Cabot Appliances, a retail chain, is trying to decide what size order it should

ID: 344432 • Letter: C

Question

Cabot Appliances, a retail chain, is trying to decide what size order it should place with its supplier of room air conditioners. Room air conditioner sales are highly seasonal, and the number of units sold is very dependent on summer weather patterns. Cabot places one order per year. Reorders are impractical after the selling season begins to develop. Although the actual sales level cannot be known for sure, Cabot analyzes past selling seasons, long-term weather reports, and the general state of the economy. The following probabilities of various sales levels are then estimated: Probabilit 0.2 0.2 0.3 0.2 Sales, units 500 750 1,000 1,250 1,500 1.0 A unit has a delivered price to Cabot of $320 and it is priced to customers at $400. Air conditioners unsold at the end of the season are discounted to $300, which clears them from inventory. Purchases can be made only in increments of 250 units, with a 500-unit minimum order. a. Assuming no inventory is to be carried to the next year, what single order size should be placed? b. Would you modify the order quantity in part a if Cabot can borrow money to support inventory at 20 percent per year? Excess units can be carried over to the next selling season.

Explanation / Answer

Given problem is solved by applying Newsvendor problem method as follows:

Retail price = p = $400/unit

Unit Cost = c = $320/unit

Salvage cost = s = $300/Unit

Cu = under-stocking cost = cost of shortage (underestimate demand) = Sales price/unit – Cost/unit

Cu = $400 – $320 = $80 per unit

Co = Over-stocking cost = Cost of overage (overestimate demand) = Cost/unit – Salvage value/unit

Co = $320 – $300 = $20 per unit

The service level or probability of not stocking out, is set at,

Service Level = critical ratio = Cu/( Cu + Co) = 80/(80 + 20)

Service Level = critical ratio = 0.8

Quantity Sold

Probability

Cumulative Probability (less than)

500

0.2

750

0.2

0.4

1000

0.3

0.7

1250

0.2

0.9

1500

0.1

1.0

Select the order quantity whose Cumulative probability is immediate greater than Critical ratio = 0.80 to maximize expected profit.

The cumulative prob. of order quantity 1250 units is 0.9, immediate greater probability than Critical ratio.

Optimal Order Quantity = Qo = 1250 units