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Chapter 12

Q. 12.EX.6

EOQ IS A ROBUST MODEL. Management in the Sharp, Inc., examples underestimates total annual demand by 50% (say demand is actually 1,500 needles rather than 1,000 needles) while using the same Q. How will the annual inventory cost be impacted?
APPROACH \blacktriangleright We will solve for annual costs twice. First, we will apply the wrong EOQ; then we will recompute costs with the correct EOQ.

Step-by-Step

Verified Solution

SOLUTION \blacktriangleright If demand in Example 5 is actually 1,500 needles rather than 1,000, but management uses an order quantity of Q = 200 (when it should be Q = 244.9 based on D = 1,500), the sum of holding and ordering cost increases to $125:

Annual cost = \frac{D}{Q}S + \frac{Q}{2}H = \frac{1,500}{200}(\$ 10) + \frac{200}{2}(\$ .50) = $75 + $50 = $125

However, had we known that the demand was for 1,500 with an EOQ of 244.9 units, we would have spent $122.47, as shown:

Annual cost = \frac{1,500}{244.9}(\$ 10) + \frac{244.9}{2}(\$ .50) = 6.125($10) + 122.45($.50) = $61.25 + $61.22 = $122.47

INSIGHT \blacktriangleright Note that the expenditure of $125.00, made with an estimate of demand that was substantially wrong, is only 2% ($2.52/$122.47) higher than we would have paid had we known the actual demand and ordered accordingly. Note also that were it not due to rounding, the annual holding costs and ordering costs would be exactly equal.

LEARNING EXERCISE \blacktriangleright Demand at Sharp remains at 1,000, H is still $.50, and we order 200 needles at a time (as in Example 5). But if the true order cost = S = $15 (rather than $10), what is the annual cost? [Answer: Annual order cost increases to $75, and annual holding cost stays at $50. So the total cost = $125.]

RELATED PROBLEMS \blacktriangleright 12.10b, 12.16 (12.36a,b are available in MyOMLab)