Solving a dynamic warehousing problem using a genetic algorithm

Abstract

Due to the dynamic nature of economic development and market exploration, an investigation of the optimal strategy for distributing products over a given period is highly desirable. A time-dependent optimisation model is developed in this paper to help determine the optimal strategy for establishing potential distribution centers. The problem is first formulated as a mixed-integer program (MIP). Solving the MIP is not computationally practical and attractive when the problem size is large. Hence, an alternative heuristic approach is proposed, in which the problem is formulated as a bi-level program (BLP) with an upper-level subprogram and a lower-level subprogram, the latter being a Hitchcock transportation problem. This approach can minimise the total system cost - which comprises the transportation cost and capital and operating costs at potential distribution centers - over the entire study period. While the lower-level subprogram is solved by standard linear programming routines, the upper-level subprogram is solved by a genetic algorithm. The state variables that represent whether a distribution center is operating in a particular period are used as the sole decision variables in the upper-level subprogram. Computational experience is also reported to demonstrate the effectiveness of the proposed methodology.