MULTIPLE CRITERIA DECISION MAKINGMAKING/ AIDING/ AIDING …sydney.edu.au/business/__data/assets/pdf_file/0004/105745/jacekz... · multiple criteria decision makingmaking/ aiding

202011 ACADEMIC11 ACADEMIC TOURTOUR: : “Applying “Applying Advanced Methods in …”Advanced Methods in …”

MULTIPLE CRITERIA DECISION MULTIPLE CRITERIA DECISION MAKINGMAKING/ AIDING/ AIDING IN IN

TRANSPORTATION & LOGISTICSTRANSPORTATION & LOGISTICSTRANSPORTATION & LOGISTICSTRANSPORTATION & LOGISTICS

Poznan University of TechnologyPoznan University of Technology Prof. Jacek ŻAK

Australia and New Zealand; July – August; 2011Sydney, August 9, 2011

P U i it f T h lP U i it f T h l

CONTENTSCONTENTSPoznan University of TechnologyPoznan University of Technology

INTRODUCTION / MOTIVATION DEFINITION OF MCDM/A; DECISION MAKING PROCESS DEFINITION OF MCDM/A; DECISION MAKING PROCESS WHY TO USE MCDM/A METHODOLOGY IN TRANSPORTATION

MULTIPLE CRITERIA DECISION MAKING / AIDING METHODOLOGY MULTIPLE CRITERIA DECISION MAKING / AIDING METHODOLOGY HISTORICAL BACKGROUND CHARACTERISTICS OF THE MULTIOBJECTIVE DECISION PROBLEMS

CLASSIFICATION OF THE MCDM/A METHODS APLICATIONS OF MCDM/A METHODS IN TRANSPORTATION/

LOGISTICS REAL LIFE CASE STUDIESLOGISTICS – REAL LIFE CASE STUDIES OPTIMIZATION OF THE DISTRIBUTION SYSTEM EVALUATION OF LOGISTICS SERVICE PROVIDERSEVALUATION OF LOGISTICS SERVICE PROVIDERS

FINAL CONCLUSIONS

Slide 2


INTRODUCTION / MOTIVATIONINTRODUCTION / MOTIVATIONMULTIPLE CRITERIA DECISION MAKING / AIDINGMULTIPLE CRITERIA DECISION MAKING / AIDING

Poznan University of TechnologyPoznan University of Technology

MULTIPLE CRITERIA DECISION MAKING / AIDING MULTIPLE CRITERIA ANALYSIS (FRENCH)U C S S ( C ) MULTIPLE CRITERIA DECISION MAKING (AMERICAN)

MCDM/A IS A DYNAMICALLY DEVELOPING FIELD WHICH AIMS AT GIVING THE DM SOME TOOLS IN ORDER TO ENABLE HIM/ HER TO SOLVE A COMPLEX DECISION PROBLEM WHERE SEVERAL (CONTRADICTORY) POINTS OF VIEW MUST BE TAKEN INTO ACCOUNT

IN CONTRAST TO CLASSICAL OR TECHNIQUES MCDM/A METHODS DO NOT YIELD “OBJECIVELY BEST SOLUTIONS” BECAUSE IT IS IMPOSSIBLE TO GENERATE SUCH SOLUTIONS WHICH ARE THE BESTTO GENERATE SUCH SOLUTIONS WHICH ARE THE BEST SIMULTANEOUSLY, FROM ALL POINTS OF VIEW

MCDM/A CONCENTRATES ON SUGGESTING “COMPROMISE SOLUTIONS”C / CO C S O SUGG S G CO O S SO U O SWHICH TAKE INTO ACCOUNT THE TRADE-OFFS BETWEEN CRITERIA &THE DM’S PREFERENCES

Slide 3


INTRODUCTION INTRODUCTION / MOTIVATION/ MOTIVATIONDECISION DECISION MAKINGMAKING/ AIDING/ AIDING PROCESS BASED ON MCDM/APROCESS BASED ON MCDM/A


ANALYST

EXPERIENCE

REAL WORLD

•PHENOMENA

•EXPERIENCE•EXPERTEESE INMATHEMATICAL MODELING

•PHENOMENA•PROCESSES•LIMITATIONS

DECISION MAKER

MATHEMATICAL MODEL

•CRITERIA•CONSTRAINTS

STAKEHOLDERSCONFLICTING INTERESTS

DECISION MAKER

•CRITERIA•PREFERENCES•EVALUATIONS

•CONSTRAINTS•PREFERENCES

DECISION MAKING(O A O ) OO S

DSS

(OPTIMIZATION) TOOLS

Slide 4

COMPROMISESOLUTIONS


INTRODUCTION INTRODUCTION / MOTIVATION/ MOTIVATIONMCDM/A BASED DECISION PROCESSMCDM/A BASED DECISION PROCESS CUSTOMIZATION TO CUSTOMIZATION TO THE CREW SIZING PROBLEMTHE CREW SIZING PROBLEM Poznan University of TechnologyPoznan University of Technology

MULTIPLE CRITERIA OPTIMIZATION OF A CREW SIZE

TRANSPORTATION TRANSPORTATION ––LOGISTICS COMPANY/LOGISTICS COMPANY/

SYSTEMSYSTEM

TRANSPORTATION TRANSPORTATION ––LOGISTICS COMPANY/LOGISTICS COMPANY/

SYSTEMSYSTEMSYSTEMSYSTEMSYSTEMSYSTEM

CUSTOMERCUSTOMER

DECISION MAKERDECISION MAKERDECISION MODEL DECISION MODEL

ANALYSTANALYSTANALYSTANALYST

DSSDSS

EMPLOYEEEMPLOYEEDECISION MAKINGDECISION MAKING

METHODSMETHODS

Slide 5

COMPROMISE SOLUTIONSCOMPROMISE SOLUTIONSCOMPROMISE SOLUTIONSCOMPROMISE SOLUTIONS


INTRODUCTION / MOTIVATIONINTRODUCTION / MOTIVATIONWHY TO USE MCDWHY TO USE MCDM/AM/A IIN TRANSPORTATION/ N TRANSPORTATION/ LOGISTICSLOGISTICS ?? Poznan University of TechnologyPoznan University of TechnologyLOGISTICSLOGISTICS ??

