A clothing retailer is selling a fashion print tee that retails for $22.95 and has a...

A clothing retailer is selling a fashion print tee that retails for $22.95 and has a total landed cost of $15.35 per unit. A new print is released each month, and any leftover inventory from the previous month is deeply discounted to $6.95 to clear space for new product. Assume that all units sell at the clearance price.

Based on sales in previous months, you've determined that full-price demand for each fashion tee is normally distributed with mean 1,380 and standard deviation 478. You expect demand this month to follow the same distribution.

Calculate the optimal order quantity using the newsvendor model. Round your answer to the nearest integer.

Suppose you had ordered the quantity from the previous question in each month of 2018. Actual demand values in each month are shown in the table below, and in the attached Excel file. Calculate total profit for the year by calculating and summing the profit in each month. On the revenue side, be sure to include both full-price and clearance-price sales. On the cost side, assume that the total landed cost per unit is the only relevant cost for this calculation.

Month	Demand
January	1130
February	2151
March	1342
April	1700
May	993
June	663
July	1204
August	677
September	1776
October	1980
November	1593
December	1351

Solutions

Expert Solution

Cost of Underage Cu = Price - Cost = 22.95 - 15.35 = 7.60

Cost of overage Co = Cost - Salvage Value = 15.35 - 6.95 = 8.40

Service Level = Cu/(Co+Cu)

Service Level = 7.60/(7.60+8.40) = 0.475

Corresponding z value = -0.06271

Q = Mean + z*SD

Q = 1380 + (-0.06271*478)

Q = 1350.025

Q = 1350 unit

Below is the calculation of profit -

Month	January	February	March	April	May	June	July	August	September	October	November	December
Demand	1130	2151	1342	1700	993	663	1204	677	1776	1980	1593	1351
Q	1350	1350	1350	1350	1350	1350	1350	1350	1350	1350	1350	1350
Profit	8588	10260	10199.2	10260	7546.8	5038.8	9150.4	5145.2	10260	10260	10260	10260
Loss on leftover	0	6728.4	0	2940	0	0	0	0	3578.4	5292	2041.2	8.4
Final Profit	8588	3531.6	10199.2	7320	7546.8	5038.8	9150.4	5145.2	6681.6	4968	8218.8	10251.6
Total Profit	86640

Below is the screenshot of the formula applied to get the result -

keosha answered 1 year ago

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