Demand Planning, Forecasting and Sales and Operations Planning

Role of Forecasting

Forecasting is the first building block of demand planning because nearly every supply chain decision — inventory, capacity, transportation, sourcing, pricing — depends on some view of future demand. It reduces uncertainty enough to plan sensibly.

Forecasting as the Foundation

• Push processes act in anticipation of customer demand. Forecasting is essential: you produce, transport, or stock based on what you think will be needed.
• Pull processes act after an actual order arrives. Even then, you need forecasts to plan capacity and inventory so that you can respond quickly when orders come.

Example – Paint retail: In a hardware store, the final mixing of paint happens after the customer asks (pull). But the store must already stock base paint and dyes (push). That push decision relies on a forecast. The paint factory and upstream suppliers also need forecasts to plan their production.

Collaborative Forecasting

When each stage in a supply chain forecasts independently, forecasts can diverge, causing supply–demand mismatches (stockouts or excess inventory). Collaborative forecasting means supply chain partners share information and align on a common view of demand.

• Example: A beverage company planning a major promotion must share that plan with its bottler. If the bottler forecasts normal weeks, capacity falls short when promotion demand hits → lost sales.

Real‑World Examples

Forecast vs. Forecast Error

• Forecast = expected level of demand.
• Forecast error = uncertainty around that expectation. It drives the buffers you need.

When forecast error is high, supply chains must decide whether to hold more safety inventory, build flexible capacity, use faster replenishment, or shape demand through pricing/promotions.

Cross‑Functional Impact

Forecasting is not just an operations activity; it affects purchasing, production, budgeting, staffing, logistics, and finance. A practical challenge is getting all functions to agree on a common forecast:

• Sales – optimistic
• Operations – conservative
• Finance – cost‑focused

If each function plans with different numbers, the firm gets mismatched decisions → excess costs or poor service.

Exam tip: Forecasting is about reducing uncertainty enough to make better decisions, not predicting perfectly. Always account for forecast error when designing buffers.

Key takeaways

• Forecasting is the starting input for most supply chain planning decisions.
• Push and pull processes both rely on forecasts, though for different purposes.
• Collaborative forecasting aligns partners and avoids demand–supply mismatches.
• Forecast error (not just the forecast itself) determines the buffers needed.
• Cross‑functional alignment on a common forecast is a major practical challenge.

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Common Features of All Forecasts

Elements of a Good Forecast

1. Timely – provides enough lead time to act.
2. Reasonably accurate, with error stated mathematically – essential for safety stock and capacity buffers.
3. Reliable – performs consistently; erratic forecasts create planning chaos.
4. In meaningful units – finance needs value, operations needs units, transportation needs truckloads.
5. Written and shared – all functions plan with the same number.
6. Simple enough to be understood and used – black‑box forecasts are often ignored.
7. Cost‑effective – benefit must exceed the cost of data, systems, and people.

Consequences of Inaccurate Forecasts

Both reduce profits and customer trust. Forecast errors can also create waves in the supply chain: one stage’s reaction (e.g., sudden order increase/decrease) can be misinterpreted by upstream partners, amplifying variability.

Exam tip: Improving forecast accuracy helps, but it’s not the only solution. Supply chains also design buffers (inventory, capacity, faster replenishment) so the system does not break when forecasts are wrong.

The Forecasting Process – Six Steps

1. Determine the purpose – What decision will it support? (capacity, inventory, promotion, staffing) → defines detail and accuracy needed.
2. Establish the time horizon – next week, month, or year? Must match decision lead time.
3. Obtain and prepare the data – clean errors, remove outliers, ensure comparability.
4. Choose a forecasting method – simple to advanced; to be covered in subsequent segments.
5. Generate the forecast using the chosen model.
6. Monitor forecast errors and update – if errors are large or patterns change, revisit assumptions, data, or method.

Final Practical Point

Forecasting is a loop, not a one‑time exercise: Forecast → Plan → Observe error → Adapt. When demand deviates significantly, managers take action (e.g., plan a promotion if too low; add overtime or expedite replenishment if too high).

Key takeaways

• All forecasts assume the past continues, are never perfect, improve with grouping, and get worse with horizon.
• Good forecasts are timely, accurate (with error stated), reliable, in meaningful units, shared, simple, and cost‑effective.
• Inaccurate forecasts cause shortages or excesses; supply chains use buffers as a complementary strategy.
• The forecasting process has six steps: purpose → horizon → data → method → generate → monitor & update.
• Forecasting is a continuous loop, not a one‑off number.

