SAMENVATTING
OPERATIONELE BELEIDSMETHODEN
4498
Fien Peerenbooms
[BEDRIJFSNAAM] [Bedrijfsadres]
,Inhoudsopgave
HC1 – HFDST 2: LINEAR PROGRAMMING: BASIS CONCEPTS ............................................ 2
1. INTRODUCTION ............................................................................................................... 2
2. CASE STUDY .................................................................................................................. 2
3. FORMULATING A BASIC MATHEMATICAL LP MODEL ........................................................................ 3
4. APPLYING THE GRAPHICAL ................................................................................................... 5
4.1. Two-dimensional graph .......................................................................................... 5
4.2 Feasible region ....................................................................................................... 5
4.3 objective function ................................................................................................... 6
4.4 Optimal solution ..................................................................................................... 7
5. METHOD INTERPRETING ...................................................................................................... 7
VOORBEELD: MINIMIZING EXAMPLE .................................................................................. 9
HC 2 - LP: FORMULATION & APPLICATIONS (CHAPTER 3) ............................................. 11
TYPE 1: RESOURCE ALLOCATION PROBLEMS.................................................................................. 11
Example 1. Wyndor Glass Company ............................................................................... 12
Example 2. Super Grain Corp. Advertising-Mix problem (HB p64-65) .................................. 12
Example 3. The TBA Airlines Problem ............................................................................. 13
TYPE 2: COST-BENEFIT TRADE-OFF PROBLEMS .............................................................................. 13
Example 1. Profit & Gambit Co. Advertising-Mix .............................................................. 13
Example 2. Union Airways personnel scheduling .............................................................. 14
TYPE 3: TRANSPORTATION PROBLEMS (HB NIET VOLGEN, ENKEL VOORBEELDEN LEZEN) ................................. 15
Example 1. The Big M Transportation Problem................................................................. 15
Example 2. Sellmore Company Assignment problem ........................................................ 16
HC 3 – PROJECT PLANNING (CHAPTER 16, NIET IN HB) ................................................ 17
PROJECT GRAFISCH VOORSTELLEN................................................................................... 18
PROJECT PLANNEN ......................................................................................................... 19
HC 4 + 5 – FORECASTING (CHAPTER 10) ....................................................................... 24
1. INTRODUCTION (HC4) ................................................................................................. 24
2. CHARACTERISTICS OF FORECASTING (HC4) ................................................................... 24
3. TIME SERIES FORECASTING (HC4) ................................................................................ 25
3.1 FORECASTING COMPONENTS (HC4) ......................................................................... 25
2.3 SEASONALITY ....................................................................................................... 28
3.3 FORECAST METHODES ........................................................................................... 30
3.2.1 Last-Value (naïve) (HC4) ..................................................................................... 30
3.2.2 Moving-Average (HC4) ........................................................................................ 31
3.2.3 Simple exponential smoothing (HC5) ..................................................................... 34
3.2.4 Exponential smoothing with trend (HC5) ................................................................ 36
4. MEASURES OF FORECAST ERROR (HC 5) ........................................................................ 39
REDEN 1: beste methode .......................................................................................... 40
4.1 Mean absolute deviation (MAD) ............................................................................... 40
4.2 Mean absolute percentage error (MAPE) ................................................................... 40
4.3 Mean squared error (MSE) ...................................................................................... 40
4.4 Vergelijking van voorspellingsmethoden (zie dia 66-67) .............................................. 41
REDEN 2: beste waarde voor parameteres (alfa, beta, X) ......................................... 41
5. THE TIME-SERIEUS FORECASTING METHODS IN PERSPECTIVE (HC5) ................................. 42
SUMMARY ..................................................................................................................... 43
,HC1 – HFDST 2: LINEAR PROGRAMMING: BASIS CONCEPTS
1. Introduction
“The management of any organization regularly must make decisions about how to allocate its
resources to various activities to best meet organizational objectives”
Budget Marketing activities Maximizing profit
Types of personnel Production activities Minimizing costs
Machine types Capital investment activities
Raw materials
Def. Linear programming
§ Programmeren: betekent optimaliseren (maximaliseren) met beperkende voorwaarden
§ Linear: betekent dat zowel u doelfunctie (winst, kosten), als u middelen (budget,
machines) een lineaire functie zijn, Y = X (een rechte)
Examen à bij de vragen zal duidelijk aangegeven zijn welke methode gebruikt moet worden
2. Case study
Het bedrijf heeft 2 nieuwe producten en verschillende materialen om deze te produceren
GEGEVENS
Consider the Wyndor Glass Co, that has developed the following new products to revamp its
product line:
§ An 8-foot glass door with aluminum framing.