COMPLEXITY OF TRANSPORTATION/ LOGISTICS PROCESSES/SYSTEMS; MANY EVALUATION MEASURES ( ECONOMICAL, TECHNICAL,

ENVIRONMENTAL & SOCIAL)MANY STAKEHOLDERS (CUSTOMERS OPERATORS EMPLOYEES MANY STAKEHOLDERS (CUSTOMERS, OPERATORS, EMPLOYEES, LOCAL COMMUNITIES & AUTHORITIES)

TRADE – OFFS “COST VS. QUALITY” RESULTS OF THE SURVEY RESEARCH (121 COMPANIES, DIFFERENT

SCOPE, DIFFERENT SIZE & LOCATION) 21 MOST IMPORTANT DECISION PROBLEMS MULTIOBJECTIVE 21 MOST IMPORTANT DECISION PROBLEMS – MULTIOBJECTIVE CHARACTER - 80% RESPONDENTS

89% OF RESPONDENTS RECOGNIZES TRADE – OFFS AND CONTRADICTORY INTERESTS

DIFFERENT GROUPS OF STAKEHOLDERS (SHAREHOLDERS & TOP MANAGEMENT 76% EMPLOYEES 54% CUSTOMERS 52%)

Slide 6

MANAGEMENT – 76%, EMPLOYEES – 54%, CUSTOMERS – 52%)


INTRODUCTION / MOTIVATIONINTRODUCTION / MOTIVATIONWHY TO USE MCDWHY TO USE MCDM/AM/A IN IN ……??


Peter F. Drucker (Management, 1974): ’’To manage a business is to balance a variety of needs and goals. And this requires multiple objectives”

Jimmy Carter (US President; mid 1970s): ’’I have been guided by four objectives for the United States economy: employment, economic growth, inflation, international h ”harmony”

Henry Ford (Beginning of 20th century): ”By introducing the „moving assembly line” Henry Ford (Beginning of 20th century): By introducing the „moving assembly line we were trying to satisfy different groups: customers (affordable car), employees (work comfort), designers (new challanges), investors (profit)…”

Herbert A. Simon (Nobel laureate in economic science, 1978): „The choice to satisfice or to accept the ’’good enough” is generally more realistic…”

Slide 7


INTRODUCTION / MOTIVATIONINTRODUCTION / MOTIVATIONMULTIPLE CRITERIAMULTIPLE CRITERIA ININ TRANSPORTATION/ TRANSPORTATION/ LOGISTICSLOGISTICS ?? Poznan University of TechnologyPoznan University of TechnologyLOGISTICSLOGISTICS ??

Portfolio selection – analysis of alternative transportation services Selecting alternative transportation services Selecting alternative transportation services Designing satisfactory portfolio

Transportation projects evaluation (network extension; highway construction) Designing and ranking the proposed solutions/ projectsg g g p p p j

Transportation job assignment and pricing Decision – accept / reject the incoming order Price definition

Facility location problem (depots; terminals; hubs; logistics centers) Selecting the most desired location; Satisfying different interests;

C Crew selection, assignment and scheduling Selecting alternative eployees for a certain position; balancing different interests

Fleet composition / selection and replacementA l i f diff t hi l l t d b diff t Analysis of different vehicles evaluated by different measures

Technical / economical diagnosis of their utility Evaluation and ranking of common carriers/ logistics service providers

Multidimensional analysis of different companies

Slide 8

Multidimensional analysis of different companies


MCDMCDM/A M/A METHODOLOGYMETHODOLOGYHISTORICAL BACKGROUNDHISTORICAL BACKGROUND


AMERICAN SCHOOL AMERICAN SCHOOL 19501950--20201010„Making optimal decisions under

EUROPEAN SCHOOL 1960EUROPEAN SCHOOL 1960--20201010„Supporting the DM in the process of „Making optimal decisions under

several criteria” solving complex, multiple objective decision problems”

1951 – T. KOOPMANS; H. KUHN + A. TUCKER - NON-DOMINATED SOLUTION

1960-s – BEGINNINGS - R.BENAYOUN, B.ROY, B. SUSSMAN (ELECTRE I)

1961 A. CHARNES; W. COOPER -GOAL PROGRAMMING

1969 – R. BENAYOUN, et al. – POP (PROGRESIVE ORIENTATION PROCEDURE) FIRST MULTIOBJECTIVE

1960 - 1970 – MULTI ATTRIBUTE UTILITY THEORY

H RAIFFA & R KEENEY

PROCEDURE)– FIRST MULTIOBJECTIVE INTERACTIVE ALGORITHM

1970 E JACQUETE LAGREZE B ROY H. RAIFFA & R. KEENEY

AHP, UTA METHODS

1970-s – E.JACQUETE-LAGREZE, B.ROY,R.BENAYOUN, P. BERTIER – EXTENSIVE DEVELOPMENT OF THE CONCEPT OF

Slide 9

THE OUTRANKING RELATION FAMILY OF ELECTRE METHODS


MCDMCDM/AM/A METHODOLOGYMETHODOLOGYCHARACTERISTICS OF MCHARACTERISTICS OF MULTIPLE CRITERIA ULTIPLE CRITERIA DDECISIONECISION PROBLEMSPROBLEMS Poznan University of TechnologyPoznan University of TechnologyDDECISIONECISION PROBLEMSPROBLEMS

MULTIPLE CRITERIA DECISION PROBLEM

MULTIPLE CRITERIA DECISION PROBLEM IS A SITUATION IN WHICH, HAVING DEFINED A SET A OF ACTIONS AND A CONSISTENT FAMILY OF CRITERIA F ONE WHISHES TO: DETERMINE A SUBSET OF ACTIONS CONSIDERED TO BE THE BEST WITH RESPECT