1. Why Identify Demand Patterns?

Before applying any forecasting formula, plot the data. Visual inspection reveals underlying patterns: stable mean, growth, peaks, economic swings. The goal is to match the forecast method to the pattern.

2. The Components of Demand

Demand over time is a combination of several systematic components plus unavoidable random variation (noise). The systematic parts can be extracted and modelled.

Horizontal (Level + Random Noise)

• Data fluctuates around a stable average; no long-term increase or decrease.
• The ups and downs are the random component (also called error, residuals, or noise).
• Supply chain context: Most desirable – forecasting is simpler, inventory and capacity planning are straightforward.
• Example: Mature staple product in a stable market (e.g., basic packaged staple in a neighbourhood store).

Trend

• A long-term upward or downward movement in the average level.
• Causes: Population shifts, rising incomes, changing preferences, new substitutes, changes in distribution reach.
• Impact: If ignored – upward trend causes shortages; downward trend causes excess inventory.
• Example: Demand for electric vehicles rising over years.

Seasonality

• Regular, fixed, and known periodicity tied to the calendar.
• Periods: weekly (weekends vs weekdays), monthly (salary month effect), yearly (summer/winter, festivals).
• Key: Seasonality repeats → can be modelled and planned for.
• Examples: Ice cream peaks in summer; rainwear peaks in monsoon; sweets and gifts around festivals.
• If ignored: Stockouts during peaks or excess inventory during troughs.

Cyclical Pattern

• Longer-term wave-like movements (typically > 1 year) with no fixed periodicity.
• Often linked to business/economic cycles: GDP, interest rates, investment booms/slumps.
• Harder to forecast; firms use scenario planning, leading indicators, conservative buffering.
• Example: Demand for capital equipment or construction materials rises/falls with investment cycle.

Irregular Variation

• Unusual, non‑typical events – severe weather, strikes, sudden disruption, one‑time policy shock, competitor shutdown, pandemic, one‑off mega promotion.
• Should be identified, flagged, and often removed from historical data for baseline forecasting, then added back as special adjustments.
• Including them distorts the forecast.

Random Component (Residual Noise)

After accounting for all systematic patterns, unavoidable random noise remains. Real life is messy → forecasts will always have errors. The goal is not perfection but measuring and tracking error to plan buffers.

3. Forecast Accuracy: Definitions

Let $t$ denote time period; $A_t$ = actual demand, $F_t$ = forecast demand.

Forecast Error (per period):

$E_t = A_t - F_t$

• Positive error: forecast too low ($A_t > F_t$).
• Negative error: forecast too high ($A_t < F_t$).

Why it matters: Underestimate → stockout and lost sales; overestimate → excess inventory and markdowns.

Summary Error Metrics

Note: Some textbooks divide by $n-1$ for MSE (sample‑based adjustment); both are acceptable – the key idea is the same.

Managerial Trade-off

• Historical accuracy vs. responsiveness.
• A very stable method can look accurate historically but react slowly to pattern changes.
• A reactive method may chase noise.
• Managers balance both.

4. Worked Example

Setting: Inventory planner forecasting daily demand for a fast‑moving SKU (e.g., 1‑litre milk packet). Eight days of data.

(The table is partially filled; the full calculation follows the same method.)

Compute metrics using the provided sums:

• Sum of absolute errors = 22 → $\text{MAD} = 22/8 = 2.75$ units. Interpretation: average forecast miss is ~2.75 units per day.
• Sum of squared errors = 76 → $\text{MSE} = 76/8 = 9.5$. Interpretation: large errors penalised; gives a sense of variability.
• Sum of absolute percentage errors = 10.26 → $\text{MAPE} = 10.26/8 \approx 1.28\%$. Interpretation: average error is about 1.28% of actual demand – excellent for high‑volume products.

Exam tip: MAPE is scale‑free; use it to compare forecasts across SKUs with different volumes. MAD is simplest for unit‑level planning; MSE when large errors are costly.

5. Key Takeaways

• Demand contains horizontal, trend, seasonal, cyclical, irregular, and random components. Plotting first reveals the dominant pattern.
• Seasonality has fixed, known periodicity; cycles are longer and not calendar‑regular.
• Forecasts are always wrong; measure error (MAD, MSE, MAPE) to plan buffers and compare methods.
• Choose metric by context: MAD for unit miss, MSE if large errors hurt more, MAPE for scale‑free comparison.
• Balance historical accuracy with responsiveness – the "best" method depends on the pattern and the cost of being wrong.

