Purpose of contents of operational planning level
-
- smoothing of seasonal variations of capacity requirements and available capacity
- determine master production schedule (which products in which quantities)
- procurement planning: which quantities of input materials are needed for master scheduling
Chase Demand vs Level Production strategy
pros and cons
Chase demand:
- low inventories, but high capacities
- updating plan every month based on incoming aggregated sales data
Level Production:
- high inventories, low capacities
Demand forecasting
Definion and Types of time series
- prediction of future values of a time series (demand patterns) under uncertainty (based on historical values)
Types of time series:
1. Level Demand
2. Linear Trend
3. Seasonal Variation
Analysis of the characteristics of a time series
- long term
- mid-term cyclical variations (eg economic cycles, product lifecycle)
- seasonal fluctuations (eg. annual seasons)
- random variations
Procedure of time series based forecasting
5 Steps
- Analysis of characteristics of time series
- selecting appropriate forecast model
- estimate coefficients of forecast model
- apply forecast model
- monitor and analyse forecast accuracy over time (tracing errors)
Ex ante forecast values
vs
Ex post forecast values
- ex ante: forecast for following period
- ex post: previous forecast
Forecasting Models
- Simple exponential smoothing (level demand time series)
- Exponential smoothing with trend adjustment (linear trend time series)
Simple Exponential Smoothing
forecasting model for level demand time series
- random variations around a constant demand level
- initialization Po has to be determined (often yo is chosen)
- smoothing paramter alpha: determines the strenght of the smoothing effect
- the higher alpha the closer you get to observed demand (naive forecast)
Formula Simple Exponential Smoothing
Pt+1 = alpha x yt + (1-alpha) x Pt
(weighting of previously observed demand and previous forecast adjusted for errors)
yt = observed demand in period t ; Pt = forecast period t
Exponential Smoothing with trend adjustment
forecasting model for trend line time series
- assumed demand process: random variations around linear trend
- simple exponential smoothing causes systematic error
- introdruce trend adjustment (correction factor) to adjust for systematic lag
- Initialization: before first forecast determination adequate initial values a0 and b0 have to be determined, e.g. through linear regressen
Exponential Smoothing with trend adjustment
Step by Step
- update of level demand at end of period t (at)
- update of trend at end of period t (bt)
- Forecast determination
Which measured can be taken to match production and demand
- build up inventories
- backlog demand
- lost sales
- additional workforce
- rent machinery
Level Demand
Type of Time Series
- levels are established with random fluctuations around them
- simple exponential smoothing
Linear Trend
Type of time series
- average going up with fluctuations around it
- exponential smoothing with trend adjustment
Seasonal Variation
3 types of time series
- seasonal peaks
- e.g. construction industry
Exponential smoothing with trend adjustment
the smaller alpha
e.g. 0.2
- the larger deviations from ideal trend line
Trend Adjustment
Exponential smoothing with trend adjustment
- correction factor
[(1 - alpha) / alph] * b
Initialization Formula
Level Demand
Exponential smoothing with trend adjustment
a(0) = y(0) - [(1-alpha/alpha) x b(0)]
b(0) = trend increase per period
Forecast Determination P(t+τ)
Formula
Exponential smoothing with trend adjustment
P(t+τ) = a(t) + b(t) x [(1-alpha) / alpha] + τ x b(t)
Update of trend
Formula
Exponential Smoothing with trend line adjustment
b(t) = alpha x (a(t) - a(t-1)) + (1-alpha) x b(t-1)
Update Level Demand
Formula
Exponential smoothing with trend adjustment
a(t) = alpha x y(t) + [(1-alpha) x a(t-1)]
Simple Exponential Smoothing
The company wants to calculate in period t=5 a demand forecat for period t=7. What is the value for the forecast?
P(7) = P(6)
- as demand y(5) is used
What is the de-trended initial value?
- a(0) of exponential smoothing with trend line
- initialization
Difference when forecasting for t(6) and t(7) from t(5) on but demand is not nown for t(6) nor (t7)
Simple exponential smoothing
vs.
Exponential smoothing with trend line adjustment
Simple exponential Smoothing
P(t+1) = α x yt + (1-α) x Pt
- y(t) = P(t)
- Smoothing will return same result as for P(5)
Exponential Smoothing with trend line adjustment
P(t+𝜏) = a(t) + b(t) x (1-α)/α + 𝜏 x b(t)
- Take coefficients from t = 5 -> a(5) and b(5) and add 1 year for P(6) and 2 years for P(7)
=> the results will vary significantly between both models
