OM Week 11

What does every operations decision start with?

A forecast

What happens in OM if we get the forecast wrong?

Everything downstream becomes “wrong” too

What are the three main pairings that get forecasted in OM?

1. Demand and Sales

• Unit sales by product, by region, by channel

• Used for production planning, inventory, and staffing

1. Prices and Costs

• Raw material prices, energy costs

• Affects procurement and budgeting

1. Supply and Lead Times

• Supplier delivery reliability

• Affects safety stock and reorder points

Right Censoring

If you sell out, sales undercount true demand

• You only observe a demand up to available supply

Four Properties of Forecasts

1. Forecasts are always wrong

• Never report just a point estimate

• Always include an error measure

2. Short term > Long term

• Next week’s forecast is more accurate than next year’s

• Uncertainty compounds over time

3. Aggregate > disaggregate

• Total company sales easier to forecast than one SKU

• Individual errors cancel out when aggregated

4. Upstream direction

• Forecast error amplify as you move up the supply chain

• Small retail fluctuation → lrge manufacturer swing

• Bullwhip effect

A forecast without an error estimate is

Just a guess

What happens when we over forecast (4 points)?

• Excess inventory sitting in warehouses

• Spoilage and waste (especially perishables)

• Holding costs eat into margins

• Markdowns to clear unsold stock

What happens when we under forecast?

• Lost sales and empty shelves

• Customers switch to competitors

• Expediting costs to rush orders

• Backorder management overhead

Random Variation Demand Fluctuation

Unpredictable, short term fluctuations

• Cannot be forecasted → only measured

Trend Demand Fluctuation

Sustained upward or downward movement

• Driven by market growth, technology shifts

Seasonality

Predictable, repeating pattern within a fixed cycle

• Weekly, monthly quarterly, annually

Business Cycles Demand Fluctuations

Long term economic expansions and contractions

• Hard to predict timing, easier to recognize

What is the forecaster’s job within OM?

Separate what is systematic (trend, seasonality) from what is random (noise)

• Forecast the systematic part, measure the random part

Four Demand Patterns

What are the two components of an observation?

1. Systematic Component (What we can forecast)

2. Noise

What are the three elements of the Systematic Component?

• Level (L): the baseline demand

• Trend (T): the rate of change per period

• Seasonal Factor (St): periodic multiplier

Multiplicative Model Formula

F_t = (L + T x t) x S_t

Multiplicative Model

Level and trend set the baseline; seasonality scales it up or down

• Most common

Additive Model Formula

F_t = L + T x t + S_t

Additive Model

Use when seasonal swings are constant regardless of level

What is the rule of thumb for using the multiplicative model?

If seasonal peaks grow as demand grows

What is the rule of thumb for using the additive model?

If peaks stay the same size

Simple Moving Average Formula

Simple Moving Average (SMA)

Forecast next period’s demand as the average of the last n observations

• Each of the last n periods gets equal weight

• Periods before that get zero weight

• The “window” slides forward each period

What are the implications of choosing a small n for SMA (4 points)?

• Reacts quickly to changes

• Picks up real shifts faster

• But also amplifies noise

• Forecast is volatile

What are the implications of choosing a large n for SMA (4 points)?

• Smooths out noise effectively

• Stable, less jumpy forecasts

• But slow to detect real shifts

• Forecast is sluggish

A Small n for SMA is [BLANK1] while a Large n is [BLANK2]

1. Responsive/Stable

2. Responsive/Stable

1. Responsive

2. Stable

Exponential Soothing Formula

a E (0,1) is the smoothing constant

What are the two equivalent interpretations of Exponential Smoothing?

1. Weighted blend:

• New forecast = blend of latest observation and previous forecast

• a controls how much weight goes to new data

2. Error correction:

• Start with previous forecast

• Adjust by a fraction a of the error

• If you under forecast, nudge up

• If you over forecast, nudge down

Error Correction Formula

What is the advantage of ES over SMA?

