COMBINATORIAL OPTIMIZATION OF THE LOCATION INVENTORY PROBLEM

In this paper we have studied the joint optimization of the input flows which have integer values, and the sizes of the storehouses (which are continuous variables) situated in the central places of different hierarchical level with different sizes of market areas. Our aim is to minimize the distribution costs (input flows and the sizes of storehouses) and the costs of risk, under some activity allocation conditions. It is supposed to have periodical movement of demand, which is a continuous stochastic variable with known probability density functions on all steps of a period. By a dynamical program on higher level new origins, new input flows could be included in the system. The combination of a parametrical programming method and Gomory's Cutting Plane algorithm is used on the first (lower) level in this optimization system.