Question

1. Saga ltd. produces electronic toys for children between the ages of 7-10 years old. The toys use a processor that is imported from Japan. Annual demand for the processor is 12,500. The holding cost per processor per year is $2. Ordering cost per order is $400. Lead time is 7 days and the number of working days in the year is 250.

a.                   What is the economic order quantity?

b.                  What is the optimal number of orders per year?

c.                   Calculate the annual holding cost if the economic order quantity is used.

d.                  What is the optimal number of days between any two orders?

e.                   What is the reorder point?

f.                   Given the EOQ, what is the total annual inventory cost?

2. Rocky Mountain Tire Centre sells 20,000 tires of a particular type per year. The ordering cost for each order is $40, and the holding cost is 20% of the purchase price of the tires per year. The purchase price is $20. per tire if fewer than 500 tires are ordered, $18. Per tire if more than 500 but fewer than 1,000 tires are ordered and $17. per tire if 1,000 or more tires are ordered. How many tires should Rocky Mountain order each time it places an order?

3. Quantity Unit Price

1-499                       $20.

500-999                   $18.

1000 & over            $17

Based on available information, lead time demand for CD-ROM drives averages 50 units (normally distributed), with a standard deviation of 5 drives. Management wants a 97% service level.

1. What value of Z should be applied?
2. How many drives should be carried as safety stock?

Answer 1

Q.1) Annual Demand = 12,500

Ordering Cost = $400

Carrying Cost = $2

a) Economic Order Quantity (EOQ) = sqrt(2 * Annual Demand * Ordering Cost / Carrying Cost)

Economic Order Quantity (EOQ) = sqrt(2 * 12500 * 400 / 2)

Economic Order Quantity (EOQ) = 2236.07 units

b) Number of orders = Annual Demand / EOQ

Number of orders = 12500 / 2236.07

Number of orders = 5.59 orders

c) Annual holding cost = EOQ/2 * annual carrying cost per unit

Annual holding cost = 2236.07/2 * 2

Annual holding cost = $2236.07

d) Number of days between two orders = Total working days in a year/number of orders

Number of days between two orders = 250 / 5.59

Number of days between two orders = 44.72

e) Standard deviation of demand during lead time = 0

Re-order point = (Annual Demand/Total working days in a year) * Lead time

Re-order point = (12500 / 250) * 7

Re-order point = 350 units

f) Total Annual Inventory Cost = Annual Ordering Cost + Annual Carrying Cost

Total Annual Inventory Cost = number of orders * ordering cost per order + EOQ/2 * annual carrying cost per unit

Total Annual Inventory Cost = 5.59 * 400 + 2236.07/2 * 2

Total Annual Inventory Cost = $4472.07

Q.2) We compare the Total Cost for different quantities and decide on the order quantity that has the minimum total cost

Total Cost = Total purchase cost + Total ordering Cost + Total Inventory carrying cost

Total purchase cost (Total Material Cost) = Annual Quantity * Price

Total Ordering Cost = Annual Quantity / Order Quantity * Ordering Cost per Order

Total Inventory carrying cost = Order quantity / 2 * Holding cost per unit

For a particular range, say 500 - 999 units, the Total Cost goes on increasing as we increase the order quantity size.

Hence, for the 1000+ bracket, Total cost will be the least at 1000 units and goes on increasing as we increase the order quantity from 1000 units

Optimal Order Quantity = 1000 units

Q.3) For a service level of 97%, using Excel function NORM.S.INV(probability),

z = NORM.S.INV(0.97)

z = 1.881

The standard deviation of demand during lead time = 5 drives

Safety stock = z * standard deviation of demand during lead time

Safety stock = 1.881 * 5

Safety stock = 9.41 =~ 10

Safety stock = 10 drives

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