Question

A bank branch must keep a stock of cash in hand for customer withdrawals. The net daily withdrawal rate is at the branch is $5000. The opportunity cost of cash is 10% per year. Replenishment of the cash stock from the central bank requires careful accounting and contracting to an armored delivery service. This costs $250 per replenishment and requires two days of notice to the carrier. Determine the following :

(i)The optimal order quantity, (ii) The reorder level. (iii) Annual holding cost, (iv) Annual replenishment cost.
2b. Suppose the actual outflow of cash per day is normally distributed with a mean of $5000 and standard deviation $500. The bank does not want to run out of cash more than once per year (assume 250 days per year). Find the optimal order quantity, the reorder level and the safety stock. (Take home part).

Answer 1

To determine the optimal order quantity and reorder level, divide the annual cash withdrawal rate by the number of replenishments per year. The optimal order quantity is $10,000 and the reorder level is $10,000. The annual holding cost is $500 and the annual replenishment cost is $31,250.

Step-by-step explanation:

To determine the optimal order quantity and reorder level, we need to consider the net daily withdrawal rate, the opportunity cost of cash, and the costs associated with replenishment. The optimal order quantity can be calculated by dividing the annual cash withdrawal rate by the number of replenishments per year. In this case, the annual cash withdrawal rate is $5,000 * 250 days = $1,250,000. Assuming a replenishment lead time of 2 days, we can calculate the number of replenishments per year as 250 days / 2 days = 125 replenishments per year. Therefore, the optimal order quantity is $1,250,000 / 125 = $10,000.

The reorder level can be calculated by multiplying the net daily withdrawal rate by the replenishment lead time. In this case, the reorder level is $5,000 * 2 days = $10,000.

The annual holding cost can be calculated by multiplying the average cash stock by the opportunity cost of cash. In this case, the average cash stock is $10,000 / 2 = $5,000 (assuming that the stock is depleted halfway through each replenishment cycle). The annual holding cost is then $5,000 * 0.10 = $500.

The annual replenishment cost can be calculated by multiplying the cost per replenishment by the number of replenishments per year. In this case, the annual replenishment cost is $250 * 125 = $31,250.