Forecasting Approaches

Forecasting methods split into two broad families: qualitative (judgment-based) and quantitative (data-driven). Quantitative methods further divide into time series (uses past values of the same variable) and associative models (uses other explanatory variables, e.g. regression). In practice, firms often use a quantitative baseline and layer on qualitative adjustments for events the data cannot foresee (promotions, competitor moves, regulatory changes).

Qualitative Methods

Useful when historical data is limited, irrelevant, or the environment is changing rapidly – e.g. new product launches, long-range strategic planning.

Exam tip: Qualitative methods are not for day‑to‑day inventory decisions – use time series. They are for exceptions: promotions, product launches, disruptions, strategic planning.

Key takeaways (qualitative)

• Qualitative forecasting relies on judgment, not historical data.
• Four main approaches: executive opinion, sales force, surveys, Delphi.
• Each has trade‑offs: speed vs. bias, breadth vs. cost, anonymity vs. consensus.
• Use when data is absent or the future is structurally different.

Time Series Averaging Methods

Time series = sequence of observations recorded at regular intervals. Core assumption: the near future will behave like the recent past unless something changes. Averaging methods smooth out random noise and are especially effective when demand has no strong trend.

Simple Moving Average

The forecast for period $t$ is the mean of the most recent $n$ actual demands:

$F_t = \frac{1}{n} \sum_{i=1}^{n} A_{t-i}$

where $A_{t-i}$ is the actual demand in period $t-i$ and $n$ is the number of periods in the average.

• Larger $n$ → smoother forecast but slower to react to real changes.
• Smaller $n$ → more responsive but may chase noise.

Choosing $n$ is a trade‑off between stability and responsiveness.

Worked Example (3‑period moving average)

Forecast for period 6:

$F_6 = \frac{43 + 40 + 41}{3} = 41.33$

Now suppose actual demand in period 6 is 38. To forecast period 7, drop the oldest (period 3) and add the newest actual:

$F_7 = \frac{40 + 41 + 38}{3} = 39.67$

The moving average “moves forward” – always using the most recent $n$ values.

Advantage: Easy to compute and understand. Disadvantage: All $n$ values are weighted equally – the oldest has the same influence as the most recent, making the forecast slow to react when demand changes.

Exam tip: A moving average forecast lags the actual demand. If demand suddenly rises, the forecast will be too low for several periods; if demand falls, it will be too high. The lag increases with $n$.

Weighted Moving Average

Assign different weights to past observations, typically giving higher weight to more recent values. This makes the forecast more responsive while still using older data.

$F_t = w_{t-n} A_{t-n} + \dots + w_{t-2} A_{t-2} + w_{t-1} A_{t-1}$

with $\sum w_i = 1$. A simple moving average is a special case where all weights are equal.

Trade‑off: Choosing weights is subjective and often done by trial and error – poor weights can overreact to noise.

Worked Example (weighted moving average)

Weights: 0.4 (most recent), 0.3, 0.2, 0.1 (oldest in window). Demand data:

Forecast for period 6:

$F_6 = 0.1(40) + 0.2(43) + 0.3(40) + 0.4(41) = 4 + 8.6 + 12 + 16.4 = 41.0$

Weighted moving average is more sensitive to the latest observation than the simple moving average – provided the weights are chosen well.

Key takeaways (time series averaging)

• Simple moving average: equal weights; $n$ controls smoothness vs. responsiveness.
• Weighted moving average: unequal weights; more responsive but weight selection is arbitrary.
• Neither method explains why demand changes; they only capture past patterns.
• Use averaging when demand lacks a strong trend and the goal is to smooth noise.

Exponential Smoothing

Exponential smoothing is a weighted-average forecasting method that assigns weights to all past observations, with weights decaying exponentially as observations grow older. Recent data matters more; older data still contributes but with diminishing influence. Unlike simple moving averages, it does not require choosing a fixed window – it updates each period using only the previous forecast and the latest actual.

Intuition: Correcting the previous forecast

The next forecast is simply the previous forecast plus a fraction of last period’s forecast error:

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

• $F_t$ – forecast for period $t$
• $F_{t-1}$ – forecast for period $t-1$
• $A_{t-1}$ – actual demand in period $t-1$
• $\alpha$ – smoothing constant ($0 < \alpha < 1$), the fraction of the error used for adjustment

Because $(A_{t-1} - F_{t-1})$ is the error, each new forecast takes a step in the direction of the error.