TO F (CHOICE PROBLEM)TO F (CHOICE PROBLEM) DIVIDE A INTO SUBSETS ACCORDING TO SOME NORMS (SORTING PROBLEM) RANK THE ACTIONS OF A FROM BEST TO WORST (RANKING PROBLEM)

MULTIPLE CRITERIA DECISION PROBLEM - ILL – DEFINED MATHEMATICAL PROBLEM –SEARCHING FOR A SOLUTION x THAT MAXIMIZES MULTIPLE OBJECTIVE FUNCTION

Subject to:

)(),...,(),(Max)( 21 xfxfxfxMaxF J=

Ax∈j

MULTIPLE CRITERIA DECISION PROBLEM IS DEFINED BY: A SET A OF ACTIONS

Ax∈

Slide 10

A CONSISTENT FAMILY OF CRITERIA F


MCDAMCDA/M/M METHODOLOGYMETHODOLOGYCHARACTERISTICS OF MCHARACTERISTICS OF MULTIPLE ULTIPLE CCRITERIA RITERIA DDECISIONECISION PROBLEMPROBLEM Poznan University of TechnologyPoznan University of TechnologyDDECISIONECISION PROBLEMPROBLEM

A SET A OF OBJECTS / SOLUTIONS

A SET A IS A COLLECTION OF OBJECTS, CANDIDADTES, VARIANTS,

A SET A OF OBJECTS / SOLUTIONS

DECISIONS, SOLUTIONS THAT ARE TO BE ANALYZED AND EVALUTED DURING THE DECISION PROCESS; A CAN BE DEFINED: DIRECTLY – BY DENOMINATING ALL ITS ELEMENTS (FINITE SET RELATIVELY DIRECTLY BY DENOMINATING ALL ITS ELEMENTS (FINITE SET, RELATIVELY

SMALL) INDIRECTLY – BY DEFINING CERTAIN FEATURES OF ITS COMPONENTS AND /

OR CONSTRAINTS (INFINITE SET FINITE SET BUT RELATIVELY LARGE)OR CONSTRAINTS (INFINITE SET, FINITE SET BUT RELATIVELY LARGE)

A SET A CAN BE: CONSTANT , A’ PRIORI DEFINED; NOT CHANGING DURING THE DECISION

PROCESS EVOLVING, BEING MODIFIED IN THE DECISION PROCESS

Slide 11

EVOLVING, BEING MODIFIED IN THE DECISION PROCESS


MCDMCDM/AM/A METHODOLOGYMETHODOLOGYCHARACTERISTICS OF MCHARACTERISTICS OF MULTIPLE ULTIPLE CCRITERIA RITERIA DDECISIONECISION PROBLEMSPROBLEMS Poznan University of TechnologyPoznan University of TechnologyDDECISION ECISION PROBLEMSPROBLEMS

A SET OF CRITERIA F

A CONSISTENT FAMILY OF CRITERIA F IS A SET OF FUNCTIONS f – DEFINED ON A AND REPRESENTING THE DM’S PREFERENCES TOWARDS A SPECIFIC ASPECT (DIMENSION) OF THE DECISION PROBLEM.

A SET OF CRITERIA F SHOULD GUARANTEE:COMPREHENSIVE AND COMPLETE EVALUATION OF VARIANTS (CONSIDERATION COMPREHENSIVE AND COMPLETE EVALUATION OF VARIANTS (CONSIDERATION OF ALL ASPECTS OF THE DECISION PROBLEM)

CONSISTENCY OF THE EVALUATION (EACH CRITERION SHOULD CORRESPOND TO THE DM’S GLOBAL PREFERENCES)TO THE DM S GLOBAL PREFERENCES)

NON-REDUNDANCY OF CRITERIA (REPETITIONS SHOULD BE ELIMINATED; MEANINGS AND SCOPES OF CRITERIA MUST BE CLEARLY DEFINED)

A SET OF CRITERIA SHOUD BE MANAGABLE: MAGIC NUMBER 7 +/- 2

Slide 12


MCDMCDM/AM/A METHODOLOGYMETHODOLOGYMCDMCDM/AM/A METHODSMETHODS


CLASSIFICATION OF MCDM/A METHODS

DIFFERENT CLASSIFICATION CRITERIA (DECISION PROCESS OBJECTIVES,MANNER OF SYNTHETIZING PREFERENCES, ACCURACY OF SOLUTIONS)

DECISION PROCESS OBJECTIVES MULTIPLE CRITERIA CHOICE (OPTIMIZATION) METHODS (INTERACTIVE

METHODS) MULTIPLE CRITERIA SORTING METHODS (ELECTRE TRI) MULTIPLE CRITERIA RANKING METHODS (ELECTRE, AHP)MULTIPLE CRITERIA RANKING METHODS (ELECTRE, AHP)

MANNER OF SYNTHETIZING (AGGREGATING) THE DM’S GLOBAL PREFERENCES MULTIOBJECTIVE METHODS BASED ON THE UTILITY FUNCTION (UTA , AHP ) MULTIOBJECTIVE METHODS BASED ON THE OUTRANKING RELATION

(ELECTRE, PROMETHEE)

Slide 13

( )


MCDMCDM/AM/A METHODOLOGYMETHODOLOGYMCDMCDM/AM/A METHODSMETHODS


METHODS BASED ON THE UTILITY FUNCTION UTILIZE THE MULTIPLE ATTRIBUTE UTILITY THEORY (R. KEENEY, H. RAIFFA; 1976) DIFFERENT POINTS OF VIEW ARE AGGREGATED INTO ONE UTILITY

FUNCTION WHICH IS MAXIMIZEDFUNCTION, WHICH IS MAXIMIZED

U = U (g1, g2, ..., gn)U U (g1, g2, ..., gn)

ALL ACTIONS ARE COMPARABLE

a P b IFF U(za) > U(zb)a I b IFF U(za) = U(zb)

Slide 14


MCDAMCDA/M/M METHODOLOGYMETHODOLOGYMCDAMCDA/M/M METHODSMETHODS


METHODS BASED ON THE OUTRANKING RELATION INTRODUCE THE CONCEPT OF THE INCOMPARABILITY BETWEEN ACTIONS

OUTRANKING REALATION IS A BINARY RELATION SDEFINED IN A SUCH THAT aSb IF GIVEN WHAT ISDEFINED IN A , SUCH THAT aSb IF, GIVEN WHAT ISKNOWN ABOUT THE DECISION – MAKER’S PREFERENCESAND GIVEN THE QUALITY OF THE EVALUATIONS OF THEACTIONS AND THE NATURE OF THE PROBLEM THEREACTIONS AND THE NATURE OF THE PROBLEM, THEREARE ENOUGH ARGUMENTS TO DECIDE THAT a IS ATLEAST AS GOOD AS b, WHILE THERE IS NO ESSENTIALREASON TO REFUTE THAT STATEMENT.

