Economic lot scheduling with lost sales and setup times

We introduce a new modeling framework for the classic economic lot scheduling problem that permits lost sales if they lead to higher profits. The model also accounts for Setup times at a facility, but assumes no explicit incremental setup Cost in the objective. Despite assumptions of deterministic demands, production rates and setup times, the cost of carrying inventory may make lost sales during a cycle economically attractive. Statistical analysis on randomly generated problems ranging in size from 100 to 1000 products indicates that the computation time grows by the square of the number of products.