Equivalent weighting form

The same formula can be rewritten as:

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

Now it is a weighted average of the previous forecast (weight $1-\alpha$) and the latest actual (weight $\alpha$). Since the previous forecast already contains all earlier actuals with decaying influence, this structure produces exponential weighting of the entire history.

Exam tip: This equivalence is often tested. Both forms appear, and you must be able to switch between them.

Worked example 1

Given: $F_{t-1}=42$, $A_{t-1}=40$, $\alpha=0.10$.

$$F_t = 42 + 0.10 \times (40-42) = 42 - 0.2 = 41.8$$

If the next actual turns out to be $43$:

$$F_{t+1} = 41.8 + 0.10 \times (43-41.8) = 41.8 + 0.12 = 41.92$$

The forecast is pulled toward the latest actual, but only by a fraction $\alpha$.

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The smoothing constant $\alpha$ – the central knob

Common range: 0.05 to 0.5. Values are rarely above 0.5.

How to choose $\alpha$?

1. Judgment – based on perceived stability of demand.
2. Trial & error on historical data – test multiple alpha values and pick the one that minimizes an error metric (MAD, MSE, or MAPE). Most software automates this tuning.
3. Consider operational costs – e.g., if stock‑outs are very expensive, prefer a more responsive (higher) alpha even if it increases squared error.

Exam tip: Lower $\alpha$ = more smoothing = slower reaction. Higher $\alpha$ = less smoothing = faster reaction. The exam often asks which alpha to use for a given demand pattern.

Starting the forecast

Exponential smoothing requires an initial forecast. Common approaches:

• Naive forecast: $F_2 = A_1$ (first actual as forecast for period 2).
• Average of first few actuals.
• Managerial estimate.

The forecast needs enough periods to “settle” into the data, so start far enough back.

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Comparison of Methods (worked example)

Compare the three methods on periods 3–11, since moving averages start at period 3:

• MA2: 2-period simple moving average.
• WMA2: 2-period weighted moving average with weights 0.60 (most recent) and 0.40 (older).
• Single exponential smoothing (ES): $\alpha = 0.10$, naive start $F_2 = A_1$.

Illustration for the first few periods

(Period 2 error is available for ES but excluded from the comparison to keep periods 3–11 consistent.)

Error metrics (computed over periods 3–11)

Results:

Exam tip: MSE penalises large errors more than MAD. Therefore the metric you optimize changes the “best” method. No single method is universally superior – the choice also depends on business costs (e.g., cost of stock‑out vs. cost of excess inventory).

How the error metrics are computed

$$\text{MAD} = \frac{1}{n}\sum_{t} |A_t - F_t|$$ $$\text{MSE} = \frac{1}{n}\sum_{t} (A_t - F_t)^2$$ $$\text{MAPE} = \frac{1}{n}\sum_{t} \left|\frac{A_t - F_t}{A_t}\right| \times 100\%$$

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Key takeaways

• Exponential smoothing is a weighted average of all past data with exponentially decaying weights.
• Two equivalent formulas: $F_t = F_{t-1} + \alpha (A_{t-1} - F_{t-1})$ or $F_t = (1-\alpha)F_{t-1} + \alpha A_{t-1}$.
• $\alpha$ controls responsiveness: low $\alpha$ → smooth & slow; high $\alpha$ → jumpy & fast.
• Starting forecast needed; naive (first actual) is simplest.
• When comparing forecast methods, the “best” depends on the error metric and the operational context.
• For the example shown: ES ($\alpha=0.1$) gave lowest MSE, WMA2 gave lowest MAD and MAPE.

Techniques for Trend

Trend is the long-term upward or downward movement in a time series. Intuitively: if you plot demand over time and the overall direction clearly rises or falls, you are seeing a trend. The naïve averaging methods (simple/weighted moving averages, single exponential smoothing) only smooth random fluctuations — they lag behind reality when a trend is present. Upward trend causes systematic under‑forecasting; downward trend causes systematic over‑forecasting. A trend model explicitly captures the direction.

The Linear Trend Equation

The simplest trend model is a straight line:

$F_t = a + b t$

• $b > 0$ → upward trend (demand increases $\approx b$ units per period on average).
• $b < 0$ → downward trend.

Example: $F_t = 45 + 5t$ At $t=0$, $F_0 = 45$; slope $b=5$ means demand rises ~5 units each period. At $t=10$: $F_{10} = 45 + 5(10) = 95$ units.

This is exactly simple linear regression with $t$ as the explanatory variable — same logic, same estimation method (ordinary least squares).

