Review problem #1 Text problem 9 - 6, 7. Weekly sales (in hundreds) of PERT shampoo at the SaveMor drug chain for the past 16 weeks are as follows: Management wishes to forecast the annual demand for PERT shampoo in order to determine an optimal order policy. Graph this time series.
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Management wishes to forecast the annual demand for PERT shampoo in order to determine an optimal order policy.
A stationary model seems to
properly describe this time series.
Go to file ch 9-6.xls
and create the graph.
Do not reject the null hypothesis. There is
insufficient evidence for the existence
of a trend at (even) 15% significance level.
H0: b1= 0
H1: b1¹ 0
The sum of the weights appears incell c9.
A firm that manages and maintains several apartment house complexes has experienced the following expenses over the last five years.
t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Yt 27 39 41 50 44 47 58 63 73 92 94 102 123 119 128 147 155 158 164 187
(a) Plot this time series using an Excel graphical tool (use an x-y scatter plot)
(b) Run a linear regression model and compare its performance to the best Holt’s model you can obtain, when optimizing alpha and gamma. Use the MAD criterion to compare.
(c) Repeat part (b), this time optimize alpha , gamma, the initial forecast and the initial trend. Which model do you select now based on the MAD?
The p-value is very small, implying that there is sufficient evidence to support the hypothesis that b1¹0Review problem 3 - Solution
Don’t forget to select “Assume non-negative”in “Options”, since alpha and gamma are both ³ 0
Notice: Only alpha and gamma are optimizedReview problem 3 – SolutionOptimizing alpha and gamma For Holt’s
Don’t select “Assume non -negative” in “Options”, since L0 and T0 might be negative. But then, add the non-negativity constraints of alpha and gamma
Notice: Both alpha, gamma,L0 and T0 are optimizedReview problem 3 - SolutionOptimizing alpha, gamma, L0,T0 for Holt’s
(i) The exponential smoothing
(ii) The weighted moving average
(iii) The Holt’s method
(v) The linear regression model.
Ann. Ordering cost
Ann. Holding cost
D = 24*52 = 1248 per year. Ch = IC = .20(1095) = 219 per unit per year.
Co = 90. Cs = 1.50(365) = 547.5 per unit per year. Cb = 0 (not included)
Then R = 8(24/6) – 10.82 = 21.18
R = 21
Q = 37.89
Problem 7 - continued
P(DL > R) = .08 P(Z > Z.08) = .08 but
Z.08 = 1.405 so (R – m)/s = 1.405 or R = mL + Z.08sL.
mL = 2(250) = 500; sL2 = (2)(80)2 = 12800 sL = 113.13