Forecasting Concepts and Time Series Notes

Forecasting Concepts and Time Series Notes

Overview

• Forecasting is about predicting what comes next to inform business decisions (production, inventory, personnel, facilities).

• Forecasts influence material planning, capacity, workforce, and facilities; poor forecasting leads to shortages or excess inventory.

• The service sector’s forecasting is as critical as manufacturing, sometimes more so.

• The lecture emphasizes applying different models across three time horizons, assessing forecast accuracy, and using qualitative and quantitative approaches.

Time horizons for forecasting

• Short-range forecast

  • Typically less than 1 year; familiar in operations.

  • Used for: procurement/purchasing, floor production scheduling, workforce leveling, and daily/weekly production planning.

  • With modern software, may extend beyond 1 year, but 1 year is a practical rule of thumb.

• Medium-range forecast

  • Approximately 3 months to 3 years.

  • Used for: planning future opportunities, sales planning, production planning, budgeting, cash budgeting, and operating plans.

  • Examples: new product development (NPD), end-of-life planning, and other transitional plans.

• Long-range forecast

  • 3 years and beyond.

  • Historically tied to R&D and capital expenditure planning (new facilities, major equipment purchases).

  • Example anecdotes: AI applications in military radios and long-term research projects; major capital investments take time to plan and implement.

• Distinctions between horizons

  • Medium/long range focus on comprehensive issues and management decision support; tends to seek order-of-magnitude estimates rather than precise numbers.

  • Short-term forecasting aims for more precise numbers; forecasting accuracy generally decreases with longer horizons.

Forecasting objectives and scope in practice

• Business outcomes forecasted: sales, production, inventory, capacity, and staffing.

• Forecasting supports decisions like supplier lead times, production scheduling, and capital investments.

• Real-world constraints: external shocks (e.g., COVID) can disrupt forecasts; some factors are outside controllable; models assume underlying stability with historical data.

• Relationship to supply chain management: good supplier relations (e.g., knowing needs 12 months out) enable better lead-time planning and on-time delivery.

• Examples of planning and communication: weekly forecast updates to suppliers, visibility from today to 12 months ahead, and using forecasts to guide procurement and production.

Forecasting approaches

• Qualitative forecasting (used when data/history is limited or for new products)

  • Jury of executive opinion: gathering expert judgments from decision-makers.

  • Delphi method: iterative rounds of feedback from a panel of experts; consensus evolves through cycles.

  • Salesforce composite: inputs from front-line salespeople who are closest to customers; regional and national aggregation.

  • Market survey: asking customers about product expectations and experiences; triangulates gut feel with data.

  • Key ideas: intuition, experience, competition awareness, and input from knowledgeable staff.

• Quantitative forecasting (data-driven)

  • Time series forecasting: patterns derived from historical data (trends, seasonality, random variation).

  • Regression and correlation analysis: modeling relationships between variables to forecast outcomes.

  • Tracking signal: monitors forecast bias over time to detect persistent over- or under-forecasting (details later).

  • Seasonal indices and decomposition: adjusting forecasts for regular seasonal patterns within a year.

• The most important practical focus: demand forecasting for existing products/services, which drives operations planning.

Time series components and intuition

• Time series is a sequence of data points spaced evenly in time (days, weeks, months, etc.).

• Components of demand (as shown in a composite diagram):

  • Trend: persistent upward or downward movement over time.

  • Seasonal: regular, repeating patterns within a year due to weather, holidays, etc.

  • Random variation: irregular, unpredictable fluctuations.

  • Overall average (center line): a reference level around which the other components fluctuate.

• Example: overlaying trend on a product life cycle curve shows: introduction (rising), growth (linear trend), maturity (flattening), decline (downward trend). A declining trend line should lie below actual demand later to avoid carrying excess inventory.

• Seasonal patterns example (lawn equipment):

  • Spring: high demand for lawn mowers and chainsaws.

  • Summer: continued mowing season; possibly adjust mix.

