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You are the buyer for your university bookstore. One of the textbooks has a cost to you of $150 and you sell it to students for $300. In this case, however, you cannot salvage any value from copies that do not sell because a new edition is published every semester. Demand for this text averages 130 copies each semester, with a standard deviation of 20 copies. Use Appendix A.
How many should you order each semester? (Round your intermediate calculations to 2 decimal places and final answer to the nearest whole number.)
Expert Answer
Cost to store = C = $150 per textbooks
Selling price for Textbook = $300 per textbooks
Salvage value or reduced price of textbooks after semester = S = $0 per textbook
Step 1:
For the given data apply single-period Inventory model
Cu = cost of shortage (underestimate demand) = Sales price/unit –Cost/unit
Co = Cost of overage (overestimate demand) = Cost/unit– Salvage value /pound
Cu = P – C = $300 – $150 = $150 per textbook
Co = C – S = $150 – $0 = $150 per textbook
Step 2:
The service level or probability of not stocking out, is set at,
Service Level = critical ratio = Cu/( Cu + Co) = 150/(150 + 150) = 0.5
Optimal Service Level = Critical ratio = 0.5
Step 3:
For the expected service level z-score for the demand’s normal distribution is determined that yields a probability of 0.5.
So 50% of the area under the normal curve must be to the right of the optimal stocking level.
Using standard normal table, for an area of 0.5, the Z score is 0.
Step 4:
Mean demand = µ = 130 copies per semester
Standard Deviation = σ = 20 copies per semester
The optimal order quantity for the expected service level is obtained as follows:
Optimal order quantity = µ + zσ = 130 + (0)20= 130 copies.
So to maximize the revenue the bookstore should order 130 copies of textbooks to achieve expected service level of 50%.
