Abstract: In classic periodic inventory model, demand is usually considered as a random variable, but in production practice, the distribution function of new equipment demand cannot be obtained due to lack of historical sale data. So companies usually take product demand data of the original equipment as reference, and invite relevant experts to provide a subjective estimate to the unit demand distribution of new equipment. To describe the randomness and subjective uncertainty of the new equipment demand,chance theory is introduced and the demand is assumed as a uncertain random variable. A periodic order optimization model is built and an optimal analytical solution for profit maximization is obtained. Finally, numerical examples verify the feasibility of the current model, and a sensitivity analysis for parameters is taken.

Key words: periodic inventory, uncertain random variable, chance theory, new equipment demand