Question

Question 15 (2 points) Corin sells Sunday papers outside a retirement home on Sunday mornings. Corin collects $2.21 per paper and pays $0.92 for a paper. The retirement home residents think fondly of Corin and aren't too upset when papers run out. On the other hand, any papers Corin is left with are thrown into the recycling bin. Corin is trying to figure out a systematic ordering policy. When Corin runs out of papers, the sale is lost. Demand is uniformly distributed between 26 and 36 newspapers per day. Calculate the optimal stocking. (round off to the nearest whole number) Your Answer: Your Answer

Answer 1

This problem will be solved using Newsvendor model

Critical ratio under profit maximization in case of newsvendor model will be defined as :

Critical Ratio =    Cu / ( Cu + Co)

Where ,

Cu = Underage cost i.e. cost of ordering one fewer unit than what one would have ordered had one known the demand (i.e situation under lost sales) = Price/unit – Cost/unit

Co = Overage cost i.e. cost of ordering one more unit than what one would have ordered had one known the demand ( i.e. one overordered) = Cost/unit – Salvage value/unit

Thus,

Critical ratio

= Cu/ ( Cu + Co)

= (Price – Cost ) / ( Price/unit – Cost/unit + Cost/unit – Salvage value/unit )

= (Price/unit – cost/unit )/( Price/unit – Salvage value/unit )

In the given case,

Price/ unit for Corin = $2.21

Cost / unit for corin = $0.92

Salvage value / unit for corin = 0

Critical ratio

= ( 2.21 – 0.92) / ( 2.21 – 0 )

= 1.29/2.21

= 0.5837

Critical ratio is also the probability associated with optimum stocking quantity.

From the given data:

Probability that demand will be at least 26 newspapers = 1

Probability that demand will be at least 36 newspapers = 0

Since , demand is uniformly distributed, demand corresponding to probability 0.5837

= 36 – ( 36 – 26) x 0.5837

= 36 – 10 x 0.5837

= 36 – 5.837

= 30.163 ( 30 rounded to nearest whole number)

OPTIMAL STOCKING QUANTITY = 30