Question

Smith Industries purchases a subcomponent critical for its most popular product from another manufacturer. The annual demand for the subcomponent is 5,000 units. The holding cost is assessed at 20% of the price of the subcomponent. The manufacturer of the subcomponent charges Smith $30 for each unit if Smith orders less than 200 units and $28 for each unit if Smith orders 200 units or more. Smith’s cost to place an order is $20. Round off your responses to the nearest unit, number of orders, etc.

a) What is the optimal order quantity for this subcomponent if the EOQ model is used?
b) What is the total of annual relevant costs of Smith Industries (considering the cost of inventory holding and cost of ordering)?
c) If the EOQ model is used, what is the optimal number of orders to be placed in a year?
d) If the manufacturer’s lead time is 1 week and Smith operates 50 weeks a year, what is the reorder point for the product?
e) What is your interpretation of the reorder point you calculated in part (d)?

Answer 1

Annual demand(D) = 5000 tires

Ordering cost (S) =$20

Holding cost(H) = 20% of purchase price

Order size Price per unit Holding cost(20% of price per unit)

0-199 30 6

200 or more 28 5.6

First find the minimum point for each price starting with the lowest price until feasible minimum point is located.This means until a minimum point falls in the quantity range for its price

Minimum point for price of $28 = Sqrt of (2DS/H)=Sqrt of [(2X5000X20)/5.6] = sqrt of (200000 / 5.6) = 189 unites.Because an order size of 189 will cost $30 rather than $28, 189 is not a minimum feasible point for $28 per unit.

Minimum point for price of $30 = Sqrt of (2DS/H) =Sqrt of [(2X5000X20)/6]= sqrt of (200000 / 6) = 183 units This is feasible as it falls in the $30 per unit range of 0-199

Now the total cost for 183 units is computed and compared to the total cost of the minimum quantity needed to obtain price of $28 per unit

Total cost for Q=183 is (Q/2)H + (D/Q)S + (PriceXD)

= [(183/2)6] + [(5000/183)20] + (30 X5000)

= 549 + 546.45 + 150000

= $151095.45

The minimum quantity needed to obtain a price of $28 is 200 units.So with order quantity(Q) = 200 units,

Total cost = (Q/2)H + (D/Q)S + (PriceXD)

= [(200/2)5.6] + [(5000/200)20] + (28 x 5000)

=560 + 500 + 140000

= $141060

a) So the optimal order quantity(Q*) is 200 units as it has the lowest total cost  

b) Total annual cost is $141060 calculated above

C) Number of orders per year = D/Q* = 5000/200 = 25

D) Number of weeks per year = 50 weeks

Average weekly demand (d) = D/number of weeks per year = 5000/50 = 100 units

Lead time (L) = 1 week

Reorder point = d x L = 100 x 1 = 100 units