Question

The SCO Company sells desks that have a demand of 4 units per month and cost $25 each, the annual carrying charge is 30 percent of the product value, and it costs $15 to place an order. The company is considering installing either a Q or a P system for inventory management. The standard deviation of demand has been 4 units per month, and the replenishment lead time is two months, a 90 percent service level is desired. For Parts a and b below, specify the two key decisions under each inventory management system, and describe the implementation of the respective system (e.g., the description of a EOQ system with reorder point R and order quantity Q will be: When the inventory level drops to the reorder point level R, then a new order of size Q will be placed). You can round your calculations to 3 decimal places.

a) How would you design a continuous review system?

b) How would you design a periodic review system?

c) What are the pros and cons of using the periodic system compared with using the continuous review system for this product?

Answer 1

Demand = 4x12 = 48 per year

EOQ = [ 2 x 48 x 15 / 0.3 x 25]^1/2

= 13.85 =14

Number of orders per year = 48/14 = 3.4 =4

Continuous review system

Reorder point = avg demand x lead time + safety stock

safety stock = z x standard deviation of demand during lead time

z x S.D. ( Lead time )^1/2

= 1.29 x 4 ( 2 )^1/2 = 7.29

Reorder point = 4 x2 + 7.29 = 15.29

Hence an order of 14 units will be placed when the stocks decline to 15.29 units.

Periodic Review system

The order up to level when the demand is variable and lead time is constant ( for a period P between the reviews)

Order up to level = Avg demand (review period +Lead time) + z SD_P+L

= 4 ( P+2) + 1.29 x SD ( P+2)^1/2

If the value of P is known, the reorder point can be calculated from the formula.

Calculation of P

P = EOQ /d = 14 / 4 =3.5 =4

Time to order = 4 ( 2+4)+ 1.29 x 4 x(6)^1/2 = 24+ 12.63 = 36.63

From the example it can be seen that Q system has following advantage

1. Review frequency can be Individualised

2.Lower safety stocks

3.Fixed lot sizes can yield quantity discounts.

Advantages of P system

1. It is convenient

2. Orders can be combined