Parkas 1000 2000 3000 2000 1000 27,011.00 A firm sells five women’s ski parkas.
ID: 336749 • Letter: P
Question
Parkas
1000
2000
3000
2000
1000
27,011.00
A firm sells five women’s ski parkas. Some data on those parkas are listed above:
?? in the above table is the optimal newsvendor quantity and “Expected Profit” is the newsvendor expected profit if ?? is ordered. Cu = p-c, the gross margin. The firm will produce some parkas well in advance of the selling season. The other parkas are produced after a trade show that occurs shortly before the season starts. After attending the trade show, the firm will basically know demand for each parka. Unfortunately, the firm’s capacity is limited after the trade show, so the firm wants to produce at least 5,000 parkas before the trade show. Furthermore, a parka should be produced either before or after the trade show, but a parka should not be produced in both production opportunities.
a) What is the firm’s total expected profit if every parka is produced before the trade show? [Hint: you can get the answer almost immediately from the above table.]
b) What is the firm’s total expected profit if every parka is produced after the trade show (assuming that the capacity is enough and all of its production arrives by the start of the selling season)?
c) With the limited capacity after the trade show, what type(s) of parkas and quantities should be produced before the trade show? And what type(s) of parkas and the expected number of units should be produced after the trade show?
d) Given part C, what are the firm’s total expected profit and mismatch cost?
Parkas
? ? Cu Co Q Expected Profit a1000
300 52.8 35.2 1076 42,601.00 b2000
800 49.2 28.7 2269 74,903.00 c3000
1500 45.6 22.8 3646 99,495.00 d2000
1200 42 17.5 2650 59,399.00 e1000
700 38.4 12.8 147227,011.00
Explanation / Answer
Solution:
A. If every parka is produced before the trade show, the demand for all the items is unknown and we directly apply the newsvendor model. The firm’s expected profit is the sum of Newsvendor expected profits for all types of parkas, which is simply the sum of the last column in the table: 42601 + 74903 + 99495 + 59399 + 27011 = 303409
B. If all units could be produced after the trade show, the demand for each item would be known at the time of the production, in which case the firm would obtain the maximum possible profit. The expected maximum profit for a specific type of parka is the mean demand times its gross margin (which corresponds to the cost of underage). For example, for parka A the maximum profit is 1000 ´ 52.8 = $52,800. The total maximum profit is 1000 * 52.8 + 2000*49.2 + 3000*45.6 + 2000*42 + 1000 * 38.4 = $410,400.
C. Some items have a higher mismatch cost, i.e. a higher difference between the maximum profit and the newsvendor profit. It is better to produce the items with high mismatch cost after the tradeshow since after the show the demand is known and that high mismatch cost is avoided. But the production quantities also matter. An item can have a high mismatch cost but very low demand, in which case it might be ok to produce it before the tradeshow. The rule is evaluating the mismatch-quantity ratio for each parka (the mismatch cost divided by the newsvendor quantity). We then sort them in increasing order: The ones with a high mismatch-quantity ratio will be at the bottom. The table of data is below:
If 5000 parkas must be produced before the tradeshow, then the order quantities should be E = 1472, D = 2650, A = 1076, C = 0 and B = 0. In other words, produce the newsvendor quantity for parkas E, D and A, but wait to produce parkas C and B until after the tradeshow.
D Expected profit is the sum of the newsvendor profits from E,D and A and the maximum profit from C and B: 27011 + 59399 + 42601 + 136800 + 98400 = $3,64,211.
Parkas ? Cu Q Expected Profit Maximum Profit Mismatch cost Mismatch cost/quantity ratio e 1000 38.4 1472 27011 38400 11389 7.74 d 2000 42 2650 59399 84000 24601 9.28 a 1000 52.8 1076 42601 52800 10199 9.48 c 3000 45.6 3646 99495 136800 37305 10.23 b 2000 49.2 2269 74903 98400 23497 10.36 Sum 303409 410400 106991