Slide 15


MCDAMCDA/M/M METHODOLOGYMETHODOLOGYMCDAMCDA/M/M METHODSMETHODS


OUTRANKING RELATION S IS A SUM OF THE INDIFFERENCE I AND PREFERENCE P RELATIONS

IPS ∪=

► SOME ACTIONS ARE INCOMPARABLE

bSaaSbIFFaIbbSaaSbIFFaPb

∧−∧

bSaaSbIFFbabSaaSbIFFaIb−∧−

∧?

Slide 16


CASE CASE STUDY STUDY II –– SINGLE CRITERION & BISINGLE CRITERION & BI--CRITERIA CRITERIA OPTIMIZATION OF THE DISTRIBUTION SYSTEMOPTIMIZATION OF THE DISTRIBUTION SYSTEM


•2 PRODUCTION PLANTS & WAREHOUSESEXISTING DISTRIBUTION SYSTEM

C1B

C2B

•DIFFERENT PRODUCT PORTFOLIOS IN PRODUCTION PLANTS (45% TRUNKING)

C

C2A

C3A

C4A

C2B C3B

C4B

CUSTOMERS SERVEDBY WAREHOUSE B

)•ORDER FULFILLMENT PROCESS IN B; FLEET IN A&B•WAREHOUSING AND MATERIAL•B

A

C1A

C5A

CUSTOMERS SERVED

WAREHOUSING AND MATERIAL HANDLING IS CARRIED OUT BY THE COMPANY ITSELF, TRANSPORTATION IS OUTSOURCEDA

C6A

C9A

C5BBY WAREHOUSE A IS OUTSOURCED

•EACH WAREHOUSE HAS A CERTAIN AREA TO COVER – “DIAGONAL LINE”400 CUSTOMERS C C

C7A C8A

•400 CUSTOMERS – C1A,...; C1B,...•DISTRIBUTION COSTS – 10 MLN ZL•DELVERY TIME – 18-24 HOURS =

Slide 17

RIDING TIME 9 – 12 HOURS (AVG. 9.5 HOURS)


CASE CASE STUDY STUDY II –– TWO MATHEMATICAL MODELSTWO MATHEMATICAL MODELSPoznan University of TechnologyPoznan University of Technology

DECISION VARIABLES1 – WAREHOUSE i IS INCLUDED IN THE PLAN{ yi = 0 – OTHERWISE{1 – REGION j IS ASSIGNED TO WAREHOUSE i

xij =0 OTHERWISE{ 0 – OTHERWISE

CONSTRAINTS

{ REGIONS ARE ASSIGNED ONLY TO WAREHOUSES INCLUDED

IN THE PLAN≤ i = 1 I j = 1 Jxij ≤ yi i = 1,.....I ; j = 1,.....J

EACH REGION IS ASSIGNED TO 1 WAREHOUSE

Slide 18j = 1,.....J1

1=

=

I

iijx



OBJECTIVES – one in model 1; two in model 2TDC – TOTAL (ANNUAL) DISTRIBUTION COSTSTDC TOTAL (ANNUAL) DISTRIBUTION COSTSMRT – MAXIMUM RIDING TIME

TDC = TTC + TPHC + TCCTTC TOTAL TRANSPORTATION COSTSTTC – TOTAL TRANSPORTATION COSTSTPHC – TOTAL PALLETS HANDLING COSTSTCC – TOTAL LOCKED-UP CAPITAL COSTS

= == ==

++

+=

I

i

J

jjjijij

I

i

J

jjiji

J

jjijii DBDATCxDBxTCBDAxTCAyTTC

1 11 11)(

= ==

+=

I

i

J

jjij

J

jjijii DBxDAxPHCyTPHC

1 11 jj

( ) ( ) = ==

+++=I

i

J

jijiji

J

jjijii DHBCRTCCBDBxDHACRTCCADAxMCCyTCC

1 11max

Slide 19

jj

DHAi, DHBi – AVG. HEADWAYS OF DELIVERIES FOR PLANTS A & B



MAXIMUM RIDING TIME

{ }ijijTTxMRT max= { }ijij

SOME TRANSFORMATION OF OBJECTIVE FUNCTIONS WAS REQUIRED TO OBTAIN A LINEAR FORMULATION OF THE PROBLEMTO OBTAIN A LINEAR FORMULATION OF THE PROBLEM

FINALY ONE OBTAINS:MIXED BINARY SINGLE CRITERION (TDC) & BI CRITERIA (TDC + MRT) MIXED BINARY SINGLE CRITERION (TDC) & BI – CRITERIA (TDC + MRT)LINEAR PROGRAMING PROBLEMS WITH IxJ+1 BINARY VARIABLES & I+1 CONTINUOUS VARIABLES

THE PROBLEM IS SOLVED BY AN EXTENDED VERSION OF MS EXCELSOLVER – PREMIUM SOLVER PLUS BY FRONTLINE SYSTEM

Slide 20


CASE CASE STUDY STUDY II –– COMPUTATIONAL EXPERIMENTSCOMPUTATIONAL EXPERIMENTSPoznan University of TechnologyPoznan University of Technology

