It is frequent occurrence in chemical, paper, pharmaceutical, steel industries that multiple products will be produced on a single facility or assembly line.  Thus, schedule is necissary to minimize cost and satisfy demand. This kind of problem often referred to as economic lot scheduling problem (ELSP).  Being different from the past studies, the situation where the production of a product may be started before the inventory level drops to zero is considered. Besides, a new algorithm is proposed to produce production sequence. A Benchmark numerical example shows the approach can obtain lower cost than that obtained by using basic period approach or common cycle approach.  The algorithm for time complexity is also given.