Each step back in time multiplies the weight by (1-a)

• The forecast is a weighted sum where recent data gets the most weight

Weights decay

Exponentially

What are the implications of choosing a Small a for ES?

• Heavy weight on history

• Very smooth, stable forecast

• Slow to react to real changes

• Like a large-n moving average

What are the implications of choosing a Large a for ES?

• Heavy weight on recent data

• Responsive, catches shifts quickly

• But amplifies noise

• Like a small-n moving average

An ES with smoothing constant a behaves roughly like an SMA with:

What level of a should you first try for stable demand?

a = 0.1-0.3

What level of a should you first try for volatile/level-shifting demand?

a = 0.3-0.5

Attributes of SMA pertaining to the following factors:

• Weights

• Data storage

• Tuning parameter

• Drops old data

• Responds to shifts

• Best for

• Equal weight on last n periods

• Must store n past observations

• n (window size)

• Completely, after n periods

• After n periods, fully

• Stable demand, no trend

Attributes of ES pertaining to the following factors:

• Weights

• Data storage

• Tuning parameter

• Drops old data

• Responds to shifts

• Best for

• Exponentially decaying weights

• Only last forecast + last demand

• a (smoothing constant)

• Gradually, never fully

• Immediately (partially)

• Stable demand, no trend

What is a limitation of both SMA and ES?

Neither handle trend or seasonality

• Both will systematically under forecast trending demand and miss seasonal patterns

Static Decomposition Approach

What is the goal of the Static Decomposition Approach?

To separate demand into Level, Trend, and Seasonality, then recombine to forecast

Step-by-step Method for the Static Decomposition Approach

1. Remove seasonality to reveal the trend

2. Fit a line through the trend

3. Measure how each season deviates from the trend

4. Put it back together: trend x seasonal factor

A p-period moving average includes every season exactly once, so

Seasonal highs and lows cancel out

To deseasonalize we average over

One full cycle (p periods)

Where does an Odd average land after deseasonalizing ?

The middle one

Where does an Even average land after deseasonalizing ?

Falls between periods

• Average two consecutive MAs to “center” at an actual period

Even Average Formula

Averages two offset windows to land on period t

Centering the Moving Average Formula

Shortcut formula for computing CMA

Step-by-step CMA Calculation

1. Compute the CMA

2. Find the trend

• Use the CMA values from Step 1 to estimate a trend line via linear regression

• =SLOPE(CMA, periods) and = INTERCEPT(CMA, periods)

1. What is a seasonal factor? What are the specific seasonal factors?

• For each period, divide actual demand by the trend value [PICTURE]

4. Average the seasonal factors

5. Put it all together

When S>1

Demand is above trend (peak)

When S<1

Demand is below trend

Seasonal factor

Ratio of actual demand to trend

What are the four error metrics you needs and what do they tell you?

What are the four error metrics and when is each best put to use?

RMSE >= MAE always (True/False)

True

• The bigger the gap, the more your errors are “spiky” rather than uniform

Forecast Interval

Gives a plausible range for demand

Forecast Interval Formula

Tracking Signal

Monitors whether errors are becoming systematically biased

Tracking Signal Formula

What does it mean if the TS ~= 0?

Errors show little cumulative signed bias

What does it mean if the TS > 0 and increasing?

Systematically under forecasting

What does it mean if the TS > 0 and decreasing?

Systematically overforecasting

If |TS_t| exceeds a threshold (typically +- 6)

The forecast method needs attention

The tracking signal is a control chart for

Your forecast

• It triggers an alarm when something systematic goes wrong

9 Step Process of Static Decomposition

• Steps 1-7 build the forecast

• Steps 8-9 tell you how much to trust it

• Never skip steps 8-9

What are the 3 limitations of Static Decomposition?

• Parameters are estimated once from all data

• Doesn’t adapt as new data arrives

• If the trend shifts or seasonal pattern changes, the forecast becomes stale

Holt’s Method Formula

Holt’s Winters Formula

Under Holt’s Method, each component

Updates every period

Forecasts are always wrong (True/False)

True