MINIMIZATION OF THE TOTAL DISTRIBUTION COSTS - 6% IMPROVEMENT

SINGLE CRITERION OPTIMIZATION

MINIMIZATION OF THE TOTAL DISTRIBUTION COSTS - 6% IMPROVEMENT NUMBER OF WAREHOUSES – 7 NEW ASSIGNMENT OF 49 REGIONS TO 7 WAREHOUSES

COMPARISON OF TWO DISTRIBUTION SYSTEMS

C OCURRENT OPTIMAL

Slide 21


CASE STUDY ICASE STUDY I -- COMPUTATIONAL EXPERIMENTSCOMPUTATIONAL EXPERIMENTS


SINGLE CRITERION OPTIMIZATIONOPTIMIZATION

Distribution t

Number of h

Total annual distribution t [PLN]

Ridind time [h:mm]system warehouses costs [PLN]

Existing 2 9 924 300 9:22Optimal 7 9 357 784 6:09

REDUCTION OF TOTAL DISTRIBUTION COSTS BY 6% - ANNUAL SAVINGS - 0.6 MLN ZL REDUCTION OF RIDING TIME BY 34% - MORE THAN 3 HOUR REDUCTIONREDUCTION OF RIDING TIME BY 34% MORE THAN 3 HOUR REDUCTION CHANGES IN THE STRUCTURE OF THE DS.

2 WAREHOUSES REPLACED BY 7 WAREHOUSES NEW ASSIGNMENT OF 49 REGIONS TO 7 WAREHOUSES (ELIMINATION OF THE

DIAGONAL LINE)DIAGONAL LINE) FROM THE MULTIPLE OBJECTIVE POINT OF VIEW THE OPTIMAL DISTRIBUTION SYSTEM

DOMINATES THE EXISTING ONE

Slide 22


CASE STUDY ICASE STUDY I -- COMPUTATIONAL EXPERIMENTSCOMPUTATIONAL EXPERIMENTSPoznan University of TechnologyPoznan University of Technology

BI - CRITERION OPTIMIZATION

Riding time Total distribution No. of g[h:mm] costs [PLN] warehouses2:41 12 972 507 232:44 12 424 210 212 59 11 653 423 182:59 11 653 423 183:28 10 813 246 154:00 10 090 964 124:20 9 802 832 104:35 9 746 413 105:23 9 543 711 96:09 9 357 784 7

APPLICATION OF ε - CONSTRAINTS METHOD TO GENERATE A SAMPLE OF PARETO OPTIMAL SOLUTIONS; RIDINGTIME CONSTRAINED FROM 6 TO 2 HOURS; COST – TIME TRADE-OFFS

RIDING TIME REDUCTION BY 46 MIN ; +2 WAREHOUSES; DISTRIBUTION COSTS INCREASE BY 0 19 MLN ZL RIDING TIME REDUCTION BY 46 MIN. ; +2 WAREHOUSES; DISTRIBUTION COSTS INCREASE BY 0.19 MLN ZL RIDING TIME REDUCTION BY 3 MIN, ; +2 WAREHOUSES; DISTRIBUTION COSTS INCREASE BY 0.55 MLN ZL

GENERATED DISTRIBUTION SYSTEMS – 7 TO 23 WAREHOUSES EXISTING DS (2 WAREHOUSES) VS. PARETO OPTIMAL DS (10 WAREHOUSES)

SIMILAR LEVEL OF DISTRIBUTION COSTS – 10 MLN ZL

Slide 23

SIMILAR LEVEL OF DISTRIBUTION COSTS 10 MLN ZL RIDING TIME REDUCTION FROM 9:22 TO 4:20 (BY 5 HOURS) – 55% REDUCTION


CASE STUDY CASE STUDY I I –– SOLUTION PROCEDURE & SOLUTION PROCEDURE & COMPUTATIONAL EXPERIMENTSCOMPUTATIONAL EXPERIMENTS –– EXPLANATIONS / EXPLANATIONS / DEFINITIONSDEFINITIONS Poznan University of TechnologyPoznan University of TechnologyDEFINITIONSDEFINITIONS

DOMINANCE RELATION - GIVEN TWO ELEMENTS a AND b OF A, a DOMINANTES b (a D b) IFF

f1

fj(a) ≥ fj (b) ; j = 1,2,…,n WHERE AT LEAST ONE OF THE INEQUALITIES IS STRICT

1

f1max

THE IDEAL POINTPARETO OPTIMAL/ EFFICIENT SOLUTIONS

ACTION a IS EFFICIENT IFF NO ACTION OF A DOMINATES IT

A

ff1min

THE NADIR POINT

Slide 24f2

f2min f2max


CASE STUDY I CASE STUDY I –– EXPLANATIONS / DEFINITIONSEXPLANATIONS / DEFINITIONSPoznan University of TechnologyPoznan University of Technology

THE IMAGE OF A IN THE CRITERIA SPACE IS THE SET Za OF POINTS IN Rna

ONE OBTAINS WHEN EACH ACTION a IS REPRESETED BY THE POINT WHOSE COORDINATES ARE: {g1(a), …,gn(a)} {g1(a),...,gn(a)}

a c b

Za ZcZbb b

Set of actions; decision space Set of evaluations; criteria space

IN MULTIPLE OBJECTIVE DECISION PROBLEMS THE CRITERIA SPACE IS VERY IMPORTANT FOR MAKING GOOD CHOICES AND SELECTINGVERY IMPORTANT FOR MAKING GOOD CHOICES AND SELECTING APPROPRIATE – MOST RATIONAL SOLUTIONS

Slide 25


CASE STUDY ICASE STUDY I –– EXPLANATIONS / DEFINITIONSEXPLANATIONS / DEFINITIONSPoznan University of TechnologyPoznan University of Technology

PAY OFF MATRIX IS THE MATRIX G(nxn) DEFINED BYGkl = gk(âl) , k,l = 1,2,…,n

• IT IS THUS THE MATRIX CONTAINING, FOR EACH ACTION âl, ITS EVALUATIONS ACCORDING TO ALL THE CRITERIA

• IN PARTICULAR Gll = Zl*

k l SOLUTION 1 SOLUTION 2 SOLUTION 3 SOLUTION n

Gll = Zl*

CRITERION 1( Max)

