A.2 Time Series Model Building

1. Divide the series into test set (the last 12 observations of the time series) and training set (the remaining observations of the time series).
2. Using the training set, build exactly three contender forecasting models for time series (MA, SES, LES) . Only use those methods taught in this module.

A.3 Time Series Forecasting

1. For each of the candidate models estimated, produce a forecast equal to the length of the test set, that is, for h=12 steps ahead. You should have three forecasts in total.
2. Calculate the in-sample and out-of-sample forecasting performance using the following metrics:
   1. Mean error (ME)
   2. Mean absolute error (MAE)
   3. Mean squared error (MSE)
   4. Root mean squared error (RMSE)
   5. Mean absolute percentage error (MAPE)

A.4 Safety Stock

Using the final best forecast:

1. Calculate the expected value of lead-time demand based on lead-time of 12 also equal to the forecast horizon, h=12.
2. Calculate the standard deviation of lead-time demand based on lead-time of 12 also equal to the forecast horizon, h=12.
3. Calculate the reorder point based on the assumption of a normal distribution of forecast errors, and a stock-out risk of 3% (97% risk cover).

PART B SIMULATION

B.1 Expected Lead Time Demand for a company

Assume that a share of the expected lead-time demand or production belongs to the company. However, there is some uncertainty associated with this share. This can be summarized using the following table:

Share

0.20.30.40.50.60.70.80.9Probability0.050.030.070.10.150.20.250.15

Using simulation and a total of 150 trials, calculate the expected lead-time demand or production achieved by the company.

B.2 Expected Profit for the company

The forecasted units are assumed to have a selling price of 8.00 and a variable cost of production per unit 4.50. Estimate the expected profit obtained by the company.