  • Fall: shift from mowing gear to snow removal equipment.

  • Winter: high demand for snow blowers.

Product life cycle overlay and planning implications

• Early introduction often has under- or over-building; growth phase may be strong and relatively predictable with a linear trend.

• Maturity can flatten the trend; some overbuilding may occur but can be sold during peak demand later.

• Decline requires careful management to avoid excess inventory; forecast should trend downward and stay ahead of actual demand.

Forecasting models (time series focus)

• Naive forecast

  • The simplest approach: forecast next period as the value of the current period.

• Moving averages (simple)

  • Definition: average the demands of the last n periods to forecast the next period.

  • Example for a 3-month moving average: use the last three actuals (Dt, D{t-1}, D_{t-2})

  • Formula:
    ext{Forecast}{t+1} = rac{Dt + D{t-1} + D{t-2}}{3}

  • Practical note: order of summation can be from most recent to oldest to minimize cognitive load.

• Weighted moving average

  • Similar to moving average but assigns weights to recent periods to reflect more influence of newer data.

  • Common weights example: 3, 2, 1 for the most recent, next, and oldest of the last three periods.

  • Formula:
    ext{Forecast}{t+1} = rac{3 Dt + 2 D{t-1} + 1 D{t-2}}{3+2+1}

• Exponential smoothing (single)

  • A form of weighted moving average where weights decay exponentially for older data.

  • Two common representations:

  • Additive form: Ft = F{t-1} +
    abla imes (A{t-1} - F{t-1}) where
    abla is the smoothing factor, often denoted as ext{alpha} =
    abla .

  • Equivalent common form: Ft = ext{alpha} imes A{t-1} + (1 - ext{alpha}) imes F_{t-1}

  • Intuition: older values fade progressively; smaller alpha yields a smoother forecast; larger alpha makes the forecast more reactive to recent errors.

• Issues with moving averages and exponential smoothing

  • Moving averages smooth the series and lag actual changes, making them slow to adjust to trends.

  • They are not good at forecasting strong trends; they lag during trend periods.

  • The forecast line often sits behind the actual demand during periods of change.

Forecast accuracy metrics (levels of measurement)

• Three levels of forecast accuracy concepts are mentioned; the following metrics are standard in practice:

  • Mean Absolute Deviation (MAD):
    ext{MAD} = rac{1}{n}
    abla{i=1}^n |Ai - F_i|

  • Mean Squared Error (MSE):
    ext{MSE} = rac{1}{n}
    abla{i=1}^n (Ai - F_i)^2

  • Mean Absolute Percentage Error (MAPE):
    ext{MAPE} = rac{100}{n}
    abla{i=1}^n igg| rac{Ai - Fi}{Ai} igg|

• Mean Squared Error (MSE) tends to emphasize larger deviations due to the squaring term.

• Absolute percentage errors (MAPE) express forecast accuracy as a percentage, making it easy to interpret and compare across items.

Tracking signal and qualitative indices

• Tracking signal (TS): monitors bias over time to detect systematic over- or under-forecasting.

  • A common definition:
    ext{TS} = rac{ ext{CFE}}{ ext{MAD}}
    where CFE is the cumulative forecast error: ext{CFE} =

  =

  (Ai - Fi)

• Seasonal indices: used to adjust forecasts for regular seasonal patterns within a year. (Details/definitions were not elaborated in the transcript, but they are part of the standard approach.)

• Regression and correlation analysis: mentioned as tools to combine with time-series data for forecasting; specific formulas not provided in the transcript.

Forecasting accuracy and model comparison (practical takeaways)

• When comparing forecast methods, the transcript notes that differences in errors (e.g., with different smoothing parameters) can be small in some cases:

  • Example discussion: comparing forecast errors for different smoothing parameters showed that mean squared error values were similar in the cited scenario.

• In practice, select models based on horizon, data stability, and the need for responsiveness vs. smoothness; understand that short-term forecasts tend to be more accurate than long-term forecasts.

