.