The newsboy model-Extension to Multiple Planning Periods The ending inventory in any period becomes the starting inventory in the next period. Consider the case in which there are infinitely many periods remaining: If excess demand is back-ordered,interpret c,as the loss- of-goodwill cost and c,as the holding cost. If excess demand is lost,interpret c,as the loss-of- goodwill cost plus the lost profit and c.as the holding cost
The newsboy model- Extension to Multiple Planning Periods The ending inventory in any period becomes the starting inventory in the next period. Consider the case in which there are infinitely many periods remaining: If excess demand is back-ordered, interpret c u as the lossof-goodwill cost and c o as the holding cost. If excess demand is lost, interpret c u as the loss-ofgoodwill cost plus the lost profit and c o as the holding cost
The newsboy model-Extension to Multiple Planning Periods Example 5.3:Suppose that Mac is considering how to replenish the inventory of a very popular paperback thesaurus that is ordered monthly.Copies of the thesaurus unsold at the end of a month are still kept on the shelves for future sales. Assume that customers who request copies of the thesaurus when they are out of stock will wait until the following month.Mac buys the thesaurus for $1.25 and sells it for 3.75.Mac estimates a loss-of-goodwill cost of 80 cents each time a demand for a thesaurus must be back-ordered.Monthly demand for the book is fairly closely approximated by a normal distribution with mean 20 and standard deviation 10. Mac uses a 20 percent annual interest rate to determine his holding cost.How many copies of the thesaurus should be purchased at the beginning of each month?
Example 5.3: Suppose that Mac is considering how to replenish the inventory of a very popular paperback thesaurus that is ordered monthly. Copies of the thesaurus unsold at the end of a month are still kept on the shelves for future sales. Assume that customers who request copies of the thesaurus when they are out of stock will wait until the following month. Mac buys the thesaurus for $1.25 and sells it for $ 3.75. Mac estimates a loss-of-goodwill cost of 80 cents each time a demand for a thesaurus must be back-ordered. Monthly demand for the book is fairly closely approximated by a normal distribution with mean 20 and standard deviation 10. Mac uses a 20 percent annual interest rate to determine his holding cost. How many copies of the thesaurus should be purchased at the beginning of each month? The newsboy model- Extension to Multiple Planning Periods
The newsboy model-Extension to Multiple Planning Periods Answer for Example 5.3: u=20 and standard deviation o=10 ©c。=1.25*0.2/12=0.208 holding cost ©c=0.80. The critical ratio is c/(c+c)-0.8/(0.208+0.8)-0.794 Hence,he ought to purchase enough copies to satisfy all of the monthly demand with probability 0.794.The optimal Q* is the 79.4th percentile of the demand distribution. ©Q*=0z+μ=10×0.82+20=28.2≈28
Answer for Example 5.3: =20 and standard deviation =10 c o=1.25*0.2/12=0.208 holding cost c u=0.80. The critical ratio is c u/(c o+c u)=0.8/(0.208 +0.8)=0.794 Hence, he ought to purchase enough copies to satisfy all of the monthly demand with probability 0.794. The optimal Q* is the 79.4th percentile of the demand distribution. Q*= z+ =10 0.82+20=28.2 28 The newsboy model- Extension to Multiple Planning Periods