| Summary: | 碩士 === 中原大學 === 企業管理研究所 === 104 === In traditional theory of inventory, the optimization solutions can be obtained by the analytic method to solve the permissible model problem. This study was to explore the inventory model of production. In 1987 and 1995, Padmanabhan and Prem Vrat published the papers concerning the different perishable ordering strategy. They developed three kinds of inventory strategies. The first is not permissible shortage model, the second is the full replenishment under permissible shortage model, and the third is partial replenishment under permissible shortage model. In this paper, we prove the existence of solutions and solve the optimal cycle time and economic order quantity by mathematical skills. By two papers of Padmanabhan and Prem Vrat we mention above, they assume that the demand rate is a fixed constant in the second inventory model. Recently, in this paper, we assume that the demand rate is a linear function of the inventory level to explore the optimal profit. In 1987 and 1995, Padmanabhan and Prem Vrat published their papers according to the second inventory model, that is allowable backlogging and replenishment needs perfectly. In this paper, we made some adjustments in assumptions condition. In other words, we assume that demand is a linear function of the inventory level and to find the maximum profit, optimal replenishment time and horizon cycle time. In the paper, we also mention the demand rate for fixed α multiplied by the constant value k between 0 and 1 in the period of backlogging time, which is not allowable stock shortage as the value k equal to 0 and stock shortage is permitted backlogging when k equal to 1. This is a generalization of an meaningful model, and we use mathematical method to prove the existence of its optimal profit.
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