Real-world examples and implications discussed

• Kodak example: road-mapping the CCD sensor milestones to plan digital camera product lines; technology forecasting supports product planning and investment decisions.

• Supplier lead times and planning at Kodak and L3 Harris: maintaining visibility to 12 months out allowed suppliers to procure materials and schedule fabrication to meet forecasted needs; forecast updates occurred weekly.

• External shocks (COVID) demonstrated the limits of forecasting when factors outside the model disrupt demand or supply chains; forecasts must adapt to sudden changes.

• Demand forecasting vs. other forecast types: while economic or technology forecasts exist, the core focus for operations is demand forecasting of existing products/services.

• Product cannibalization (market cannibalization) example related to new product launches:

  • When a new product (e.g., a new iPhone model) is announced, existing customers may delay purchases, fearing the newer model; forecasting must consider potential cannibalization effects.

  • Government contracts: advance knowledge of procurement timelines (six months to a year) allows firms to prepare materials and plan production; contract awards can reduce the number of competitors and affect forecast accuracy.

• Operational planning example: planning to increase demand for common components in anticipation of award; shared components used by multiple products can be leveraged to meet the new contract.

• Product development and capital expenditure example: keg washer installation at Genesee Brewery highlighted long lead times and multi-year planning for capital equipment.

• Qualitative methods are valuable for new products without a historical data series, while quantitative methods rely on historical data but may be complemented with qualitative input.

Practical guidance and caveats

• Underlying assumption of many forecasting techniques: some stability in the system and availability of past data.

• Product family forecasts tend to be more accurate than forecasts for individual products due to diversification of demand within the family.

• External factors (e.g., pandemics, policy changes) can disrupt model accuracy; planners should monitor and adjust forecasts using tools like tracking signals.

• Forecasting is iterative: update forecasts regularly, use multiple methods, and combine qualitative insights with quantitative data for robust planning.

Quick reference formulas and concepts

• 3-month moving average forecast:
  ext{Forecast}{t+1} = rac{Dt + D{t-1} + D{t-2}}{3}

• Weighted moving average (example weights 3,2,1):
  ext{Forecast}{t+1} = rac{3 Dt + 2 D{t-1} + D{t-2}}{3+2+1}

• Exponential smoothing (single):
  Ft = F{t-1} + ext{alpha} (A{t-1} - F{t-1})
  or equivalently
  Ft = ext{alpha} A{t-1} + (1 - ext{alpha}) F_{t-1}

• Mean Absolute Deviation (MAD):
  ext{MAD} = rac{1}{n}
  abla{i=1}^n |Ai - F_i|

• Mean Squared Error (MSE):
  ext{MSE} = rac{1}{n}
  abla{i=1}^n (Ai - F_i)^2

• Mean Absolute Percentage Error (MAPE):
  ext{MAPE} = rac{100}{n}
  abla{i=1}^n igg| rac{Ai - Fi}{Ai} igg|

• Tracking Signal (TS):
  ext{TS} = rac{ ext{CFE}}{ ext{MAD}} ext{ with } ext{CFE} =
  abla{i=1}^n (Ai - F_i) $$

Summary

• Forecasting involves choosing appropriate horizons and methods (qualitative for new products; quantitative for existing demand).

• Time series decomposition into trend, seasonal, and random components helps explain observed demand patterns and informs model selection.

• Simple models (naive, moving averages) are easy to implement but have limitations during trend and seasonality; exponential smoothing provides a more responsive alternative.

• Forecast accuracy metrics (MAD, MSE, MAPE) quantify forecast error and guide model selection; tracking signals help detect biases over time.

• Real-world examples (Kodak, Genesee Brewery, cannibalization, supplier lead times, external shocks) illustrate how forecasting informs planning and the need for regular updates and integration of qualitative insights.

• Understanding the interplay of horizon, data stability, and operational needs is essential for effective forecasting in both manufacturing and service contexts.