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When the annual demand rate for a product or goods is constant, the inventory model is called deterministic. However, when the demand rate is not constant and not deterministic, the inventory model is called probabilistic and is best described by a probability distribution. The minimum-cost order quantity and re-order policies are based on the assumptions of the demand rate.

PROBABILISTIC INVENTORY MODELS

1. A single-period inventory model with probabilistic demand The single-period inventory model refers to inventory situations in which one order is placed for the product; at the end of the period, the product has either sold out, or there is a surplus of unsold items that will be sold for a salvage value. The single-period inventory model is applicable in situations involving seasonal or perishable items that cannot be carried in inventory and sold in future periods. Example of items or goods that fit to the single-period inventory model is seasonal clothing like swim wears for summer. Purchaser of swim wear outlets places one preseason order for this item and then experience stock out or hold clearance sale of surplus stocks at the end of the season. No items are carried in inventory to be sold during the rainy season. Another example is newspapers which are ordered daily and either sold or not. Newspapers cannot be carried in inventory to be sold the following day or following week. Since the items are ordered once for the period, the only inventory decision to be made is how much of the product to order at the start of the period.

1.a. Incremental analysis Incremental analysis is a method that can be used to determine the optimal order quantity for a single-period inventory model. It addresses the how-much-to-order question by comparing the cost or loss of ordering one additional unit with the cost or loss of not ordering one additional unit. The optimal order quantity, Q is determined when the incremental analysis shows that the expected loss due to ordering one additional unit is equal to the expected loss due to not ordering one additional unit.

1.b. Probability Distribution of Demand The key to establishing an optimal order quantity for a single-period inventory model is to identify the probability distribution that describes the demand for the item and the costs of overestimation and underestimation. Using the information for the costs of overestimation and underestimation, the location of Q under the probability distribution can be determined.…...

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