§ A 4-foot by 6-foot double-hung, wood-framed window.
The company has three plants
§ Plant 1 produces aluminum frames.
§ Plant 2 produces wood frames.
§ Plant 3 produces glass and assembles the windows and doors.
VRAAG
What would be the most profitable mix of products to produce per week (i.e., the number of units
to produce of each new product), in order to maximize profit per week?
What information do we need to solve this product mix problem?
§ Hoeveel uren zijn er beschikbaar?
§ Hoeveel heeft ieder product nodig in uren?
§ Hoeveel brengen deze ramen en deuren mij op? Wat is de maximale winst die we hieruit
kunnen halen?
INFORMATION
Gegevens worden gegeven op het examen maar je moet deze zelf in een tabel kunnen plaatsen.
§ Production time needed for both products in the 3 plants (hours used per unit produced)
§ Available capacity in the plants (hours available per week)
§ Profit per product unit (unit profit)
, 3. Formulating a basic mathematical LP model
Toepassen op case
Telkens 3 stappen doorlopen om het probleem te formuleren!!
à Op elke stap staan punten op het examen
STAP 1: In woorden formuleren
1) Waarover ga je een beslissing nemen? Antwoord: Hoeveel deuren en ramen gaan we
maken?
2) Wat gaan we maximaliseren? Antwoord: We willen de totale winst van deze 2 producten
maximaliseren.
3) Wat zijn mijn beperkingen? Antwoord: De beschikbare uren.
STAP 2: formules maken
1) D = X1 = #deuren en W = X2 = #ramen (per week)
2) Max Profit = 300*X1 + 500*X2
3) Beperkingen (variabele definiëren)
§ Eerste beperking = fabriek 1 à 1*X1 =< 4 (dus max 4 deuren maken)
§ Tweede beperking = fabriek 2 à 2*X2 =< 12 (dus max 6 ramen maken)
§ Derde beperking = fabriek 3 à 3*X1 + 2*X2 =< 18
§ Extra beperking: X1 >= 0 en X2 >= 0
HOE FORMULEREN OP EXAMEN?
Def. Solution = iedere mogelijke combinatie van X1 en X2
Def. Feasible solution = een combinatie van X1 en X2 die aan alle beperkingen voldoet
Def. BEST feasible solution = is de combinatie die de beste uitkomst geeft (de meeste winst)
OPERATIONELE BELEIDSMETHODEN
4498
Fien Peerenbooms
[BEDRIJFSNAAM] [Bedrijfsadres]
,Inhoudsopgave
HC1 – HFDST 2: LINEAR PROGRAMMING: BASIS CONCEPTS ............................................ 2
1. INTRODUCTION ............................................................................................................... 2
2. CASE STUDY .................................................................................................................. 2
3. FORMULATING A BASIC MATHEMATICAL LP MODEL ........................................................................ 3
4. APPLYING THE GRAPHICAL ................................................................................................... 5
4.1. Two-dimensional graph .......................................................................................... 5
4.2 Feasible region ....................................................................................................... 5
4.3 objective function ................................................................................................... 6
4.4 Optimal solution ..................................................................................................... 7
5. METHOD INTERPRETING ...................................................................................................... 7
VOORBEELD: MINIMIZING EXAMPLE .................................................................................. 9
HC 2 - LP: FORMULATION & APPLICATIONS (CHAPTER 3) ............................................. 11
TYPE 1: RESOURCE ALLOCATION PROBLEMS.................................................................................. 11
Example 1. Wyndor Glass Company ............................................................................... 12
Example 2. Super Grain Corp. Advertising-Mix problem (HB p64-65) .................................. 12
Example 3. The TBA Airlines Problem ............................................................................. 13
TYPE 2: COST-BENEFIT TRADE-OFF PROBLEMS .............................................................................. 13
Example 1. Profit & Gambit Co. Advertising-Mix .............................................................. 13
Example 2. Union Airways personnel scheduling .............................................................. 14
TYPE 3: TRANSPORTATION PROBLEMS (HB NIET VOLGEN, ENKEL VOORBEELDEN LEZEN) ................................. 15
Example 1. The Big M Transportation Problem................................................................. 15
Example 2. Sellmore Company Assignment problem ........................................................ 16
HC 3 – PROJECT PLANNING (CHAPTER 16, NIET IN HB) ................................................ 17
PROJECT GRAFISCH VOORSTELLEN................................................................................... 18
PROJECT PLANNEN ......................................................................................................... 19
HC 4 + 5 – FORECASTING (CHAPTER 10) ....................................................................... 24