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Estimating the Trend Line (Conceptual + Excel)

Step 1 – Plot the data. Always inspect visually first. If the points show a clear upward or downward drift (not just noise), a linear trend is appropriate.

Step 2 – Estimate $a$ and $b$ using least squares (minimises sum of squared errors). In practice, use software (Excel: Data → Data Analysis → Regression).

Step 3 – Write the equation $F_t = a + b t$.

Step 4 – Forecast future periods by plugging the corresponding $t$ into the equation.

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Worked Example: Cell Phone Sales

Data: weekly unit sales for 10 weeks.

(Full data not given; results from Excel regression output.)

• Intercept $a = 699.4$
• Slope $b = 7.5$

Trend equation: $F_t = 699.4 + 7.5 t$

Interpretation: Sales increase by 7.5 units per week on average.

Forecasts:

• Week 11: $F_{11} = 699.4 + 7.5(11) = 782$ units
• Week 12: $F_{12} = 699.4 + 7.5(12) = 789.5 \approx 790$ units

The model captures the overall direction, not every wiggle.

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Why Ignoring Trend Hurts Decisions

Trend modelling protects planning (inventory, capacity) from being consistently wrong in one direction.

Exam tip: When a time series has a clear trend, moving averages and simple exponential smoothing will lag — they are not designed to handle trending data. The linear trend equation is the simplest fix and is equivalent to regression on time.

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Key Takeaways

• Trend = long‑term upward/downward movement; averaging methods cannot track it.
• Linear trend equation: $F_t = a + bt$ (regression with time as $x$).
• $b>0$ → increasing; $b<0$ → decreasing.
• Estimate $a,b$ via least squares (Excel’s regression tool).
• Always plot first to check if a linear fit is reasonable.
• Forecasting: plug $t$ into estimated equation.
• Ignoring trend leads to systematic errors: under‑forecast on uptrend, over‑forecast on downtrend.

Trend Adjusted Smoothing

Simple exponential smoothing performs well when demand is stationary, but fails when a linear trend is present: forecasts lag behind the actual series – systematically too low when demand rises, too high when it falls. Trend-adjusted exponential smoothing (also called double exponential smoothing or Holt’s method) fixes this by tracking two components separately:

1. Level – the current baseline demand
2. Trend – the slope (units per period)

The forecast for the next period is simply the sum of the current level and trend.

The method

Let

• $S_t$ = smoothed level at the end of period $t$
• $T_t$ = smoothed trend at the end of period $t$
• $TAF_t$ = forecast made in period $t-1$ for period $t$ (i.e., $TAF_t = S_{t-1} + T_{t-1}$)
• $A_t$ = actual demand in period $t$

Forecast equation: $TAF_{t+1} = S_t + T_t$

Level update: $S_t = TAF_t + \alpha (A_t - TAF_t)$ Take the previous forecast and adjust it by a fraction $\alpha$ of the forecast error.

Trend update: $T_t = T_{t-1} + \beta \big[ (TAF_t - TAF_{t-1}) - T_{t-1} \big]$ The term $(TAF_t - TAF_{t-1})$ is the observed change in the forecast. If the previous trend $T_{t-1}$ was accurate, that change equals $T_{t-1}$. The difference is the trend error, and $\beta$ controls how quickly the trend estimate adjusts.

Two smoothing constants are required: $\alpha$ for the level, $\beta$ for the trend. Both are between 0 and 1, chosen by trial and error (often by minimising forecast error).

Initialization

Use a small set of early periods to get a starting level and trend. A common approach (used in the worked example below):

• Use the first 4 periods.
• Set the initial level $S_4 = A_4$.
• Compute the average change per period: $T_4 = \frac{A_4 - A_1}{3}$ (number of steps = 3).

Then produce forecasts from period 5 onward.

Worked example: cell‑phone sales (Holt’s method, $\alpha=0.4,\ \beta=0.3$)

Data (weeks 1–4):

Initialisation:

• $S_4 = 728$
• $T_4 = (728 - 700)/3 = 9.33$

Forecast for week 5: $TAF_5 = S_4 + T_4 = 728 + 9.33 = 737.33$

Update level and trend using actual week 5 sales $A_5=740$:

Level: $S_5 = TAF_5 + \alpha(A_5 - TAF_5) = 737.33 + 0.4(740 - 737.33) = 738.40$

Trend:

$$\begin{aligned} T_5 &= T_4 + \beta\big[(TAF_5 - TAF_4) - T_4\big] \\ TAF_4 &= 728 \\ &= 9.33 + 0.3\big[(737.33 - 728) - 9.33\big] \\ &= 9.33 + 0.3(9.33 - 9.33) = 9.33 \end{aligned}$$

(The trend did not change because the forecast change exactly matched the previous trend.)

