Question

In: Operations Management

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 2 years ago
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