Approximation solution to optimal packing problem by renewal process

We are concerned with the packing policy which determines the optimal packing of products with variable sizes to minimize the penalty costs for idle space and product splitting. Optimal packing problem is closely related to the optimal packet/record sizing problem in that a randomly generated data stream with variable bytes is divided into units of packet/record for transmitting or storing. Assuming the product size and the production period are independently determined by renewal process, we can approximate the renewal process and formulate the optimization problem that minimizes the expected packing cost for a production period. The problem is divided into two cases according to whether a product is alllowed to split or not. Computational results for various distributions will be given to verify the approximation procedure and the resulting optimization problem.