G11 = 250 G12 = 150 G13 = 125 G1n = 175

CRITERION 2 G 0 60 G 0 95 G 0 80 G 0 75CRITERION 2(Max)

G21 = 0.60 G22 = 0.95 G23 = 0.80 G2n = 0.75

CRITERION 3 G31 = 67 G32 = 44 G33 = 29 G3 = 58CRITERION 3(Min)

G31 67 G32 44 G33 29 G3n 58

CRITERION n Gn1 = 0.12 Gn2 = 0.09 Gn3= 0.05 Gnn = 0.16

Slide 26

(Max)


CASE STUDY CASE STUDY I I –– COMPUTATIONAL EXPERIMENTSCOMPUTATIONAL EXPERIMENTSPoznan University of TechnologyPoznan University of Technology

COMPUTATIONAL EXPERIMENTS – PHASE II A SAMPLE OF SOLUTIONS IS EVALUATED WITH AN APPLICATION OF LIGHT

BEAM SEARCH METHOD (A. JASZKIEWICZ, R. SLOWINSKI – 1995) THE RANGES OF CRITERIA VALUES ARE AS FOLLOWS: THE RANGES OF CRITERIA VALUES ARE AS FOLLOWS:

CRITERIATDC

[MLN ZL]MRT

[H:MIN]… …

IDEAL POINT 9 36 2 41

THE LBS METHOD HELPS THE DM TO CARRY OUT A GRAPHICAL

IDEAL POINT 9.36 2:41 … …

NADIR POINT 12.97 6:09 … …

THE LBS METHOD HELPS THE DM TO CARRY OUT A GRAPHICAL & NUMERICAL ANALYSIS OF THE SOLUTIONS

Slide 27


CASE STUDY ICASE STUDY I –– COMPUTATIONAL EXPERIMENTSCOMPUTATIONAL EXPERIMENTSPoznan University of TechnologyPoznan University of Technology

SOFTWARE LBS (LIGHT BEAM SEARCH)

Slide 28



REVIEW OF THE SOLUTIONS

MRT[H:MIN]

REVIEW OF THE SOLUTIONS

2:41THE IDEAL POINT

A

6 09

REFERENCE POINT10; 4:00

6:09THE NADIR POINT

Slide 29TDC[MLN ZL]

12.97 9.36



SET OF 20 SELECTED (FILTERED) SOLUTIONS( )

(LP)(EP)

(PZP)(KRP)

Slide 30


CASE CASE STUDY STUDY II –– RESULTS & RECOMMENDATIONSRESULTS & RECOMMENDATIONSPoznan University of TechnologyPoznan University of Technology

RESULTS TDC REDUCTION → INCREASED NUMBER OF WAREHOUSES (SINGLE

CRITERION OPTIMIZATION) TDC INTERRELATED WITH MRT (BI-CRITERION OPTIMIZATION)

RECOMMENDATIONS RECOMMENDATIONS 9÷10 WAREHOUSES; 1% TO 4% REDUCTION OF TDC AND 43% TO 54%

REDUCTION OF MRT SUBSTANTIAL TIME REDUCTION SHOULD RESULT IN THE INCREASE

OF THE MARKET SHARE► OUTPUT

ORIGINAL MODEL – DESCRIPTION OF THE OPERATIONS OF THE DISTRIBUTION SYSTEMDISTRIBUTION SYSTEM

RESULTS INTERESTING FOR THE DM; TRADE-OFFS ANALYSIS UNIVERSAL APPROACH – FLEXIBILITY OF THE DECISION PROCESS

Slide 31


CASE CASE STUDYSTUDY II II –– PROBLEM DESCRIPTIONPROBLEM DESCRIPTIONPoznan University of TechnologyPoznan University of Technology

SELECTION OF LOGISTICS SERVICE PROVIDERS –MULTIOBJECTIVERANKING OF CARRIERS FOR A LARGE MANUFACTURER OFCONSUMER GOODS

INTERNATIONAL COMPANY LOCATED IN WARSAW, POLAND IS SEARCHING FOR A NEW CARRIER

COMPANY’S PROFILE COMPANY S PROFILE• ENTERED POLISH MARKET IN 1991• PRODUCTION & SALES OF COSMETICS, DETERGENTS

& AS G A C S& WASHING ARTICLES• ANNUAL TURNOVER – $ 130 MLN (400 MLN PLN)

85% – POLAND15% – EXPORT

• IN POLAND60% OF SALES WHOLESALERS60% OF SALES – WHOLESALERS20% OF SALES – SUPERMARKETS (LARGE CHAINS)15% OTHERS

Slide 32

• 15% MARKET SHARE• LOW PROFITABILITY

P U i it f T h lP U i it f T h lCASE CASE STUDYSTUDY II II –– PROBLEM DESCRIPTIONPROBLEM DESCRIPTION


THE COMPANY CONDUCTED THE ANALYSIS OF ITSTRANSPORTATION / LOGISTICS OPERATIONS AND THE MANAGEMENT TEAM CAME TO THE FOLLOWINGCONCLUSIONS

IN – COMPANY WAREHOUSING IS SUBSTANTIALLYCHEAPER THAT EXTERNAL WAREHOUSING SERVICESCHEAPER THAT EXTERNAL WAREHOUSING SERVICES

THE CONTRACT WITH THE EXISTING PROVIDER OF TRANSPORTATION SERVICES IS NOT SATISFACTORYOF TRANSPORTATION SERVICES IS NOT SATISFACTORY

THE COMPANY WANTS A NEW TRANSPORTATIONSERVICE PROVIDER AND DECIDES TO CARRY OUT ITSOWN WAREHOUSING OPERATIONS

Slide 33


CASE CASE STUDY II STUDY II –– PROBLEM DESCRIPTIONPROBLEM DESCRIPTIONPoznan University of TechnologyPoznan University of Technology

