Bank4 is a local bank with an automatic teller machine (ATM) on a college campus

Question

Bank4 is a local bank with an automatic teller machine (ATM) on a college campus. It has a steady demand for cash, at the rate of exist2,000 per day. It costs Bank4 exist50 to have a private security company go to the ATM and stock it with cash. The cost of capital that Bank4 estimates for money is an annual rate of 15%. How much cash should be placed in the ATM during each trip to minimize Bank4s annual holding and cash-filling costs? How frequently should the ATM be replenished in a year? What will be the average amount of cash in the ATM? Currently the ATM can hold exist50,000. Bank4 currently fills up this ATM during each trip. What is the percent increase in Bank4s annual holding and cash-filling costs (over the optimal) as a result of this policy? Bank4 operates two ATMs on campus. Each of these ATMs faces similar demands and costs. Bank4 could shut down the two ATMs and have one new location that is as easily accessible to all customers who use ATMs. This new ATM will also cost Bank4 exist50 to fill up, demand at this new ATM will be the total demand across the two old ATM locations, and holding costs will remain the same rate of 15% annually. How much cash should be placed in the ATM during each trip to minimize Bank4s annual holding and cash-filling costs? How frequently should the ATM be replenished in a year? What will be the average amount of cash in the ATM? Does the new single-location ATM decrease Bank4s costs over the old two-location ATM system? Explain. The Parts Company has a single central warehouse that supplies parts to four regional warehouses. We will focus on the inventory policies for the TX54 spring, which is sold to customers from the five regional warehouses. Parts purchases the TX54 from a manufacturer for exist50 and sells it at the regional warehouses for exist75. Parts estimates an annual carrying cost equal to 25% of the value of product in inventory. Demand faced by the central warehouse each week has a mean of 400 units and a standard deviation of 150 units. The central warehouse estimates that the cost to place an order with the supplier is exist1,000. The central warehouse maintains a service level of 99%. Lead time to get delivery from the supplier is four weeks.

Explanation / Answer

(a) Cash withdrawals at the Bank4 ATM is $2000 per day.

So the approximate withdrawal per year= $2000 * 365 = $730000

Annual cost of money for the bank = 15% of $730000 = $109500

But the fixed cost to fill the ATM = $50

So the number of times the ATM refilled = Total cost per ATM Annually/ fixed cost per refill= $109500/$50= 2190 times.

So the money should be put into the ATM each time it is refilled = the approximate withdrawal per year /the number of times the ATM refilled $730000/2190 = $333 (approx).

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