Forecast for week 6: $TAF_6 = S_5 + T_5 = 738.40 + 9.33 = 747.73$

Continue recursively for weeks 7–11.

Comparison with linear trend regression

Exam tip: The key difference to remember: regression gives one fixed trend line; Holt’s method gives a trend that “learns” as new data arrives. If the exam asks why a forecast using simple exponential smoothing is consistently low, the reason is the presence of an upward trend – Holt’s method or a linear trend line would be needed.

Intuition check

Suppose a daily baseline level is 100 units, trend is +2 units/day. Forecast for tomorrow = 102. Over the next few days demand rises faster (closer to +4/day). Holt’s method will gradually push the trend estimate upward (controlled by $\beta$) rather than remaining stuck at +2. The level is also updated via $\alpha$ to reflect the new baseline.

Key takeaways

• Trend‑adjusted (Holt’s) smoothing extends simple exponential smoothing by separately tracking level and trend.
• Forecast: $TAF_{t+1} = S_t + T_t$.
• Level update uses $\alpha$ to correct forecast error; trend update uses $\beta$ to correct trend error.
• Initialise level as the last known actual and trend as the average change over a few early periods.
• Holt’s method adapts to changing trends, unlike a fixed linear regression slope.
• Choosing $\alpha$ and $\beta$ is a trade‑off between responsiveness and stability – higher values react faster but risk over‑reacting to noise.

Seasonality

Seasonality refers to regularly repeating demand patterns tied to the calendar or recurring events (weather, festivals, school terms, travel seasons). Demand moves in a known, repeating up‑down cycle with a fixed frequency (daily, weekly, monthly, quarterly, yearly). Unlike trend (a long‑term movement), seasonality loops predictably.

Additive vs. Multiplicative Models

Two ways to model seasonality:

Why multiplicative is often preferred: If a category grows year‑over‑year, the monsoon spike typically grows too. A percentage‑based (multiplicative) effect fits better than a fixed‑unit additive model.

Seasonal Relatives (Seasonal Indices)

A seasonal relative (also called seasonal index) is the multiplier that captures the seasonal effect in the multiplicative model.

• $\text{Seasonal relative} = 1.2$ → demand $20\%$ above average/trend level.
• $\text{Seasonal relative} = 0.75$ → demand $25\%$ below average/trend level.

Two standard uses (workflows):

Workflow 1: Deseasonalize

Given actual demand $A_t$ and its seasonal relative $S_t$: $\text{Deseasonalized value} = \frac{A_t}{S_t}$ This removes the seasonal wave, revealing the underlying trend or level.

Workflow 2: Forecast with Seasonality

1. Forecast the underlying trend/level for the target period (using moving average, exponential smoothing, trend equation, etc.).
2. Multiply that forecast by the seasonal relative for that period: $\text{Final forecast} = (\text{Trend forecast}) \times S_t$

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Worked Example 1: Coffee Shop Hot Chocolate

Context: A coffee shop owner wants to estimate hot‑chocolate demand (gallons) for the next two quarters. Sales data (periods 1–8) contain both trend and seasonality. Quarterly seasonal relatives (quarter relatives) are:

Trend equation (from data): $F_t = 124 + 7.5t$ (where $t$ = period number).

Part A – Deseasonalise sales for periods 1–8.

(Periods 1 and 3 illustrate the calculation. For the rest, divide sales by the appropriate relative. Deseasonalising strips out the seasonal wave so the underlying trend becomes easier to fit.)

Part B – Forecast demand for periods 9 and 10 using the trend equation and seasonal relatives.

• Period 9 is Q1 (since period 8 was Q4): Trend forecast $F_9 = 124 + 7.5 \times 9 = 191.5$ Final forecast $= 191.5 \times 1.2 = 229.8$ gallons.

• Period 10 is Q2: Trend forecast $F_{10} = 124 + 7.5 \times 10 = 199$ Final forecast $= 199 \times 1.1 = 218.9$ gallons.

Key insight: Forecast the underlying level first, then “re‑seasonalise” by multiplying by the seasonal relative. Seasonality is an adjustment layer on top of a trend/level forecast.

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Computing Seasonal Relatives: Simple Average Method

When seasonal relatives are not given, they can be estimated from historical data.

