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• Script Part 4: Demand Forecasting
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I did not take lecture notes on Production Management. Below is an AI-generated summary of this chapter, and you’ll want to check out the resources above.

Demand Forecasting

Demand forecasting is a crucial part of the Operative Planning level (which also includes Master Production Scheduling and Material & Capacity Requirements Planning). It focuses on predicting the future development of demand based on historical values under uncertainty.

1. Operative Planning Level

The purpose of the operational planning level includes:

• Smoothing of seasonal variations of capacity requirements and available capacity.
• Determination of the master production schedule: Deciding which products shall be produced in which quantities across various periods during the planning horizon.
• Procurement planning: Determining the required quantities of input materials (raw materials, supplied parts, and in-house sub-assemblies) for the fulfillment of the master schedule.
• Smoothing of demand and production based on forecasts.

Strategies to Match Production and Demand

Companies typically choose between two main strategies to handle fluctuating demand:

• Chase Demand: Adjusting production to match demand period-by-period. Pros: Lower inventory costs.
• Level Production: Maintaining a constant production rate. Pros: Less dependent on supply chain fluctuations.

2. Procedure of Time Series Based Forecasting

A structured approach to time series forecasting involves five steps:

1. Analysis of the characteristics of a time series:
   • Long-term trend: Consistent increase or decrease over time.
   • Mid-term cyclical variations: e.g., economic cycles or product lifecycle effects.
   • Seasonal fluctuations: Regular patterns based on annual seasons.
   • Random variations: Unpredictable noise.
2. Selection of an appropriate forecast model.
3. Estimation of the coefficients of the forecast model.
4. Application of the forecast model (calculation of the forecast values).
5. Monitoring and analysis of the forecast accuracy over time.

Types of Time Series

• Level demand: Random variations around a constant mean.
• Linear trend: Demand consistently increases or decreases over time.
• Seasonal variation: Demand exhibits regular repeating patterns.

3. Data Structure of Demand Forecasts

Forecasting requires a solid data structure referencing past and future periods:

• $y_t$: Observed historical demand in period $t$.
• $P_t$: Ex-ante forecasted demand for period $t$.
• $e_t$: Ex-post forecast error in period $t$ ($e_t=P_t-y_t$).
• $t$ (Forecast date): The point in time separating past (known historical data) from the future.

4. Forecasting Methods

Simple Exponential Smoothing

Used when the assumed demand process involves random variations around a constant demand level.

Forecast formula:
$P_{t+1}=\alpha y_t+(1-\alpha )P_t$

• $y_t$: Observed demand in period $t$.
• $P_{t+1}$: Forecast for period $t+1$.
• $\alpha$: Smoothing parameter (generally $0.1\le \alpha \le 0.3$). It determines the strength of the smoothing effect. A larger $\alpha$ makes the forecast more responsive to recent demand.
• Initialization: Before the first forecast (for $t=1$), an adequate initial value $P_0$ has to be determined (an estimate of the level demand). Often, $y_0$ is chosen.

Exponential Smoothing with Trend Adjustment

Used when the assumed demand process involves random variations around a linear trend, i.e., $y_t=A+B\cdot t+{\epsilon }_t$.
Applying simple exponential smoothing directly to a time series with a linear trend causes a systematic error (lag). This requires a trend adjustment (correction factor).

Update of level demand at the end of period $t$:
$a_t=\alpha \cdot y_t+(1-\alpha )\cdot a_{t-1}$

Update of trend at the end of period $t$:
$b_t=\alpha \cdot (a_t-a_{t-1})+(1-\alpha )\cdot b_{t-1}$

Forecast determination for periods $t+1,t+2,\dots ,t+n$:
$P_{t+\tau }=a_t+b_t\cdot \frac{1-\alpha }{\alpha }+\tau \cdot b_t\text{for }\tau =1,2,\dots ,n$

• $\frac{1-\alpha }{\alpha }\cdot b_t$: The trend adjustment (correction factor) that offsets the systematic error caused by the smoothing lag.
• $a_t$: Smoothed level.
• $b_t$: Smoothed trend.

Initialization:
Before the first forecast determination (for $t=1$), adequate initial values $a_0$ and $b_0$ have to be determined (e.g., through linear regression).
$a_0=y_0-\frac{1-\alpha }{\alpha }\cdot b_0$