IB122 0-QAM-II - Lecture notes all PDF

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M

Knut Nyman

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Table of content Confidence Intervals ................................................................................................................................................. 3 Calculating a confidence interval .............................................................................................................................. Standard Error of the Mean SEM ............................................................................................................................ Calculating a confidence interval .............................................................................................................................. Simple Linear Regression ....................................................................................................................................... 7 Method of least squares .......................................................................................................................................... 7 Multiple Linear regression ...................................................................................................................................... 7 Model selection (Backward/forward elimination) .............................................................................................. 7 Dummy variables ..................................................................................................................................................... 8 Hypothesis testing.................................................................................................................................................... 8 Multicollinarity.......................................................................................................................................................... 8 Time series - Introduction ...................................................................................................................................... 9 Trend/seasonality/white noise etc........................................................................................................................ 9 Time series – Moving Average .............................................................................................................................10 Simple Moving Average (k=uneven). ................................................................................................................. 10 Centred Moving Average (k=even). ................................................................................................................... 10 Time series – Classical Decomposition ............................................................................................................. 11 Additive Model (Y=T+S+I) . .............................................................................................................................. 11 Multiplicative Model (Y=T*S*I). ........................................................................................................................ 11 Seasonal Component. ............................................................................................................................................ 11 Irregular Component. ............................................................................................................................................ 11 Time series – Forecasting ......................................................................................................................................12 Decision Analysis .....................................................................................................................................................14 Payoff Table. ........................................................................................................................................................... 14 Maximin Criterion.................................................................................................................................................. 14 Minimax Criterion.................................................................................................................................................. 14 EMV ........................................................................................................................................................................ 15 EPPI......................................................................................................................................................................... 15 EVPI ........................................................................................................................................................................ 15 Decision Analysis - Sensitivity Analysis ............................................................................................................16 Decision Tree. ........................................................................................................................................................ 16 Sensitivity Analysis Example. ............................................................................................................................... 17 Multi-stage Decision Analysis ..............................................................................................................................18" Analyst example ..................................................................................................................................................... 18 "

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Linear Programming – Introduction ................................................................................................................. 20" Decision Variables ................................................................................................................................................. 20 Formulating Constraints ....................................................................................................................................... 20 Objective Function ................................................................................................................................................ 20 Linear Programming – Solving Problems Graphically ................................................................................21" Steps of Solving ...................................................................................................................................................... 21 Walkthrough Example .......................................................................................................................................... 22 Linear Programming – Sensitivity Analysis ................................................................................................... 24" Binding constraints ................................................................................................................................................ 24 Shadow prices ......................................................................................................................................................... 24 Inventory Management ........................................................................................................................................ 25" Ordering Costs (Co) .............................................................................................................................................. 25 Carrying Costs (Cc)................................................................................................................................................ 25 Total Cost ................................................................................................................................................................ 26 Economic Order Quantity (EOQ) ..................................................................................................................... 26 EOQ with Discounts ............................................................................................................................................ 27 Inventory Management – Reorder Point/Safety Stock ............................................................................... 28" " Reorder Point + Example ................................................................................................................................... 28 Safety Stock + Example ....................................................................................................................................... 29 Project Planning ..................................................................................................................................................... 30 Project Planning – Activity Crashing ................................................................................................................31"

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Confidence Intervals Confidence interval for the population mean 1 − ! 100% = !"#$%&!!"#$ ± (!!/!! ×!"#) !

!

If n>30 use Z | If n < 30 and population SD is unknown use t !" !"#$%#&%!!""#"!!"!!ℎ!!!"#$!!"# =

!

Confidence interval for the population proportion 1 − ! 100%!!" = ! ! ! ± !! /!! ×!"# !

!"# =

!

!!(1 − !!) !

Difference between means Confidence interval for differences for small samples n...