1. INTRODUCTION (HC4) ................................................................................................. 24
2. CHARACTERISTICS OF FORECASTING (HC4) ................................................................... 24
3. TIME SERIES FORECASTING (HC4) ................................................................................ 25
3.1 FORECASTING COMPONENTS (HC4) ......................................................................... 25
2.3 SEASONALITY ....................................................................................................... 28
3.3 FORECAST METHODES ........................................................................................... 30
3.2.1 Last-Value (naïve) (HC4) ..................................................................................... 30
3.2.2 Moving-Average (HC4) ........................................................................................ 31
3.2.3 Simple exponential smoothing (HC5) ..................................................................... 34
3.2.4 Exponential smoothing with trend (HC5) ................................................................ 36
4. MEASURES OF FORECAST ERROR (HC 5) ........................................................................ 39
REDEN 1: beste methode .......................................................................................... 40
4.1 Mean absolute deviation (MAD) ............................................................................... 40
4.2 Mean absolute percentage error (MAPE) ................................................................... 40
4.3 Mean squared error (MSE) ...................................................................................... 40
4.4 Vergelijking van voorspellingsmethoden (zie dia 66-67) .............................................. 41
REDEN 2: beste waarde voor parameteres (alfa, beta, X) ......................................... 41
5. THE TIME-SERIEUS FORECASTING METHODS IN PERSPECTIVE (HC5) ................................. 42
SUMMARY ..................................................................................................................... 43
,HC1 – HFDST 2: LINEAR PROGRAMMING: BASIS CONCEPTS
1. Introduction
“The management of any organization regularly must make decisions about how to allocate its
resources to various activities to best meet organizational objectives”
Budget Marketing activities Maximizing profit
Types of personnel Production activities Minimizing costs
Machine types Capital investment activities
Raw materials
Def. Linear programming
§ Programmeren: betekent optimaliseren (maximaliseren) met beperkende voorwaarden
§ Linear: betekent dat zowel u doelfunctie (winst, kosten), als u middelen (budget,
machines) een lineaire functie zijn, Y = X (een rechte)
Examen à bij de vragen zal duidelijk aangegeven zijn welke methode gebruikt moet worden
2. Case study
Het bedrijf heeft 2 nieuwe producten en verschillende materialen om deze te produceren
GEGEVENS
Consider the Wyndor Glass Co, that has developed the following new products to revamp its
product line:
§ An 8-foot glass door with aluminum framing.
§ A 4-foot by 6-foot double-hung, wood-framed window.
The company has three plants
§ Plant 1 produces aluminum frames.
§ Plant 2 produces wood frames.
§ Plant 3 produces glass and assembles the windows and doors.
VRAAG
What would be the most profitable mix of products to produce per week (i.e., the number of units
to produce of each new product), in order to maximize profit per week?
What information do we need to solve this product mix problem?
§ Hoeveel uren zijn er beschikbaar?
§ Hoeveel heeft ieder product nodig in uren?
§ Hoeveel brengen deze ramen en deuren mij op? Wat is de maximale winst die we hieruit
kunnen halen?
INFORMATION
Gegevens worden gegeven op het examen maar je moet deze zelf in een tabel kunnen plaatsen.
§ Production time needed for both products in the 3 plants (hours used per unit produced)
§ Available capacity in the plants (hours available per week)
§ Profit per product unit (unit profit)
, 3. Formulating a basic mathematical LP model
Toepassen op case
Telkens 3 stappen doorlopen om het probleem te formuleren!!
à Op elke stap staan punten op het examen
STAP 1: In woorden formuleren
1) Waarover ga je een beslissing nemen? Antwoord: Hoeveel deuren en ramen gaan we
maken?
2) Wat gaan we maximaliseren? Antwoord: We willen de totale winst van deze 2 producten
maximaliseren.
3) Wat zijn mijn beperkingen? Antwoord: De beschikbare uren.
STAP 2: formules maken
1) D = X1 = #deuren en W = X2 = #ramen (per week)
2) Max Profit = 300*X1 + 500*X2
3) Beperkingen (variabele definiëren)
§ Eerste beperking = fabriek 1 à 1*X1 =< 4 (dus max 4 deuren maken)
§ Tweede beperking = fabriek 2 à 2*X2 =< 12 (dus max 6 ramen maken)
§ Derde beperking = fabriek 3 à 3*X1 + 2*X2 =< 18
§ Extra beperking: X1 >= 0 en X2 >= 0
HOE FORMULEREN OP EXAMEN?
Def. Solution = iedere mogelijke combinatie van X1 en X2
Def. Feasible solution = een combinatie van X1 en X2 die aan alle beperkingen voldoet
Def. BEST feasible solution = is de combinatie die de beste uitkomst geeft (de meeste winst)
