Question

18.

A medical device distributor sells coronary stents and is considering one final bulk order from the manufacturer for an end-of-life product to cover the product's final year on the market. Based on the company’s observations, the demand for these stents is normally distributed with a mean of 14,230 per year and a standard deviation of 906. The stents are sold for $450 and cost $230 to purchase. If they go unsold, the stents remain in inventory for 3 months before they can be safely discarded. The annual holding cost is 20%. Additionally, the company earns a $20 rebate per stent discarded from the federal government to incentivize responsible disposition. If the distributor was able to negotiate the stent acquisition costs down, how would the profit maximizing order quantity change?

It would not change

It would decrease

Unable to determine from given information

It would increase

Answer 1

1. D. IT WOULD INCREASE.

COST PRICE = 230
SALES PRICE = 450
SALVAGE VALUE = 8.5(20 - 3 MONTHS HOLDING COST)

Cost of shortage(Cs) = sales price - cost price = 450 - 230 = 220
Cost of overage(Co) = Cost price - salvage value = 230 - 8.5 = 221.5

Service level = Cs / (Cs + Co) = 220 / (220 + 221.5) = 0.4983
The Z value that corresponds to a service level of 0.4983 is = -0.004

Mean demand = 14230
Standard deviation = 906

Optimal stocking level = Mean demand + (Z * Standard deviation)

= 14230 + (-0.004 * 906) = 14227(APPROX)

WITH A LOWER PURCHASE COST, THE OPTIMAL ORDER QUANTITY WOULD INCREASE BECAUSE OF HIGHER COST OF SHORTAGE AND LOWER COST OF OVERAGE