An extended problem of supply chain contract with options

It is only an order quantity which is decided for a spot selling time in the previous supply chain contract with options. However, the effect of the lead-time on the supply chain is indispensable. This paper considers the options contract with the time-based parameters on the background of food supply chain in which the model analyze that the contract parameters and accuracy of forecasting demand is correlative with the lead-time. The method and procedure to find the optimal solution is presented and the conditions for realizing the coordination of the whole supply chain is given out. And the difference between the optimal profit of this model and the model without considering the lead-time is analyzed by a numeric example, the results of which show that it is necessary and beneficial to consider the lead-time in the model.