Consider a newsvendor retailer who purchases a product for $7.50 and can sell th

Question

Consider a newsvendor retailer who purchases a product for $7.50 and can sell that product for $15.00. This product experiences expected demand of 1,000 with a standard deviation of 150 units. This retailer is considering two options:

Option 1

Dispose of leftover items for $0 per item

Option 2

Donate leftover items for a refund of $2 per item

Fill in the blanks of the following sentence:

Under option 1, the retailer's optimal order quantity is ____ units; under option 2, the retailer's optimal order quantity is ____ units; if demand winds up being exactly 1,200 units, the retailer is better off using option___.

Explanation / Answer

For option 1 :

Selling price = P = $15 / unit

Purchase price = C = $7.5 / unit

Salvage price = S = 0

Therefore ,

Underage cost = Cu = P – C = $15 - $7.5 = $7.5

Overage cost = Co = C – S = $7.5 – 0 = $7.5

Therefore , critical ratio = Cu/( Cu + Co ) = 7.5 / ( 7.5 + 7.5) = 7.5/15 = 0.5

Critical ratio is the probability of the optimum order quantity .

Corresponding Z value for probability 0.5 = NORMSINV ( 0.5 ) = 0

Therefore, optimum order quantity

= Expected demand + Z value x standard deviation of demand

= 1000 + 0 x 150

= 1000

For option 2 :

Selling price = P = $15 / unit

Purchase price = C = $7.5 / unit

Salvage price = S = 2

Therefore ,

Underage cost = Cu = P – C = $15 - $7.5 = $7.5

Overage cost = Co = C – S = $7.5 – 2 = $5.5

Therefore , critical ratio = Cu/( Cu + Co ) = 7.5 / ( 7.5 + 5.5) = 7.5/13 = 0.5769

Critical ratio is the probability of the optimum order quantity .

Corresponding Z value for probability 0.5 = NORMSINV ( 0.5769) = 0.1939

Therefore, optimum order quantity

= Expected demand + Z value x standard deviation of demand

= 1000 + 0.19339 x 150

= 1000 +29.08

= 1029.08 ( 1029 rounded to nearest whole number )

For optimum order quantity combination of ( 1000, 1029) , if the demand becomes 1200 units :

For order quantity = 1000, opportunity loss of profit is for 200 units @ $7.5 ( i.e. Cu) per unit = $1500

For order quantity = 1029 , opportunity loss of profit is for = 1200 – 1029 = 171 units @ 7.5 per unit = $1282.50

Opportunity loss of profit is therefore less for option 2 ( i.e. order quantity 1029 ) and therefore , retailer is better off using option 2

Under option 1 , retailer’s optimal order quantity is 1000 units ; under option 2, retailer’s optimal order quantity is 1029 units; if demand winds up being exactly 1200 units , the retailer is better off using option 2

Under option 1 , retailer’s optimal order quantity is 1000 units ; under option 2, retailer’s optimal order quantity is 1029 units; if demand winds up being exactly 1200 units , the retailer is better off using option 2

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