Procedure:

1. For each season (e.g., quarter), compute the season average over all years: $\text{Season average} = \frac{\text{Total demand in that season across all years}}{\text{Number of years}}$
2. Compute the overall average across all seasons: $\text{Overall average} = \frac{\text{Sum of all season averages}}{\text{Number of seasons}}$
3. Compute the seasonal relative: $\text{Seasonal relative} = \frac{\text{Season average}}{\text{Overall average}}$

Worked Example 2: Beverage Brand Quarterly Demand

Three years of quarterly sales (in thousands of units):

Step 1 – Quarter totals Q1: $20+23+17 = 60$ Q2: $10+12+8 = 30$ Q3: $25+19+22 = 66$ Q4: $28+30+26 = 84$

Step 2 – Quarter averages (divide totals by 3 years) Q1: $60 \div 3 = 20$ Q2: $30 \div 3 = 10$ Q3: $66 \div 3 = 22$ Q4: $84 \div 3 = 28$

Step 3 – Overall average across all quarters $\frac{20 + 10 + 22 + 28}{4} = 20$

Step 4 – Seasonal relatives Q1: $20 \div 20 = 1.0$ Q2: $10 \div 20 = 0.5$ Q3: $22 \div 20 = 1.1$ Q4: $28 \div 20 = 1.4$

Interpretation:

• Q1: average quarter (1.0)
• Q2: demand typically only $50\%$ of the average quarter (0.5)
• Q3: demand $10\%$ above average (1.1)
• Q4: demand $40\%$ above average (1.4)

These relatives can now be used to deseasonalise data or to adjust future forecasts.

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Cycles vs. Seasonality

• Cycles are longer wavelike movements with no fixed periodicity (e.g., economic cycles, industry cycles).
• Because timing is not fixed, cycles are much harder to forecast using simple seasonal indices.

Key takeaways

• Seasonality is a repeating, calendar‑linked pattern; trend is long‑term movement.
• Use the multiplicative model when seasonal swings scale with the series level.
• Seasonal relatives (indices) are multipliers >1 (above average) or <1 (below average).
• Two workflows: deseasonalise (divide actual by relative) and forecast (multiply trend forecast by relative).
• Compute seasonal relatives via simple average: season average ÷ overall average.
• Cycles (non‑fixed frequency) are not handled by seasonal indices.

Associative Techniques

Associative forecasting uses one or more related predictor variables (e.g., price, rainfall, calendar events) to forecast demand, rather than relying solely on past demand patterns. It answers: What observable factors drive demand?

Simple Linear Regression

The simplest form assumes a straight‑line relationship between one predictor $X$ and the forecast $Y$:

$Y = a + bX$

• $Y$ = predicted demand (dependent variable)
• $X$ = predictor (independent variable)
• $a$ = intercept – value of $Y$ when $X=0$
• $b$ = slope – expected change in $Y$ for a one‑unit increase in $X$

The least squares method fits the line that minimizes the sum of squared vertical deviations between actual data points and the line.

Worked Example: Trend as Predictor

Given sales data for weeks 1–10:

1. Plot the data – a scatter plot reveals an upward trend; a linear fit is reasonable.

2. Estimate $a$ and $b$ using Excel’s Regression tool:

   • Input $Y$ range: Sales
   • Input $X$ range: Week number
   • Output: Intercept $a = 699.4$, Slope $b = 7.5$

   Trend equation: $F_t = 699.4 + 7.5 \times t$

   Interpretation: weekly sales increase by about 7.5 units per week on average.

3. Forecast for weeks 11 and 12:

   • Week 11: $F_{11} = 699.4 + 7.5 \times 11 = 782$ units
   • Week 12: $F_{12} = 699.4 + 7.5 \times 12 = 789.5$ (≈790) units

Practical Cautions for Regression Forecasting

1. Do not extrapolate far beyond the observed $X$ range – relationships may change.
2. The relationship should be roughly linear in the range of interest.
3. Residuals (deviations from the line) should appear random – patterns indicate missing structure.

Extensions

• Multiple linear regression: use several predictors (price, promotion, competitor pricing, rainfall, day of week). Requires more data and careful handling of overfitting.
• Nonlinear relationships: curves, saturation, threshold effects may require transformations or nonlinear regression.

Exam tip: The real value of associative forecasting is not the technique itself but forcing the question “What actually drives demand?” – this improves both the forecast and managerial decisions.

