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The essential decision problem in buying on a fluctuating market is the timing of the purchases and the decision of how much to purchase when the time arises. This study presents a solution to the problem of determining inventories of raw material when the price of this raw material fluctuates from period to period. The study is presented in two parts Part II develops a formal dynamic-programming model and its analytic solution under the assumptions that the following data are available for decision making: (a) the existing inventory, (b) the current market price, (c) the cost of holding inventory and the cost of shortage, and (d) probability-density functions for future price and demand of the raw material. Part I presents the results of an actual case study that represents a generalization of the model developed in Part II. In the actual case study, not only was information available concerning the probability-density functions for future price, but price forecasts for the next three periods were also available. Because of the difficulty of solving the original dynamic-programming model developed in Part II when the probability-density functions for future price are dependent from period to period, a surrogate model was developed. This surrogate model combines the analytic solution in its original form with a series of simple decision rules which were easily implemented. Percentage cost savings are also presented in Part I.
Fábián et al. (Sun,) studied this question.