Session 12 OM — Forecasting models

12 May, 2026

What this session covered

This lecture extended the forecasting unit with a hands-on walk-through of two baseline time-series forecasting models—Naïve forecast and Moving Average—and (more importantly) how to evaluate them using forecast errors (absolute deviation, Mean Absolute Deviation, Co-efficient of Variation, period-wise error distribution). It also connected forecasting accuracy to inventory/stockout decisions and gave examples from retail outlets, ATMs, e-commerce delivery restrictions, and policy/incentive design.

1) Forecasting fundamentals (time series assumption)

1.1 Core assumption of time series forecasting

• Past patterns repeat in the future (this is the baseline assumption to test).
• Forecasting is framed as hypothesis-driven:
  • You’re effectively testing whether past patterns can be projected.

1.2 Why forecasting matters in OM

• Forecasting provides scientific grounding (“$y=mx+c$ is science”) and increases decision rationality.
• Decisions depend on forecasts; but the key managerial insight is:
  • Forecast errors matter more than the forecast itself.

2) Model 1 — Naïve forecast

2.1 Logic

• Next period forecast = last period actual.
• The first period has no prior observation → forecast is N/A.
• Interpretation: the naive model is essentially a one-period lag of actual values.

2.2 Error calculation: Absolute deviation

• After you have a forecast, compute absolute deviation:
  • $|Actua{l}_t-Forecas{t}_t|$
• Errors can be positive or negative; in absolute terms, both count as deviation.

2.3 Aggregate measure: MAD (Mean Absolute Deviation)

• MAD is the average of absolute deviations across periods.
• Interpretation:
  • MAD is an overall indicator of how close the model is to reality.
  • Lower MAD = better (all else equal).

2.4 Manager takeaway

• Don’t stop at a single MAD number:
  • Look at period-wise error distribution (disaggregate analysis) because that’s often more useful for operational decisions.

3) Model 2 — Moving Average

3.1 Logic (3-period moving average example)

• Needs a minimum number of observations.
  • For a 3-period moving average, the first 3 periods are N/A.
• Forecast for period 4 = average(period 1 to 3).
• Each new period:
  • Drop the oldest observation.
  • Add the newest observation.
  • This is why it is called “moving” average (rolling window).

3.2 Choosing the window size (n)

• There is no universal scientific rule for the “best” n.
• In practice: trial and error; compare models using error measures.

3.3 Practical note: bucket size depends on industry

Examples referenced to explain why period choice differs:

• FMCG: often monthly buckets.
• Automobile: often quarterly buckets.
• Restaurants/food services: often weekly buckets.
• Some contexts (e.g., policing / public services) vary depending on planning horizon.

4) Model comparison and selection (key learning)

4.1 You need at least two models

• You cannot say a model is “good” in isolation.
• Evaluation is relative: compare at least two models.

4.2 Aggregate vs disaggregate evaluation

• Aggregate measure: MAD (and other totals/averages).
• Disaggregate measure: period-by-period error distribution.
• Important insight:
  • Model choice can change depending on whether you prioritize aggregate or disaggregate evaluation.

4.3 Different products may need different models

• The lecture discussed how MS (petrol) and HSD (diesel) can behave differently.
• Therefore, the best model for one may not be best for the other.

5) Additional statistical concepts referenced

5.1 Standard deviation and dispersion

• Standard deviation indicates how data is distributed around the mean.

5.2 Coefficient of Variation (CV)

• CV = Standard Deviation / Average.
• Ratio-based measures (like CV) can be more discriminating than absolute measures.

6) Implications of forecast error for operations (inventory & stockouts)

A key OM bridge:

• Higher forecast error → higher inventory / higher risk of shortage.
• Forecast errors reflect inventory management challenges.
• Real-world examples referenced:
  • Retail outlets (petrol pumps): frequent stockouts create bad reputation ("always dry").
  • ATMs: “dry ATM” reputation; cash stocking is an inventory problem.
  • Competition effects: adjacent outlets/ATMs influence stocking policies.

7) Policy / operations design examples (applied perspective)

• ATM policy:
  • Limits on number of non-home-bank transactions, per-transaction limits, and bill-dispensing caps (e.g., 40 notes) connect to security + inventory management.
• E-commerce distribution restrictions:
  • Some items available in one geography but not another due to demand/policy/logistics constraints.
• Incentive design (managerial implication):
  • Government incentives for solar / EVs; future managers need to decide incentive levels and rationale.

8) Technology + career insight (automation & interpretation)

• AI tools can solve optimization/analytics tasks quickly, shifting the premium to:
  • Interpretation, judgment, and knowing what to do with the output.
• Tools named in discussion: Excel/statistical software (SPSS/SAS) and optimization tools.
• Message: adapt continuously; skills need to evolve as automation increases.

9) Exam-focused checklist (from what was emphasized)

• Be able to:
  • Construct a Naive forecast table (Forecast + Absolute deviation).
  • Construct a 3-period moving average (with proper N/A handling).
  • Compute MAD for both models.
  • Compare models and recommend one using:
    • MAD (aggregate)
    • Period-wise errors (disaggregate)
• Practice calculation with a calculator (no Excel expected in exam conditions).

Quick glossary

• Naive forecast: $F_{t+1}=A_t$
  • Variables: $F$ = forecast, $A$ = actual, $t$ = current period, $t+1$ = next period
  • Example: If actual demand in period 5 is $A_5=120$, then forecast for period 6 is $F_6=A_5=120$.
• Moving average (n-period): $F_{t+1}=(A_t+A_{t-1}+...+A_{t-n+1})/n$
  • Variables: $n$ = number of past periods averaged; $A_t...A_{t-n+1}$ are the last $n$ actuals
  • Example (3-period MA): If $A_3$ = $100, A₄ = $130, A₅ = $110, then, F₆ = (110 + 130 + 100)/3 = 113.33.
• Absolute deviation (absolute error): $|A_t-F_t|$
  • Variables: $A_t$ = actual in period $t$, $F_t$ = forecast for period $t$, $||$ = absolute value
  • Example: If $A_6$=125 and F₆ = 113.33, then $AD$= |125 - 113.33| = 11.67.
• MAD (Mean Absolute Deviation): $\text{MAD}=\frac{1}{T}{\sum }_{t=1}^T|A_t-F_t|$
  • Variables: $T$ = number of forecasted periods included; $\sum$ = “sum across periods”
  • Example: If absolute deviations over 4 periods are 10, 8, 12, 6, then $MAD$= (10+8+12+6)/4 = 9.
• CV (Coefficient of Variation): $\text{CV}=\sigma /\mu$ (standard deviation / mean)
  • Variables: $\sigma$ = standard deviation, $\mu$ = mean
  • Example: If mean demand is $\mu =200$ and standard deviation is $\mu$ = 50, then CV $=50/200=0.25$ (25%).