The economic lot scheduling problem (ELSP) creates challenge between lot sizing and sequencing. The ELSP’s primary goal is to minimize the total setup and holding expenditures of different products on a single machine. ELSP is a mathematical model. It deals with a company’s planning what to manufacture, when to manufacture and how much to manufacture. This paper deals with the Economic Lot Scheduling (ELS) of a Jute industry for time varying demand with Stock out. This model will help to understand the total production time and allocate individual time against each product. This also increases the cycle time for a given aggregate inventory. In reality, demands and capacities are varying with time. An aggregate plan is expected to give time varying capacities since the plan is to meet fluctuating demand. It is therefore necessary to model the more realistic situation where the demand and capacity vary each day. This model will provide a production schedule of a set of items in a single machine to minimizing the long run average holding and set up cost under the assumptions of time varying demand and production rates, allowing material stock out.