Hoofdstuk 1 & Hoofdstuk 9.
Linear Programming Models & Integer Linear Programming Models.
Samenvatting aan de hand van veel voorbeelden!
O.a.
- Giapetto Model
- Graphical Solution to (I)LP Models
- Resource Allocation Problem
- Blending Problem
- If-Then & Either-Or Constraints
Zie inl...
OR MODELS FOR THE PRE-
MASTER IEM
Summary 2023/2024
Abstract
Summary for the course OR Models For The Pre-Master Industrial Engineering &
Management.
Based on the book ‘Operations Research’ by Wayne L. Winston & Slides by L. van der Wegen
(Utwente).
This summary follows the 4 lecture slides on ‘LP and ILP’, ‘DP’, ‘IM’ and ‘Queuing’.
All page numbers in this summary refer to pages in Operations Research by Winston.
Klep, (Julian, Student Utwente)
, Julian Klep
OR Models for Pre-Master IEM
Winston Ch. 1, 3, 9, 15, 16, 18, 20
TABLE OF CONTENTS
Lecture 1 – LP & ILP Models .............................................................................................................................4
Time Notation........................................................................................................................................... 4
Example 1 – Giapetto Model – Soldiers & Trains (p.49) ..................................................................................... 4
Graphical Solution To Problem (Example 1) ............................................................................................. 5
Special Cases Of LP Models ................................................................................................................................ 5
Lecture 2 – LP & ILP Models .............................................................................................................................6
Example 2 – Marketing Research Problem ......................................................................................................... 6
Example 3 – Work Scheduling (p.72) .................................................................................................................. 6
Example 4 – Production Scheduling Problem (p.101) ........................................................................................ 7
Assumptions – LP Model........................................................................................................................... 7
Example 5 – Transportation Problem (p.360)..................................................................................................... 8
Example 6 – Production Process Problem (Simple Version) (p.95) .................................................................... 8
Lecture 3 – LP & ILP Models .............................................................................................................................9
Example 6 – Production Process Problem (Extended Version) (p.95) ................................................................ 9
Units In Constraints .................................................................................................................................. 9
Example 7 – Blending Problem (p. 86) .............................................................................................................. 10
Integer Linear Programming ILP ....................................................................................................................... 12
Graphical Clarification ILP ...................................................................................................................... 12
Example 8 – Investment Problem – (PEN) ........................................................................................................ 13
Lecture 4 – LP & ILP Models ........................................................................................................................... 14
Either-Or & If-Then Constraint ......................................................................................................................... 14
Either-Or Constraint (p.488) ................................................................................................................... 14
If-Then Constraint ................................................................................................................................... 16
Example 9 – Fixed Charge (Big M-Constraint) (p.480) ...................................................................................... 17
Lecture 5 – DP Models ................................................................................................................................... 18
Example 10 – Network Problem (p.964) ........................................................................................................... 18
Characteristics Of DP-Applications ......................................................................................................... 18
Example 11 – Fishery Example (p.990) ............................................................................................................. 19
Lecture 6 – DP Models ................................................................................................................................... 20
Example 12 – Production Inventory Problem (p.969) ...................................................................................... 20
Assumptions for LP In DP Models ........................................................................................................... 22
Example 13 – Resource Allocation (p.974) ....................................................................................................... 22
Lecture 7 – DP Models ................................................................................................................................... 25
Example 14 – Wagner-Whitin Method (p.1002)............................................................................................... 25
Example 15 – Silver-Meal Method (p.1003) ..................................................................................................... 26
Example 16 – Equipment Replacement Proplem (p.985) ................................................................................. 27
1
, Julian Klep
OR Models for Pre-Master IEM
Winston Ch. 1, 3, 9, 15, 16, 18, 20
Lecture 8 – Inventory Management ............................................................................................................... 28
Background Info + Terminology........................................................................................................................ 28
