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Final

# ECON 438 Lecture 2: Single-Period Inventory Problem_Needless MakeupExam

Department
Economics
Course Code
ECON 438
Professor
erics jhonson
Study Guide
Final

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SAYED M. IRFAN | M.Engg. (Industrial Engineering) / Certified Supply Chain Design Analyst, MIT
NEEDLESS MAKEUP INVENTORY PROBLEM
November 13, 2016
Question:
Needless Markup (NM), a famous "high end" department store, must decide on the quantity of a
high-priced woman's handbag to procure in Spain for the coming Christmas season. The unit cost of
the handbag to the store is \$28.50 and the handbag will sell for \$150.00. Any handbags not sold by
the end of the season are purchased by a liquidator for \$10.00 each. In addition, the store
accountants estimate that there is a cost of \$0.40 for each dollar tied up in inventory, as this dollar
invested elsewhere could have yielded a gross profit. Assume that this cost is attached to unsold
bags only.
1. Due to the long distance and limited capacity, NM must place the order 6 months in advance. A
detailed analysis of past data shows that if forecasting 6 month in advance, the number of bags
sold can be described by a normal distribution, with mean 150 and standard deviation 60. What is
the optimal number of bags to purchase?
2. What is the expected cost of mismatch under the optimal purchase quantity? What is the optimal
expected profit?
3. Another supplier in the US, offers the same product but at a higher price of \$35 due to its higher
production cost. For this supplier, NM only needs to place the order 3 months in advance which
results in a much better forecast. Past data shows if ordering 3 months in advance, the number
of bags sold can be described by a normal distribution, with mean 150 and standard deviation 20.
Which supplier should NM choose?
Let us first establish the required data attributes for implementing the procedure. The relevant
terms, therefore, are:
Selling price, p = \$150
Cost, c = \$28.50
Cost of holding and disposal, h = \$0.40
Salvage value, s = \$10
Now, the underage and overage costs and the critical ratio can be computed as:
Cu = (p c) = 150 28.50 = 121.5
Co = (c + h s) = 28.5 + 0.40 10 = 18.9
Critical Ratio = 121.5 / (121.5 + 18.9) = 0.865
At the optimal order quantity, the probabilities of marginal expected costs and benefits (profits) of
ordering the Qth unit are equal. The critical ratio, in effect, implies that probability. Therefore, we
need to find the point in our demand distribution that corresponds to the cumulative probability
equal to the critical ratio. Using the NORMSINV function to get the number of standard deviations,