Question

You have recently been hired as a purchasing coordinator. Your primary product has an annual demand of 3,650 units. You buy the product from a famous supplier with the cost of $40 per unit and you sell the product for $80 per unit. Before you arrived, shortages (or backorders) were not allowed, but management would like to see how inventory decisions would change if shortages were allowed. They are assuming that they can offer a 5% discount to any customer who has a backorder to prevent them from purchasing the product elsewhere. Your company purchases the product from a wholesaler, and it costs $25 to process the order, and the annual holding cost is $5 per unit per year. Assume each year has 365 days.

(a) If shortages are allowed, how many units should be ordered each time that an order is placed?

Now some of the information in the problem changes. For the following options, please specify whether these changes would influence your decision (as calculated in part (a)).

(b) If Instead of knowing the information of the primary product has an annual demand of 3,650 units, you know the daily demand of the primary product is 10 units. Will this change influence your decision in part (a)?

(c) If the cash on hand in the company is $8000, will this change influence your decision in part (a)?

(d) If you buy the product from a famous supplier with the cost of $60 per unit (instead of $40), will this change influence your decision in part (a)?

Answer 1

(a)

Annual demand, D	3650	units
Cost per unit, C	$40
Holding cost, Ch	$5
Order/Setup cost, Co	$25
Backorder cost, Cb = 80*5% =	$4
Optimal order Qty, Q	287	= SQRT((2DCo/Ch)*(Ch+Cb)/Cb)

(b) This change will not influence the decision, because daily demand of 10 units amounts to annual demand of 3650 units only.

(c) Yes, this change will influence the decision, because the total value of optimal order quantity is 287*40 = 11463, which is more than available budget of $ 8000. Therefore, order quantity need to be reduced.

(d) This will not influence the decision, because inventory holding cost or backorder cost are not dependent upon the purchase cost.