Quantitative Demand Forecasting

Introduction

In this lesson, we will focus on the foundational task of predicting demand. The learning outcome is to apply quantitative forecasting methods (e.g., moving average, exponential smoothing) to predict demand.

Forecasting is the starting point for most operational planning. Decisions about how much inventory to hold, how many staff to schedule, and what production capacity is needed all depend on a reliable estimate of future demand.

Given your background in applied mathematics and quantitative finance, you'll find that the time-series techniques we'll cover are conceptually similar to methods used in signal processing and financial modeling. Our focus here will be on their specific application within a business operations context.

We will cover three core methods:

1. Simple and Weighted Moving Averages
2. Exponential Smoothing
3. Evaluating Forecast Accuracy

Let's begin by understanding the role of forecasting in operations.

1. Quantitative Forecasting in Operations

Quantitative forecasting models use historical data to predict future outcomes. They are most effective when you have numerical data and can assume that past patterns will continue into the future. These methods form the bedrock of modern demand planning, even as more complex AI/ML models become prevalent.

To get an overview, please read the following sections from an introductory text on Operations Management.

As the text highlights, time-series methods are about extracting patterns from past data. The core challenge is to distinguish the underlying signal (trend, seasonality) from random noise.

2. Moving Average Methods

Moving averages are among the most straightforward forecasting techniques. They work by smoothing out short-term fluctuations in a time series.

Simple Moving Average (SMA)

The simple moving average forecast is the arithmetic mean of the demand from the most recent "n" periods.

Formula: $F_{t+1}=\frac{D_t+D_{t-1}+...+D_{t-n+1}}{n}$

The key decision is choosing the value of n.

• A small n makes the forecast very responsive to recent changes but also susceptible to noise.
• A large n creates a smoother, more stable forecast but is slower to react to underlying changes in demand.

Weighted Moving Average (WMA)

The WMA is a refinement of the SMA that allows you to assign more importance to recent data. Each of the past n periods is assigned a weight, with the sum of weights typically equaling 1.

Formula: $F_{t+1}=w_1{D}_t+w_2{D}_{t-1}+...+w_n{D}_{t-n+1}$ where $\sum w_i=1$.

The following video provides a clear, practical demonstration of how to calculate a WMA.

3. Exponential Smoothing

Exponential smoothing is a sophisticated and widely used forecasting method. It's a type of weighted average where the weights applied to past observations decline exponentially over time. A key advantage is its computational efficiency: you only need the previous period's forecast and actual demand to compute the next forecast.

The most common form is Single Exponential Smoothing, which uses the following formula:

$F_{t+1}=\alpha D_t+(1-\alpha )F_t$

Where:

• $F_{t+1}$ is the forecast for the next period.
• $D_t$ is the actual demand in the current period t.
• $F_t$ is the forecast for the current period t.
• $\alpha$ (alpha) is the smoothing constant, a value between 0 and 1.

The choice of $\alpha$ is a classic parameter-tuning problem.

• A high $\alpha$ (e.g., 0.8) places more weight on the most recent actual demand, making the forecast highly responsive.
• A low $\alpha$ (e.g., 0.2) places more weight on the previous forecast, resulting in a much smoother forecast that is less reactive to recent fluctuations.

This next video provides an excellent walkthrough of the calculation.

Note that there are more advanced versions, like Double (Holt's method) and Triple (Holt-Winters method) Exponential Smoothing, which incorporate trend and seasonality, respectively. For this lesson, we are focusing on the single smoothing method.

4. Evaluating Forecast Accuracy

Creating a forecast is only half the battle. In a business setting, you must be able to measure how accurate your forecast is to evaluate its performance and compare different models.

Three standard metrics are:

• Mean Absolute Deviation (MAD): The average of the absolute forecast errors. It's easy to interpret as the average error magnitude.
  $MAD=\frac{\sum |D_t-F_t|}{n}$
• Mean Squared Error (MSE): The average of the squared forecast errors. By squaring the errors, this metric penalizes large misses more heavily. This is analogous to an L2 loss function in machine learning.
  $MSE=\frac{\sum (D_t-F_t{)}^2}{n}$
• Mean Absolute Percentage Error (MAPE): The average of the absolute errors taken as a percentage of actual demand. This is useful for comparing forecast accuracy across products with different demand volumes.
  $MAPE=\frac{1}{n}\sum \frac{|D_t-F_t|}{D_t}\times 100\%$

The following reading demonstrates how to calculate these metrics using a simple table.

A lower value for MAD, MSE, or MAPE indicates a more accurate forecast. When comparing different forecasting methods (e.g., a 3-period SMA vs. exponential smoothing with $\alpha =0.4$), you would calculate these metrics for each and choose the model with the lower error.

5. Practice Problem

Let's apply what you've learned. Using the data below, calculate the forecast for June using each of the requested methods.

Data: Monthly sales of light bulbs.

Calculate the forecast for June using:

1. The Naïve method.
2. A three-month simple moving average.
3. A three-month weighted moving average using weights of 0.5, 0.3, and 0.2 for the most recent, second most recent, and third most recent months, respectively.
4. Exponential smoothing using an alpha ($\alpha$) of 0.2 and a May forecast of 350.

Take a few minutes to perform the calculations. Once you're ready, you can check your answers against the solutions provided in the "End of Chapter Problems" section of the "Forecasting – Introduction to Operations Management" reading, under Problem #1.

Conclusion

In this lesson, we explored several fundamental quantitative methods for demand forecasting.

Key Takeaways:

• Time-series forecasting uses historical data to predict future demand, forming a critical input for operational planning.
• Moving Averages (SMA and WMA) smooth out data to generate a forecast. WMAs improve on SMAs by giving more weight to recent data. The key parameter is n, the number of periods.
• Exponential Smoothing is an efficient method that computes a forecast using only the most recent actual demand and forecast. Its responsiveness is controlled by the smoothing constant, $\alpha$.
• Forecast accuracy is measured with metrics like MAD, MSE, and MAPE, which are essential for comparing and selecting the best forecasting model for a given situation.

In our next lesson, we will shift from predicting demand to analyzing the processes that meet that demand. We will learn to formalize and analyze an operational process using a process flow diagram to identify the bottleneck and calculate throughput. The demand forecast you learned to generate today is the primary driver of any process analysis.