Abstract: The distribution network design model for a class of deteriorating items with short selling seasons is investigated in this paper.It is assumed that the shortage costs of the retailers are dependent on the holding costs of the distribution centers which are assigned to serve the retailers, re sp ecti vel y, and the supplier offers a second order opportunity to the retailers at the end of the selling season.The suppliers choose the optimal locations to set up distribution centers, as well as determining each retailer served by which distribution center, and to minimize the total operation costs(facility location cost, transportatio n co st, inventory co st and deterioratio n co st), where the transportation cost and inventory cost of the distribution centers are dependent on the order quantities of the retailers'.The retailers determine the optimal replenishment decision according to the supplier's deci sio n, respectively.The method of Stackelberg game analysis is introduced, and a class of distribution network design models for deteriorating items is established A Lagrangian relaxation algorithm is also presented to solve the proposed models.At last, a numerical example is given to illustrate the sensitivity of the optimal solution on the change of the parameter.

Key words: distribution network design, facility location, deteriorating items, Stackelberg game