Publications

The purpose of this study is to incorporate the cost of raw material into the classical production model with planned shortages. A mathematical model is developed to account for the cost of producing and holding the finished product, the administrative and backorder costs of shortages, as well as the cost of acquiring and holding the raw materials used in the production process. Explicit expressions for the optimal production and planned shortage quantities are derived from the mathematical model. Moreover, a proof of the uniqueness of the optimal solution is provided. Numerical examples are presented to analyze the sensitivity of the optimal solution relative to changes in the parameters of the model.