SCOPE OF TRANSPORTATION OPERATIONS ( EXISTING SITUATION)• ANNUAL MILEAGE – 5 MLN KM

(74% COVERED BY THE OPERATOR’S OWN FLEET)• FLEET – 25 TRACTORS & SEMITRAILOR UNITS (33 EURO PALLETS) +

SUBCONTRUCTED TRUCKS WITH TRAILORS• SHIPMENTS 19 000 – 26 000 PALLETS PER MONTHS

(45% – TRUNKING = SHIPMENTS BETWEEN WAREHOUSES; 55% – DIRECT DELIVERIES TO CUSTOMERS))

• AVERAGE SHIPMENT : 8 PALLETS BY TRUCKS; 22 PALETS TO CUSTOMERS, 33 PALLETS – TRUNKING

• CUSTOMERS – 400 DISPERSED ALL OVER POLAND; AVERAGE NUMBER• CUSTOMERS 400, DISPERSED ALL OVER POLAND; AVERAGE NUMBER OF CUSTOMERS SERVED ON EACH ROUTE – 2

TRANSPORTATION MARKET• VERY COMPETITIVE – 120 000 CARRIERS ( 99% VERY SMALL)• MOST OF THE TRANSPORTATION COMPANIES FOCUSED ON FREIGHT

TRANSPORTATION

Slide 34

• SIZE – 3.3 BLN ZL



CARRIERS CONSIDERED

ERD – POLISH CARRIER, FOUNDED – 1990, ANNUAL SALES – 40 MLN ZL, FIXED ASSETS – 15 MLN ZL, EMPLOYEES – 190, FLEET – 100 TRACTORS & TRAILORS (33 EURO PALLETS) + 100 TRUCKS (15-18 EURO PALLETS), AVG FLEET AGE 2 YEARS DELIVERY TIME 24 HOURS IN THE PROCESSAVG. FLEET AGE – 2 YEARS, DELIVERY TIME – 24 HOURS; IN THE PROCESSOF INTRODUCING QUALITY STANDARDS – ISO 9000

HARTKAT – INTERNATIONAL CARRIER, LONG TRADITION ON THE POLISH,MARKET- POLISH DEVISION FOUNDED – 1958, ANNUAL SALES – 91 MLN ZL,FIXED ASSETS – 10 MLN ZL, EMPLOYEES – 850, FLEET – 45 TRACTORS &TRAILORS (33 EURO PALLETS) + 10 TRUCKS (15-18 EURO PALLETS) + 10 VANS(UP TO 8 EURO PALLETS), AVG. FLEET AGE – 3 YEARS, DELIVERY TIME – 24 HOURS

TRANS-UNI - POLISH CARRIER FOUNDED – 1990 ANNUAL SALES – 28 MLN ZLTRANS-UNI - POLISH CARRIER, FOUNDED 1990, ANNUAL SALES 28 MLN ZL,FIXED ASSETS – 6.5 MLN ZL, EMPLOYEES – 180, FLEET – 84 TRACTORS &TRAILORS (33 EURO PALLETS) + 3 TRUCKS (15-18 EURO PALLETS) + 3 VANS(UP TO 8 EURO PALLETS), AVG. FLEET AGE – 4 YEARS, DELIVERY TIME

Slide 35

(UP TO 8 EURO PALLETS), AVG. FLEET AGE 4 YEARS, DELIVERY TIME – 24 HOURS



NOLIM – POLISH CARRIER, FOUNDED – 1990, ANNUAL SALES – 7.5 MLN ZL,FIXED ASSETS – 3 5 MLN ZL EMPLOYEES – 65 FLEET – 10 TRACTORS

CARRIERS CONSIDERED

FIXED ASSETS 3.5 MLN ZL, EMPLOYEES 65, FLEET 10 TRACTORS & TRAILORS (33 EURO PALLETS) + 8 TRUCKS (15-18 EURO PALLETS) + 10 VANS( UP TO 8 EURO PALLETS), AVG. FLEET AGE – 8 YEARS,DELIVERY TIME – 48 HOURS; QUALITY CERTIFICATE – ISO 9000; Q

POLBI – POLISH CARRIER, FOUNDED – 1991, ANNUAL SALES – 25 MLN ZL,FIXED ASSETS – 7.5 MLN ZL, EMPLOYEES – 53, FLEET – 5 TRACTORS & TRAILORS (33 EURO PALLETS) + 1 VAN( UP TO 8 EURO PALLETS)& TRAILORS (33 EURO PALLETS) + 1 VAN( UP TO 8 EURO PALLETS), AVG. FLEET AGE – 7 YEARS, DELIVERY TIME – 72 HOURS

SPOL – POLISH CARRIER, FOUNDED – 1991, ANNUAL SALES – 182 MLN ZL,FIXED ASSETS – 41 MLN ZL, EMPLOYEES – 990, FLEET – ALL VEHICLESARE SUBCONTRUCTED, AVG. FLEET AGE – 5 YEARS, DELIVERY TIME – 24 HOURS; QUALITY CERTIFICATE – ISO 9000

RIDPOL (EXISTING CARRIER) – INTERNATIONAL CARRIER, POLISH DIVISION FOUNDED – 1997, ANNUAL SALES – 22 MLN ZL, FIXED ASSETS – 1.3 MLN ZL, EMPLOYEES – 65, FLEET – 24 TRACTORS & TRAILORS

Slide 36

, ,(33 EURO PALLETS), AVG. FLEET AGE – 2 YEARS, DELIVERY TIME – 24 HOURS



POTRANS – INTERNATIONAL CARRIER, POLISH DIVISION FOUNDED – 1995,

CARRIERS CONSIDERED

ANNUAL SALES – 25 MLN ZL, FIXED ASSETS – 33 MLN ZL, EMPLOYEES – 130, FLEET – 300 TRACTORS & TRAILORS (33 EURO PALLETS) + 83 TRUCKS (15-18 EURO PALLETS) 28 VANS ( UP TO 8 EURO PALLETS),AVG. FLEET AGE – 5 YEARS, ALL VEHICLES SUBCONTRUCTED – LONGTERM CONTRACTS, USUALLY 30% OF FLEET USED FOR THE POLISHMARKET, DELIVERY TIME – 24 HOURS; QUALITY CERTIFICATE – ISO 9000