Basic EOQ Model .............................................................................................................................................. 29
Example 17 – Ordering Cameras (p.854) .......................................................................................................... 30
Nonzero Lead Time ........................................................................................................................................... 30
Definitions .............................................................................................................................................. 30
Effect of NonZero Lead Time .................................................................................................................. 31
Lecture 9a – Inventory Management (Deterministic Demand)....................................................................... 32
Example 18 – EOQ With 2 Quantity Discounts ................................................................................................. 32
Example 19 – EOQ With 3 Quantity Discounts (p.863) ..................................................................................... 32
Continuous Rate EOQ Model ............................................................................................................................ 33
Example 20 – Macho Auto Company (p.867) ................................................................................................... 33
When To Use EOQ Models ...................................................................................................................... 34
Example 21 – Test If EOQ May Be Used ........................................................................................................... 34
Lecture 9b – Inventory Management (Stochastic Demand)............................................................................ 35
Newsboy Problem............................................................................................................................................. 35
Example 22 – Newsboy Problem (p. 881) ......................................................................................................... 36
Lecture 10 – Inventory Management ............................................................................................................. 37
Terminology ............................................................................................................................................ 37
(r,q) In Case Of Backlogging (p.890).................................................................................................................. 37
Demand During Lead Time (p.890) ......................................................................................................... 38
Determine TC(q,r) (Holding Cost, Shortage Cost, Order Cost) ................................................................ 38
Marginal Analysis To Determine Reorder Point ..................................................................................... 40
Example 23 – Disk Stock (p.894) ....................................................................................................................... 41
(r,q) In Case Of lost sales .................................................................................................................................. 42
(s,S) In Case Of Backlogging Or Lost Sales......................................................................................................... 42
Lecture 11 – Inventory Management ............................................................................................................. 43
Service Level Approach ........................................................................................................................... 43
Example 24 – SLM1 & SLM2 ............................................................................................................................... 43
Determining r* And Safety Stock For SLM1 ....................................................................................................... 44
Determining E(Br) ................................................................................................................................... 44
Example 25 – Bads, Inc. (p.903) ........................................................................................................................ 45
Determining r* And Safety Stock Level For SLM2 .............................................................................................. 46
Example 26 – Bads. Inc (2) (p. 906) ................................................................................................................... 46
(R,S) Periodic Review Model ............................................................................................................................. 47
Example 27 – Lowland Appliance ..................................................................................................................... 48
Lecture 12 – Queing ....................................................................................................................................... 49
2
Voordelen van het kopen van samenvattingen bij Stuvia op een rij:
Verzekerd van kwaliteit door reviews
Stuvia-klanten hebben meer dan 700.000 samenvattingen beoordeeld. Zo weet je zeker dat je de beste documenten koopt!
Snel en makkelijk kopen
Je betaalt supersnel en eenmalig met iDeal, creditcard of Stuvia-tegoed voor de samenvatting. Zonder lidmaatschap.
Focus op de essentie
Samenvattingen worden geschreven voor en door anderen. Daarom zijn de samenvattingen altijd betrouwbaar en actueel. Zo kom je snel tot de kern!
Veelgestelde vragen
Wat krijg ik als ik dit document koop?
Je krijgt een PDF, die direct beschikbaar is na je aankoop. Het gekochte document is altijd, overal en oneindig toegankelijk via je profiel.
Tevredenheidsgarantie: hoe werkt dat?
Onze tevredenheidsgarantie zorgt ervoor dat je altijd een studiedocument vindt dat goed bij je past. Je vult een formulier in en onze klantenservice regelt de rest.
Van wie koop ik deze samenvatting?
Stuvia is een marktplaats, je koop dit document dus niet van ons, maar van verkoper julian19. Stuvia faciliteert de betaling aan de verkoper.
Zit ik meteen vast aan een abonnement?
Nee, je koopt alleen deze samenvatting voor €2,99. Je zit daarna nergens aan vast.
