Hello, since I am not that great wih this subject I would like a double check of
ID: 327848 • Letter: H
Question
Hello, since I am not that great wih this subject I would like a double check of my work, because I feel it may be incorrect. If it is can you please help me reach the correct one, because I really want to understand this, along with where I might have made the mistake. Thank You
This is what I got out of the problem:
R= $10, C=$8, and off season (s)= $5
A) 475 units using norm.inv.
B) 0.60
C) 525 units using norm.inv.
D) 604 units
Thank You!
A retail outlet sells holiday decorations for $10 per bag. The cost of the product is $8 per bag. Any units not sold during the selling season can be sold for $5 a bag at the end of the season. Assume that demand for these decorations is normally distributed with a mean of 500 and standard deviation of 100 bags. a. What is the recommended order quantity? b. What is the probability that at least some customers will ask to purchase the product after the outlet is sold out? C. Suppose at the end of the selling season, the decorations have no value and have to be disposed of at a cost of $0.10 per bag. Now what is the optimal order quantity? d. To keep customers happy and coming back, the owner of the store feels that stock-outs should be avoided. What is the recommended order quantity if the owner is willing to tolerate only a 0.15 probability of a stock-out? e. Using your answer to part (d) what is the goodwill cost you are assigning to a stock-out?Explanation / Answer
PLEASE FIND ANSWERS TO FIRST 4 QUESTIONS AS REQUIRED :
Selling price = P = $10/ bag
Purchase cost = C = $8 / bag
Salvage value = S = $5 / bag
Underage cost , Cu = P – C = $2
Overage cost , Co = C – S = $3
Critical ratio = Cu/ Cu + Co = 2/( 2 + 3 ) = 2/5 – 0.4
Critical ratio is same as in stock probability
Therefore in stock probability = 0.40
Corresponding Z value for in stock probability = NORMSINV ( 0.40 ) = - 0.2533
Recommended order quantity
= Mean demand + Z value x Standard deviation of demand
= 500 – 0.2533 x 100
= 500 – 25.33
= 474.67 ( 475 rounded to nearest whole number )
RECOMMENDED ORDER QUANTITY = 475
Stockout probability = 1 – In stock probability = 1 – In stock probability = 1 – 0.4 = 0.6
Probability that at least some customers will ask to purchase the product after the outlet is sold out = 0.60
Overage cost , Co = Cost / unit – Salvage Price/ unit = $ 8 - $0.1 = $7.9
Critical ratio = Cu/( Cu + Co) = 2/ ( 2 + 7.9) = 2/9.9 = 0.202
Z value for critical ratio 0.202 = NORMSINV ( 0.202) = - 0.8344
Optimal order quantity
= Mean demand + z value x Standard deviation of demand
= 500 – 0.8344 x 100
= 500 – 83.44
=416.56 ( 417 rounded to nearest whole number )
OPTIMAL ORDER QUANTITY = 417
d)Probability of stockout = 0.15 . Therefore in stock probability = 1 – 0.15 = 0.85
Z value for instock probability of 0.85 = NORMSINV ( 0.85 ) = 1.0364
Therefore , recommended order quantity
= 500 + 1.0364 x 100
= 500 + 103.64
= 603.64 ( 604 rounded to nearest whole number )
Recommended order quantity = 604
RECOMMENDED ORDER QUANTITY = 475
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