Question

Suppose that Dr. Su really want to get out of academia for more $$ but driving for Uber may not be ideal for him. He decides to start a new business and now sells sunglasses to a retailer called Ultimate Vision (UV). UV purchases each one of the pairs of sunglasses from Dr. Su for $75 and retails them for $115. Dr. Su’s sourcing cost from Alibaba is $35. At the end of the season, UV estimates the salvage value is only about $25 each pair. UV believes this season’s demand can be represented by a normal distribution with a mean of 250 and a standard deviation of 125.

The following is the supply chain:

Alibaba --> Dr. Su’ store --> UV retail --> customers

(a) What is UV’s optimal order quantity?

(b) What is Dr. Su’s profit when UV order at optimal?

(c) From a maximize-your-own-profit perspective, should UV order at a different amount than (a), (state your reason)?

(d) Consider Dr. Su's store and UV retail store as a single entity, what is the optimal order quantity for the single entity?  

(e) What can Dr. Su do to encourage UV order at the amount in (d)?

Answer 1

(a) What is UV’s optimal order quantity?

Cost -75

Price -115

Salvage price =25

Demand distribution:

Mean demand, u=            250

Standard Deviation of demand, s =   125

Overage cost is the per-unit cost of over ordering. Underage cost is the per-unit opportunity cost of ordering below demand.

Cost of Overage (Co) = cost - salvage = $`75 - $25 = $50

Cost of Underage (Cu) = Price - cost = $ 115- $ 75 = $ 40

STEPS

• Find critical ratio.
• then Find z value using critical ratio
• Convert Z into order quantity, Q= u + z*standard deviation

(Service level required)

Critical ratio, F(Q )

=Cu/(Cu + Co)

=40/(40+50)

= 0.4444

Now we find z-value corresponding to critical ratio=0.4444. . Z( 0.4444 ) =   -0.14

If the critical ratio falls between two values in the standard normal distribution table, choose the greater z-statistic

Profit maximizing order quantity

= u + z*standard deviation

=250+ (-0.14) (125)

= 232.5 or 236 units

(b) What is Dr. Su’s profit when UV order at optimal?      

Profit

= UV order quantity * (selling price of Dr SU-cost for Dr su)

=236*(75-35)

=9440

(c) From a maximize-your-own-profit perspective, should UV order at a different amount than (a), (state your reason)?

No.

If UV orders above this amount, it may not be able to sell and may incur high salvage costs resulting in decreased profit

If UV orders below this amount, then it may lose some sales and the profits will decrease

(d) Consider Dr. Su's store and UV retail store as a single entity, what is the optimal order quantity for the single entity?  

If we consider as a single entity, then the item enters the entity at a cost of 35 and leaves the entity at a price of 115. Salvage value remains the same

Cost -35

Price -115

Salvage price =25

Demand distribution:

Mean demand, u=            250

Standard Deviation of demand, s =   125

Overage cost is the per-unit cost of over ordering. Underage cost is the per-unit opportunity cost of ordering below demand.

Cost of Overage (Co) = cost - salvage = $`35 - $25 = $10

Cost of Underage (Cu) = Price - cost = $ 115- $ 35 = $ 80

STEPS

• Find critical ratio.
• then Find z value using critical ratio
• Convert Z into order quantity, Q= u + z*standard deviation

Service level required

Critical ratio, F(Q )

=Cu/(Cu + Co)

=80/(80+10)

= 0.8889

Now we find z-value corresponding to critical ratio=0.4444 from standard normal distribution table. Z( 0.8889) = 1.23

If the critical ratio falls between two values in the standard normal distribution table, choose the greater z-statistic.

Profit maximizing order quantity

= u + z*standard deviation

=250+ 1.23* (125)

= 403.75 units

(e) What can Dr. Su do to encourage UV order at the amount in (d)?

The underage cost for UV should rise or the overage cost for UV should decrease. Ie either the cost of purchase should decrease or the salvage value should increase

Dr Su can either

• decrease his selling price for UV (so that cost for UV reduces )
• assure to rebuy unsold items at high salvage value