Consider the case of a dealer of a certain product for which the probability distribution of daily demand and the probability distribution of the lead time, both developed empirically by observations made over a long span of period, are as follows:

Probability distribution of daily demand

Probability distribution of lead time

The ordering cost is known to be Rs 80 per order, the holding cost per unit per day is estimated at Rs 2, while the unit shortage cost, representing the loss in profits is Rs 20 per unit per day.
The dealer is anxious to known, for specific re-order levels and re-order quantities, what would be the total inventory costs (made up of the ordering, holding, and shortage costs), and thereby selecting an appropriate combination of the two

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Units demanded : 3 4 5 6 7 8 9 10 11 12 Probability : 0.02 0.08 0.11 0.16 0.19 0.13 0.10 0.08 0.07 0.06