The newsboy model Since F(Q*)is defined as the probability that the demand does not exceed Q*,the critical ratio is the probability of satisfying all the demand during the period if Q*units are purchased at the beginning of the period. Example 5.1-Mac's newsstand fx) Q*=oZ+μ=4.74×0. Suppose that the demand for the Journal 74+11.73=15.24≈15 is approximately normally distributed with mean u=11.73 and standard Area=.77 deviation o=4.74.co=25-10=15,and c,=75-25=50 cents.The critical ratio is c/(c.+c)-0.50/(0.15+0.5)=0.77.Hence, 11.73 he ought to purchase enough copies to satisfy all of the weekly demand with probability 0.77.The optimal Q*is the Fig.5-4 Determination of the Optimal 77th percentile of the demand distribution. Order Quantity for Newsboy Example
The newsboy model Since F(Q*) is defined as the probability that the demand does not exceed Q*, the critical ratio is the probability of satisfying all the demand during the period if Q* units are purchased at the beginning of the period. Example 5.1- Mac’s newsstand Suppose that the demand for the Journal is approximately normally distributed with mean =11.73 and standard deviation =4.74. c 0=25-10=15, and c u=75-25=50 cents. The critical ratio is c u/(c o+c u)=0.50/(0.15 +0.5)=0.77. Hence, he ought to purchase enough copies to satisfy all of the weekly demand with probability 0.77. The optimal Q* is the 77th percentile of the demand distribution. Fig. 5-4 Determination of the Optimal Order Quantity for Newsboy Example Q*= z+ =4.74 0. 74+11.73=15.24 15 F(Q*)
The newsboy model-Optimal Policy for Discrete Demand .In some cases,accurate representation of the observed pattern of demand in term of continuous distribution is difficult or impossible .In the discrete case,the critical ratio will generally fall between two values of F(Q) The optimal solution procedure is to locate the critical ratio between two values of F(Q)and choose the Q corresponding to the higher value
The newsboy model- Optimal Policy for Discrete Demand •In some cases, accurate representation of the observed pattern of demand in term of continuous distribution is difficult or impossible. •In the discrete case, the critical ratio will generally fall between two values of F(Q). • The optimal solution procedure is to locate the critical ratio between two values of F(Q) and choose the Q corresponding to the higher value