An inventory model with trapezoidal type demand and deteriorating items for instant customization

The inventory model for deteriorating items with general trapezoidal type demand rate and partial backlogging rate is investigated in this paper. The deteriorating rate is a generous positive time-varying Weibull function, and the demand rate is a general trapezoidal type function. In this model, we allow the product out of stock. Assume that production function is a linear function of inventory level function and demand rate function. Derive the mathematical expression of the optimal order quantity and the corresponding inventory costs, under the conditions of minimum cost, which is so-called optimal inventory principal of the production inventory. By a related example confirms the effectiveness of inventory policy.