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THE NEWSBOY PROBLEM – INVENTORY MODELS FOR PERISHABLES ( C= cost of shortage of

ID: 452974 • Letter: T

Question

THE NEWSBOY PROBLEM – INVENTORY MODELS FOR PERISHABLES ( C= cost of shortage of 1 unit, C= cost of excess of 1 unit)

SERVICE LEVEL =                 C              

                                C    +      C

Sally’s Silk Screening produces special T-shirts that are primarily sold on the Halloween day.She must decide how many to produce for the coming Halloween.During the event itself, which lasts one day, Sally can sell a T-shirt for $20 a-piece.However, when the event ends, any unsold T-shirts are sold for $4 a-piece.It costs Sally $8 to make a specialty T-shirt.Using Sally’s estimated distribution of demand, how many T-shirts should she produce for the coming event?

DEMAND                      Probability          COMPUTE COMULATIVE PROBABILITY

      300                         .05

      400                         .10

       500                         .40

       600                         .30

      700                         .10

      800                         .05                                                         

Hint: What is the optimal service level? What is the cumulative probability distribution?

Explanation / Answer

demand probability Cumulative Probability (demand*prob) 300 0.05 15 400 0.1 40 500 0.4 200 600 0.3 180 700 0.1 70 800 0.05 40 mean, m 90.8 selling price, p 20 std dev, s 79.0 cost price, c 8 Critical ratio 0.75 salvage cost,k 4 z 0.67 cu = $ p - $ c 12 Q=m+s*z 143.78 co= $ c -$k 4 Q= quantityto store = std dev * z + mean Critical ratio = cu / (cu + co) z calculated from z score table (probaility for z score is the critical ratio calculated by above formula)