Question

A firm uses 200,000 units of an inventory item evenly throughout the year. The firm’s order cost is $400 per order and carrying cost is $40 per unit per year.

(A) Suppose an order placed at the end of the day will arrive in time before the next day’s production begins and the firm does not keep a safety stock. How many units of this inventory item should the firm order each time?

(B) Suppose it takes the supplier two days to process an order, another two days for the firm to receive the shipment and prepare it for production, and the firm has a policy of maintaininga safety stock equal to five days of usage. What should be the firm’s reorder point for this inventory item? Assume a commercial year.

Answer 1

Given values:

(A) Annual demand, D = 200,000 units

Order cost, Co = $400 per order

Carrying cost, Cc = $40 per unit per year

If an order is placed at the end of the day and it arrives in time before the next day’s production begins and the firm does not keep a safety stock. The number of units of this inventory item that the firm should order each time is given by the Economic Order Quantity (EOQ). EOQ is calculated as;

EOQ = SQRT [(2 x D x Co) / Cc]

EOQ = SQRT [(2 x 200000 x 400) / 40]

EOQ = SQRT (4000000)

EOQ = 2000 units

Number of units to order = 2000 units

(B) Now,

Lead time, L = 2 + 2 = 4 days

Safety stock = 5 days of usage

In a commercial year, number of days = 360

Daily usage, d = Annual demand / Number of days

Daily usage, d = 200000 / 360 = 555.56 units

Reorder point (ROP) is calculated as;

ROP = (Average daily usage x Delivery lead time) + Safety stock

Given that the firm maintains a safety stock of 5 days usage, therefore,

Safety stock = 5 x daily usage = 5 x 555.56 = 2777.8 units

ROP = (555.56 x 4) + 2777.8

ROP = 5000.04 or 5000 (rounding off to nearest whole number)

Reorder point = 5000 units