After observing demand in period 1, the buyer can cancel a part of the order previously given for period 2, or can add new units to this standing order to increase the stocking level for period 2. Using an additive demand model, they consider a setting in which orders for both periods are placed before the first period. Petruzzi and Dada (2001) study a two-period problem in which expected demand decreases linearly in demand. They also present numerical results for a three-period problem in which lead time for the second order is one period. Serel, in Information Systems for the Fashion and Apparel Industry, 2016 7.2.2 Price-sensitive demandĪssuming negative binomial distribution for demand with a price-dependent distribution parameter, Subrahmanyan and Shoemaker (1996) use dynamic programming to find optimal prices and order quantities in a two-period problem. This is a continuous probability distribution and its equation is given byĭ.A. If results indicate that the mean time between failures is 1000 hours, then what is the probability that the equipment will work for 700 hours or more without a failure? Calculating K as 700/1000 = 0.7 then from Table 17.2 the area beyond 0.7 is 0.497 which is the probability that the equipment will still be working after 700 hours. Interpolation between ordinal values can be achieved in steps of 0.02 by using the remaining 4 columns.Īs an example suppose that the time between failures of a piece of equipment is found to vary exponentially. 17.6.8.4 Exponential DistributionĬolumn 1 lists the ordinal values of K and the corresponding values of area are presented in column 2. Therefore 5000 × 0.023 or 115 lamps are expected to fail after 800 hours. Ignoring the negative sign, Table 17.1 gives the probability of lamps not failing as 0.977 so that the probability of failure is 1 − 0.977 or 0.023. How many lamps will fail in the first 800 hours? from equation ( 17.72) Interpolation between ordinal values can be achieved in steps of 0.02 by using the remaining 4 columns. Column 1 lists the ordinal values of ω and the corresponding values of area are presented in column 2.
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