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Forecasting Demand

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Forecasting Demand

Chapter 11

- Subjective Models
- Delphi Method
- Cross-Impact
- Historical Analogy

- Causal Models
- Regression Models
- Econometric Models

- Time Series Models
- N-Period Moving Average
- Simple Exponential Smoothing
- Exponential Smoothing with Trend or Seasonal Adjustment

- Delphi Method
- Developed at the Rand Corporation by Olaf Helmer
- Method is based on expert opinion
- People with expertise are asked to answer some question (no interaction among respondents)
- Answers are grouped and the placed into quartiles based on the frequency in which they were mentioned
- Respondents review the results and answers in the extreme quartiles must be justified.
- Continued iterative process

- Cross-Impact Analysis
- This analysis assumes that a future event is related to the occurrence of an earlier event
- If historical data shows that as gas prices go up by 50 cents a gallon, mass transit rider-ship increases by 100 people
- If there are deviations in this trend, experts go back and evaluate what happened

- Historical Analogy
- Assumes the introduction and growth pattern of a new service will mimic the pattern of a similar concept

- Regression Analysis
- Shows the relationship between a dependent variable and one or more independent variables
- Independent Variables: Age, IQ
- Dependent Variable: Computer Ability

- To what extent do age and IQ impact computer ability?

- Shows the relationship between a dependent variable and one or more independent variables

- Econometrics
- Similar to regression models
- Involves a system of equations that are related to each other
- Solve for simultaneous equations that express the dependent variable in terms of several different independent variables

- N Period Moving Average
- This approach smoothes out random fluctuations that may occur
- As a manager, you don’t want to overreact to random changes

- MAT = (AT + AT-1 + AT-2 + …..+ AT-N+1)/N
- where: MAT = The N period moving average
- AT = Actual observation for period T

Saturday Occupancy at a 100-room Hotel

Three-period

Saturday Period Occupancy Moving Average Forecast

Aug. 1 1 79

8 2 84

15 3 8382*

22 4 8183**82

29 5 98 8783

Sept. 5 6 1009387

12 793

* (83+84+79)/3 = 82

** (84+83+81)/3 = 82.67 ≈ 83

- Very inexpensive and easy to understand
- Gives equal weight to all observations
- Does not consider observations older than N periods

Simple Exponential Smoothing

- Most frequently used for demand forecasting
- Based on the concept of feeding back the “forecast error” to correct the previous smoothed value

St = St-1 + α (At – St-1)

Where:

St = smoothed value for time period t

(At – St-1) represents the forecast error

α = a weight which allows the manager to

determine how much weight or importance

to give to recent data (large values give

higher values to recent data)

Saturday Hotel Occupancy ( α=0.5)

Actual Smoothed Forecast

Period Occupancy Value Forecast Error

Saturday t At St Ft |At - Ft|

Aug. 1 1 7979.00

8 2 8481.50* 79 5#

15 3 8382.25** 82 1

22 4 8182.88 82 1

29 5 9890.44 8315

Sept. 5 6 10095.22 9010

*79.00 + 0.5 (84.00 - 79.00) = 81.50

** 81.50 + 0.5 (83.00 - 81.50) = 82.25

# 84.00 – 79.00 = 5

- This approach helps to prevent over-reaction to extremes in observed values
- The older observations never disappear entirely from the calculation of St like they do in N Period Moving Average approach
- To measure the accuracy of our forecasts, we can calculate the Mean Absolute Deviation (MAD)

Saturday Hotel Occupancy ( α=0.5)

Actual Smoothed Forecast

Period Occupancy Value Forecast Error

Saturday t At St Ft |At - Ft|

Aug. 1 1 7979.00

8 2 8481.50* 79 5#

15 3 8382.25** 82 1

22 4 8182.88 82 1

29 5 9890.44 8315

Sept. 5 6 10095.22 9010

MAD = 6.4

MAD = (5 + 1 + 1 + 15 + 10) / 5

*79.00 + 0.5 (84.00 - 79.00) = 81.50

** 81.50 + 0.5 (83.00 - 81.50) = 82.25

# 84.00 – 79.00 = 5

- A trend in a set of Data is the average rate at which the observed values change from one period to the next over time.
- Requires the addition of the trend value to the smoothed value equation
- St = α(At) + (1- α) (St-1 + Tt-1)
- Tt = β (St – St-1) + (1 – β) Tt-1
- Ft+1 = St + Tt