Question

First City Bank orders cash from the Federal Reserve Board to meet daily transaction needs. Linda Davis, the operations manager, estimates that $5,000,000 in cash will be needed next month. She has estimated that the cost to order, receive, and store each shipment of cash from the Federal Reserve Board will be $675 per shipment. First City Bank is open for business 250 days each year. These are considered its working days for the year. The bank’s related carrying cost for cash is 0.65 percent per month. That is, each dollar held in the bank’s vault costs $0.0065 per month in foregone profits.

a) How much should Linda order from the Federal Reserve Board each time a cash order is placed if she wants to minimize her cost?

b) What is the expected total annual holding cost plus ordering cost?

c) If the lead time is 4 days what is the reorder point? Also, what is the inventory position immediately after reordering?   

d) If it is against First City Bank’s policy to order more than $800,000 when placing a cash order. How much should it order each time? Explain or support your answer.

Answer 1

Monthly Demand D = 5000000

Ordering Cost S = 675

Holding Cost H = 0.65% per month

a)

EOQ = (2DS/H)^(1/2)

EOQ = (2*5000000*675/0.65%)^(1/2)

EOQ = 1019049

b)

Annual Holding Cost = (EOQ*12/2)*H = (1019049*12/2)*0.65% = 39742.91

Annual Ordering Cost = (D/EOQ)*S = (5000000*12/1019049)*675 = 39742.94

Total Holding Cost + Ordering Cost = 39741.91+39742.94 = 79484.85

c)

Annual Demand = 5000000*12 = 60000000

Work Days = 250

Daily Demand = 60000000/250 = 240000

Lead Time = 4 days

Demand During Lead Time = 240000*4 = 960000

Reorder Point = Demand During Lead Time = 960000

EOQ = 1019049

Inventory Position after reorder = Demand During Lead Time = 960000

d)

With Order Size 800000 -

Annual Holding Cost = (Q*12/2)*H = (800000*12/2)*0.65% = 31200

Annual Ordering Cost = (D/EOQ)*S = (5000000*12/800000)*675 = 50625

Total Holding Cost + Ordering Cost = 31200+50625 = 81825

With Order Size 750000 -

Annual Holding Cost = (Q*12/2)*H = (750000*12/2)*0.65% = 29250

Annual Ordering Cost = (D/EOQ)*S = (5000000*12/750000)*675 = 54000

Total Holding Cost + Ordering Cost = 29250+54000 = 83250

Since, With every fall in value of placing cash order, the ordering cost increases more than decrease in carrying cost and hence sum total of ordering and carrying cost increases.

Hence First City bank order with 800000.