Optimal Solution in a Constrained Distribution System

We develop a method to obtain an optimal solution for a constrained distribution system with several items and multi-retailers. The objective is to determine the procurement frequency as well as the joint shipment interval for each retailer in order to minimize the total costs. The proposed method is applicable to both nested and non-nested policies and ends up with an optimal solution. To solve this large nonlinear and integer problem, a two-level algorithm is proposed. In the first level, the functional constraints are relaxed and a solution is obtained by taking advantage of its special structure. Then, we apply separable programming technique for finding the optimal solution of the original problem. To decrease the size of the problem, some appropriate bounds on variables are introduced. We will show that under some conditions, the optimal solution of the original problem is proportional with the solution of its unconstrained problem.