Question

QUESTION 2 It is a requirement that you complete Industrial Engineering Practice I and II before you can raduate. Your brother owns a hardware store and on the occasions you have worked in the store you have notice his business experience problems with inventory holding. You offered your assistance in solving some of the inventory problems. During your observations you determine the annual demand for number six screws is 100 000. For the purpose of the Work Integrated Learning exercise, your brother made you responsible for all purchases. After studying previous records, you estimate the ordering cost to be R10 every time the business place an order for the screws. Furthermore, you estimate that the cost of carrying one screw in inventory for a year is one-half of one cent. Observing the process over time, you determine it takes approximately 8 working days for an order of number six screw to arrive once you place 13 an order. The de mand for number six s crews is constant, and on average, you observe the store sells 500 of the se screws each day. You are of the opinion stocks outs can be eliminate if the screws are ordered at the correct time. Your brother is unhappy with t you place for the screws. He is of the opinion orders should be placed twice a year. You are required to: a. Through the application of the correct equation, compute the number of screws to be ordered at a time if you wish to minimise total inventory cost b. Through the application of the correct equation, compute the number of orders to be placed annually as well as the annual ordering cost. c. Through the application of the correct equation, compute the average inventory as wel as the annual holding cost. d. Through the application of the correct equation, compute the reorder point (ROP). you adhere to the policy prescribed by you brother, how much how much more would e. If this cost every year over the policy you developed? If only two orders year, what effect would this have on the ROP? were placed each 125]

Answer 1

Solution:

Total cost will be minimum when EOQ (Economic Order Quantity) is followed where, Carrying cost will be equal to Ordering Cost.

Using the following formula we can calculate EOQ :

Ordering cost = Carrying cost

=> Annual order / Ordering Quantity * Cost per Order = 1/2*Ordering Quantity * Carrying cost per unit

=> A / OQ * O = 1/2 * OQ * C

=> 2A / OQ * O = OQ * C (Multiplying 2 on both sides)

=> 2A * O = OQ² * C

=> 2A * O / C = OQ²

=> OQ = $\sqrt{2A * O / C}$

Here we have A = 100,000 units

O = $10

C = $0.005 (being one half of a cent)

Accordingly we get OQ =

2 100000 10/0.005

or, OQ =

400, 000, 000

Or, OQ = 20000

Hence the ordering quantity should be 20,000 units per order.

(a) Number of screws to be ordered at a time to reduce total inventory cost will be the point when the ordering and carrying cost will be equal i.e. at 20,000 units per order.

(b) Number of orders to be placed annually = Total Annul demand / Units to be ordered per order = 100000/20000 = 5 Orders.

Annual Ordering cost will be = No. of orders * Cost per order = 5 * 10 = $50.

(c) Average inventory level = EOQ Quantity / 2 = 20000/2 = 10,000 units

Annual holding cost = Average inventory level * Holding cost per unit per year = 10000 units * 0.005 = $50

(d) Reorder Point = Daily demand * Time taken to complete an order = 500 units * 8 days = 4000 units

(e) If two orders will be placed in a year the following will be the total cost :

Total cost = Carrying Cost + Ordering cost

TC = (Avg. Inventory held * Holding cost per unit) + (No. of Orders * Cost per order)

TC = (50000/2 * 0.005) + ( 2* 10)

TC = 125 + 20

TC = 145

If five orders are placed as per EOQ Total cost will be as follows:

Total cost = Carrying Cost + Ordering cost

TC = (Avg. Inventory held * Holding cost per unit) + (No. of Orders * Cost per order)

TC = ( 20000/2 * 0.005) + ( 5 * 10)

TC = 50 + 50

TC = 100

Excessive cost if two orders will be placed = 145-100 = $45

Effect on ROP if two orders will be placed :

The ROP will remain unchanged even if two orders will be placed.

ROP = Daily demand * Time taken to complete an order = 500 units * 8 days = 4000 units