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Unformatted text preview: Newsvendor Model Let’s Practice 1 s o s c c c Q x Q F + = ≤ = *) Pr( ) ( A retail outlet sells a seasonal product for $10 per unit. The cost of the product is $8 per unit. All units not sold during the regular season are sold for half the retail price in an endofseason clearance sale. Assume that the demand for the product is normally distributed with μ = 500 and σ = 100. a. What is the recommended order quantity? Example 1: b. What is the probability of a stockout? c. To keep customers happy and returning to the store later, the owner feels that stockouts should be avoided if at all possible. What is your recommended quantity if the owner is willing to tolerate a 0.15 probability of stockout? d. Using your answer to part (c), what is the goodwill cost you are assigning to a stockout? Solution to Example 4: a . Selling price=$10, Purchase price=$8 Salvage value=10/2=$5 c s =10  8 = $2, c o = 810/2 = $3 SinglePeriod Models (Continuous Demand) G(Q*)= = = 0.4 Now, find the Q so that G(Q*) = 0.4 or, area (1) = 0.4 3 2 2 + s o s c c c + Probability Demand μ =500 Area=0.40 z = 0.255 σ = 100 (1) So, Q * = μ + z σ =500+(0.255)(100)= 474.5 units. b. P(stockout)=P(demand ≥ Q )=1P(demand< Q )=1 p =10.4=0.6 SinglePeriod Models (Continuous Demand) Probability Demand μ =500 Area=0.60 z = 0.255 σ = 100 c . P(stockout)=Area(3)=0.15 SinglePeriod Models (Continuous Demand) Probability σ = 100 Area=0.15 Q * = μ + z σ =500+(1.035)(100)=603.5 units. Demand μ =500 z = 1.035 d. p =P(demand< Q )=1P(demand ≥ Q ) =1P(stockout)=10.15=0.85 For a goodwill cost of g c u =10  8+ g = 2+ g , c o = 810/2 = $3 SinglePeriod Models (Continuous Demand) Now, solve g in p = = =0.85 Hence, g =$15. u o u c c c + 3 2 2 + + + ) ( g g Example 2: • The J&B Book Shop orders a book monthly . Unsold books are kept on the shelves for future sales. Assuming that customers who request the book when they are out of stock will wait until the following month. The J&B Book Shop buys the books for $1.15 and sells it for $2.75. They estimate a lossofgoodwill cost of $50 cents each time a book is backordered. Demand follows a normal distribution with μ=18 and σ =6. The J&B Book Shop uses a 20 percent annual terest rate to determine its holding cost, interest rate to determine its holding cost, • 1. How many books should they purchase at the beginning of each month? • 2. Solve the problem assuming sales are lost • Backorder case: c o = Holding cost • Lost sales case: c s =Lossofgoodwill cost + lost profit Example 2 solution a. Backorder case: Selling price=$2.75, Purchase price=$1.15 lossofgoodwill cost = $.50 D  N(18,16 2 ) c s = lossofgoodwill cost = $.50 c o = ( i% * c /12)=(0.2*1.150/12=0.0192 8 9630 ....
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This note was uploaded on 04/25/2010 for the course IE 654 taught by Professor Smith during the Spring '10 term at 카이스트, 한국과학기술원.
 Spring '10
 smith

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