Question

A large bakery buys flour in 20-pound bags. The bakery uses an average of 1050 bags a year. Preparing an order and receiving a shipment of flour involves a cost of $15 per order. Annual Carrying costs are $ 55 per bag. a) Determine the economic order quantity? b) What is the average number of bags on-hand? c) How many orders per year will there be? d) Compute the total cost of ordering and carrying flour? e) If holding costs were to increase by $5 per year, how much would the minimum total annual cost?

Answer 1

Given the following:

• Demand = 1050
• Ordering cost = 15
• Holding cost = 55

The economic order quantity is 24.

What is the economic order Quantity?

Eoq = √2 * demand * ordering cost / holding cost)

= √(2 * 1050 * 15 / 55)

EOQ = 24

What is the average number of bags on-hand?

The  Average inventory = EOQ / 2

= 24 / 2

= 12

How many orders per year will there be?

Expected number of orders = demand / EOQ

= 1050 / 24

= 44

What is the total cost of ordering and carrying flour?

Annual holding cost (AHC) = (EOQ / 2) * Holding cost

= (24 / 2) * 55

= 660

Annual ordering cost (AOC) = (demand / EOQ) * ordering cost

= (1050 / 24) * 15

= 656

Thus,

Total cost of managing = AHC + AOC

= 660 + 656

TCM = 1,316

If holding costs were to increase by $5 per year, how much would the minimum total annual cost?

5. For holding cost of 60

EOQ= √(2 * demand * ordering cost / holding cost)

= √(2 * 1050 * 15 / 60)

= 23

Annual holding cost = (EOQ / 2) * holding cost

this gives us

= (23 / 2) * 60

= 690

Annual ordering cost = (demand / EOQ) * ordering cost

= (1050 / 23) * 15

= 685

Total cost of managing = AHC+ AOC

= 690 + 685

= 1375

Change in total annual cost = new - old

= 1375 - 1316

= 59

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