To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 1© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Kapittel 9 Transport og tildelingsmodeller

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 2© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Temaer i kapittel 10 Formulering av transport- problemer Løsning av transportproblemer med nordvestre hjørne og VAM metoden Tildelingsmodeller Løsningen med den ungarske metoden

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Spesialiserte problemer Transportproblemer Distribusjon av produkter fra en kilde (produksjonsenhet) til en destinasjon (varehus). Produksjonskapasitet (tilbud) og behov (etterspørsel) er kjent Tildelingsproblemer Hvordan fordeler ulike arbeids- oppgaver mellom flere mennesker Spesialiserte algoritmer sparer tid!

9/1/2014To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458Transportproblem Des Moines (100 units) capacity Cleveland (200 units) required Boston (200 units) required Evansville (300 units) capacity Ft. Lauderdale (300 units) capacity Albuquerque (300 units) required

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 5© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Setting Up a Transportation Problem The Executive Furniture Corporation  Anslag på behov i hvert varehus og kapasitet i hver fabrikk er vist under

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Transportkostnader Fra (Kilde) Til (Destinasjon) Albuquerque Boston Cleveland Des Moines Evansville Fort Lauderdale $5 $8 $9 $4 $7 $3 $5

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 7© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Transportkostnader pr. enhet Des Moines (D) Evansville (E) Fort Lauderdale (F) Behov Albuquerque (A) Boston (B) Cleveland (C) Kapasitet

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 8© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Totalt tilbud og etterspørsel Des Moines (D) Evansville (E) Fort Lauderdale (F) Behov Albuquerque (A) Boston (B) Cleveland (C) Kapasitet

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 9© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Transport tabell Des Moines (D) Evansville (E) Fort Lauderdale (F) Behov Albuquerque (A) Boston (B) Cleveland (C) Kapasitet

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 10© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Første løsning med nordvestre hjørne regelen Start i cellen øverst til venstre og fordel enheter slik: Bruk hele tilbudet i en rad før du går til neste rad Dekk etterspørselen i hver kolonne før man går til høyre til neste kolonne. Sjekk at alle betingelser for tilbud og etterspørsel er dekket

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 11© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Første løsning Des Moines (D) Evansville (E) Fort Lauderdale (F) Behov Albuquerque (A) Boston (B) Cleveland (C) Kapasitet

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 12© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Stepping stone Nordvestre hjørne er en første løsning som i regelen ikke er optimal Stepping stone metoden er en metode som forbedrer løsningen. Antatt belagte celler må være 1 lavere enn summen av rader og kolonner i problemet Vi spør Kan løsningen bedres? Hvilke endringer i transport- opplegget foretas?

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 13© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Stepping-Stone Method - The Des Moines-to-Boston Route Des Moines (D) Evansville (E) Fort Lauderdale (F) Warehouse Req. Albuquerque (A) Boston (B) Cleveland (C) Factory Capacity Start The Executive Furniture Corporation

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Stepping-Stone Method - The Ft. Lauderdale-to- Albuquerque Route Des Moines (D) Evansville (E) Fort Lauderdale (F) Warehouse Req. Albuquerque (A) Boston (B) Cleveland (C) Factory Capacity Start The Executive Furniture Corporation

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 15© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Stepping-Stone Method - The Evansville-to- Cleveland Route Des Moines (D) Evansville (E) Fort Lauderdale (F) Warehouse Req. Albuquerque (A) Boston (B) Cleveland (C) Factory Capacity Start The Executive Furniture Corporation

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 16© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Stepping-Stone Method - The Des Moines-to- Cleveland Route Des Moines (D) Evansville (E) Fort Lauderdale (F) Warehouse Req. Albuquerque (A) Boston (B) Cleveland (C) Factory Capacity Start The Executive Furniture Corporation

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 17© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Stepping-Stone Method - The Ft. Lauderdale-to- Albuquerque Route Des Moines (D) Evansville (E) Fort Lauderdale (F) Warehouse Req. Albuquerque (A) Boston (B) Cleveland (C) Factory Capacity Start The Executive Furniture Corporation

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 18© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Steppping stone

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 19© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Vogel’s Approximation 1. For hver rad/kolonne i tabellen, finn forskjellen mellom de to laveste kostnadene (Alternativkost) 2. Finn rad/kolonne med størst alternativkostnad. 3. Tildel så mange enheter som mulig til cellen med lavest kostnad i raden/kolonnen med høyest alternativkost. 4. Eliminer rad/kolonne hvor tilbud/behov er dekket 4. Start på nytt. Se bort fra eliminerte rader/kolonner

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 20© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Ubalanserte problemer Etterspørsel mindre enn tilbud Etterspørsel større enn tilbud Degenererte problemer Men enn en optimalløsning Spesielle problemer

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 21© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Etterspørsel mindre enn tilbud Fabrikk 1 Fabrikk 2 Fabrikk 3 Behov Kunde 1 Kunde 2 Dummy Kap

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 22© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Tilbud mindre enn etterspørsel Fabrikk 1 Fabrikk 2 Dummy Behov Kunde 1 Kunde 2 Kunde 3 Kapa

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 23© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Degenerert Fabrikk 1 Fabrikk 2 Fabrikk 3 Behov Kunde 1 Kunde 2 Kunde 3 Kapasitet

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 24© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458Lokalisering

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 25© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458Lokalisering

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 26© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Tildelingsproblemet Prosjekt Person123 Adams$11$14$6 Brown$8$10$11 Cooper$9$12$7

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 27© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Ungarske metode 1. Trekk det minste tallet i hver rad fra alle tall i raden trekk det minste tallet i hver kolonne fra alle tallene i kolonnen 2. Tegn det minste antall rette linjer som er nødvendig for å dekke alle 0er i tabellen Hvis antall linjer er lik antall rader eller kolonner, kan optimum finnes.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 28© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Ungarske metode 3. Hvis antall linjer ikke tilsvarer antall rader eller kolonner trekk det laveste tallet som ikke er dekket av en linje fra alle andre udekkede tall legg det samme tallet til ethvert tall som ligger i skjæringen mellom to linjer Gå til steg 2 4. Finn optimal allokering ved å bruke 0 cellene i tabellen

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 29© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Ungarske metode Første tabell PersonProsjekt 123 Adams Brown81011 Cooper9127

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 30© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Ungarsk metode Rekke reduksjon PersonProsjekt 123 Adams Brown Cooper

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 31© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Ungarsk metode Kolonne reduksjon PersonProsjekt 123 Adams560 Brown003 Cooper230

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 32© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Ungarsk metode PersonProsjekt 123 Adams Brown Cooper Testing Dekker Linje 2 Dekker Linje 1

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 33© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Ungarsk metode PersonProsjekt 123 Adams340 Brown005 Cooper010 Revidert tabell over alternativkostnad

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 34© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Ungarsk metode PersonProsjekt 123 Adams 340 Brown 005 Cooper 010 Testing Dekker Linje 1 Dekker Linje 2 Dekker Linje 3

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 35© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Ungarsk metode Tildelinger PersonProsjekt 123 Adams 6 Brown10 Cooper 9