| Summary: | 碩士 === 中原大學 === 應用數學研究所 === 92 === In classical stock model,The model with complete backlogging
is more difficult to find out the optimal solution. This paper mainly discusses G. Padmanabhan and Prem Vrat proposed a study of ordering strategy of the deterioration items. The authors developed three kinds of stock model based on different situations. First is the model that backlogging is not permitted. Second is the model that complete backlogging is permitted. Third is the model that partial backlogging is permitted. The authors seek the optimal solution and decide the maximum profit from these models with numerical methods. However, from the study of the theory, It can not prove if its optimal solution is existing. Therefore, this paper uses mathematical
analysis to prove the existence of the optimum.
Besides, our discussion in G. Padmanabhan and Prem Vrat dissertation, based on the second stock model with complete backlogging, the demand rate is the linear function which uses stock as variable, and stock can be completely or partially backlogging. In this way, we can develop a meaningful model, prove the optimum solution is existing. Meanwhile, we can determine the optimum order time by using the mathematical analysis.
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