Key takeaways

• Associative forecasting links demand to observable drivers (price, weather, events).
• Simple linear regression: $Y = a + bX$; $b$ = change in demand per unit change in $X$.
• Always plot data first; check linearity and random residuals.
• Extrapolation beyond the data range is risky.
• Multiple predictors and non‑linear patterns can be handled, but with added complexity.

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Aggregate Planning

Aggregate planning bridges demand forecasts and medium‑term capacity decisions (typically 3–18 months). It answers: Given a demand forecast, how do we plan production, capacity, and inventory to meet demand profitably?

Why Aggregate Planning Exists

In an ideal world (unlimited, free capacity with zero lead times), firms could react instantly. In reality:

• Capacity costs money – hiring/training workers, buying machines, securing supplier contracts all take time.
• Lead times are long – e.g., hiring takes 4–6 weeks, supplier lead times 8+ weeks.
• Reacting weekly to demand is too late; aggregate planning pre‑positions resources in advance.

Key Decision Variables (Outputs)

These decisions are tightly linked. Increasing production may require more workforce or overtime; reducing capacity may require building inventory earlier or accepting backlogs.

The Aggregate Planning Problem

Objective: Maximize profit over the planning horizon by choosing period‑by‑period levels of production, inventory, capacity, and backlogs.

Inputs needed:

• Demand forecast per period
• Production costs: regular time, overtime premium, subcontracting cost
• Costs of changing capacity: hiring, layoff, adding/reducing machine capacity
• Holding cost: storage, working capital, obsolescence risk
• Backlog / stockout cost: lost sales, lost future demand, customer dissatisfaction

Constraints:

• Limits on overtime, subcontracting, hiring/layoffs
• Supply constraints

The Three Cost Categories

Aggregate planning balances three trade‑off groups:

Reducing one cost typically increases another:

Exam tip: Aggregate planning is not just inventory planning – it co‑optimises inventory, capacity, and demand‑side levers (e.g., promotions). Profit comes from meeting demand with the least painful combination of these costs.

Key takeaways

• Aggregate planning sits between short‑term scheduling and long‑term strategy (3–18 months).
• Decision variables: production rate, workforce, overtime, subcontracting, inventory, backlog/stockout.
• Inputs: demand forecast, cost data (production, capacity change, holding, backlog), constraints.
• Three cost categories: capacity, inventory, backlog/stockout – trade‑offs are inevitable.
• The objective is to maximise profit, not just minimise cost; missing demand loses margin.

Sales and Operations Planning

Aggregate planning is the process of determining production, capacity, and inventory levels over a 3–18 month horizon to meet forecasted demand profitably. Sales and Operations Planning (S&OP) is the cross-functional process that aligns the demand plan, supply plan, and financial plan into one agreed-upon plan. Without S&OP, each function optimises locally – marketing pushes promotions, operations wants stable runs, procurement buys in bulk, finance cuts working capital – leading to conflicting actions and suboptimal overall performance.

Three Classic Aggregate Planning Strategies

In practice firms use hybrids, but these archetypes clarify the logic behind trading off capacity, utilisation, and inventory.

Exam tip: A firm never uses a pure strategy; the cheapest lever varies by context. Hybrids combine overtime, inventory, subcontracting, and limited backlog.

Why S&OP Matters

S&OP answers key questions before execution:

• What promotion can we support without breaking service levels?
• How much inventory should we pre‑build?
• Should we use overtime or subcontract?
• What is the cost impact – is the margin worth it?

Without S&OP, a festive‑season promotion might be approved by marketing while operations lacks plant capacity, distribution has no truck slots, procurement cannot source packaging in time, and finance fears bloated working capital.

S&OP is a Process, Not a Meeting

The meeting is the visible step, but the real work involves:

1. Creating one demand forecast (cross‑functional input).
2. Checking feasibility against capacity, supplier, and inventory constraints.
3. Choosing trade‑offs consciously.
4. Committing to one plan across all functions.

Big-Picture Flow

Forecasting → Demand signal → Aggregate planning (capacity, inventory, backlog decisions) → S&OP aligns cross‑functional commitment → Feasible, profitable plan.

Key Takeaways

• Aggregate planning strategies: chase (capacity lever), flexibility (utilisation lever), level (inventory lever).
• Each strategy trades off cost, risk, and responsiveness – no single best choice applies to all industries.
• S&OP is the cross‑functional process that aligns demand, supply, and financial plans.
• Without S&OP, functions optimise locally; with S&OP, the firm commits to one integrated plan.
• S&OP is a process, not just a meeting – the real work is forecast creation, feasibility checks, and trade‑off decisions.