Slide 37



• BASED ON EXPERT OPINIONS AND ANALYSES ADDITIONAL

ADDITIONAL INFORMATION

EVALUATIONS OF THE CARRIERS HAS BEEN CARRIED OUT

• EXPERTS ESTIMATED TOTAL ANNUAL COSTS OF TRANSPORTATIONBASED ON THE DELIVERY SCHEME PROPOSED BY EACH CARRIERAND DIFFERENT UNIT COSTS PER TKM AND VKM IN EACH VEHICLECATEGORY, PROPOSED BY CONCRETE CARRIERS

• TWO ADDITIONAL MEASURES OF MERIT WERE INTRODUCED BY EXPERTS, INCLUDING:

— SERVICE COMPLEXITY & FLEXIBILITY ( PACKAGING,TRANSHIPMENTS, TEMPORARY WAREHOUSING, INSURANCE,ON-LINE COMPUTER COMMUNICATION WITH CUSTOMER GPS)ON-LINE COMPUTER COMMUNICATION WITH CUSTOMER, GPS)

— QUALITY OF HUMAN RESOURCES (EDUCATION, EXPERIENCE,TRAINING)

Slide 38

)



CARRIER TOTAL SERVICE QUALITY

ADDITIONAL INFORMATION

CARRIER TOTAL SERVICE QUALITYTRANSPORT. COMPLEXITY OF HUMANCOSTS & FLEXIBILITY RESOURCES[MLN ZL] [POINTS] [POINTS][MLN ZL] [POINTS] [POINTS]

ERD 8,75 7.0 5.0

HARTKAT 16 40 3 0 5 0HARTKAT 16,40 3.0 5.0

TRANS-UNI 14,00 6.0 2.0

NOLIM 10,80 8.0 7.0

POLBI 12,40 2.5 7.5

SPOL 12,20 9.5 4.0

RIDPOL 22,10 4.0 8.0

Slide 39POTRANS 7,90 9.0 5.0


CASE CASE STUDY II STUDY II –– SOLUTION PROCEDURESOLUTION PROCEDUREPoznan University of TechnologyPoznan University of Technology

VARIANTS

CRITERIA UNIT ERD TRANS UNI POLBI RIDPOL

EVALUATION MATRIX EVALUATION MATRIX

CRITERIA UNIT ERD TRANS-UNI POLBI RIDPOLHARTKAT NOLIM SPOL POTRANS

1 MARKET EXPERIENCE YEARS 14 46 14 14 13 13 7 9EXPERIENCE YEARS 14 46 14 14 13 13 7 9

2 FIXED ASSETSTURNOVER — 2,67 9,10 4,31 2,14 3,33 4,44 16,92 0,76

3 TRANSPORTATION TRANSPORTATION COSTS COSTS MLN ZL MLN ZL 8,75 8,75 16,40 14,00 10,80 12,40 12,20 22,10 7,9016,40 14,00 10,80 12,40 12,20 22,10 7,90

4 DELIVERY TIME HOURS 24 24 24 48 72 24 24 24

5 SALES/EMPLOYEE ZL 210 107 156 115 472 184 338 192

6 MARKET SHARE [%] 1,21 2,76 0,85 0,23 0,76 5,52 0,67 0,76

7 FLEET QUALITY& SUITABILITY POINT 6,5 7,5 7,0 6,5 5,5 9,0 5,0 9,5

8 SERVICE COMPLEXITY & FLEXIBILITY POINT 7,0 3,0 6,0 8,0 2,5 9,5 4,0 9,0

Slide 40

9 QUALITY OF HUMAN RESOURCES POINT 5.0 5.0 2.0 7.0 7.5 4.0 8.0 5.0


CASE CASE STUDY II STUDY II –– SOLUTION PROCEDURESOLUTION PROCEDUREPoznan University of TechnologyPoznan University of TechnologyEVALUATION MATRIX – DATA ENTERED

INTO THE ELECTRE III/IV PROGRAM

Slide 41



ELECTRE METHODELECTRE METHOD

ELECTRE III METHOD IS A MULTIOBJECTIVE DECISION AID METHOD DESIGNATED TO RANK A FINITE SET OF OBJECTS / VARIANTS, EVALUATED BY A SET OF CRITERIA

ELECTRE III – 3RD METHOD IN THE ROW OF THE ELECTRE FAMILY (B.ROY – 1980-S), BASED ON THE OUTRANKING RELATION USED AS A GENERAL MODEL OF PREFERENCESA GENERAL MODEL OF PREFERENCES

COMPUTATIONAL ALGORITHM IS COMPOSED OF THREE PHASES:

• PHASE I – CONSTRUCTION OF THE EVALUATION MATRIX ANDTHE DEFINITION OF THE DECISION MAKER’S PREFERENCES

• PHASE II CONSTRUCTION OF THE VALUED OUTRANKING• PHASE II – CONSTRUCTION OF THE VALUED OUTRANKINGRELATION

• PHASE III – EXPLOITATION OF THE VALUED OUTRANKING

Slide 42

PHASE III EXPLOITATION OF THE VALUED OUTRANKINGRELATION


CASE STUDY II CASE STUDY II -- ELECTRE METHODELECTRE METHODPoznan University of TechnologyPoznan University of Technology

Set of variants A Family of Criteria F

Phase I: Construction of the Evaluation Matrix & Definition of DM’s Preferences

Composed of criteria gj

For each variant definition of the criteria values gj and the threshold values qj & pj

Definition of veto thresholdsDefinition of veto thresholds vj for each criterion

Definition of weights wjfor each criterion

Phase II: Construction of the valued outranking relation

Calculating concordance coeffients cj (a,b)

Calculating the discordance indexes D (a b)

Calculating the concordance index C (a b) discordance indexes Dj (a, b) index C (a,b)

Calculating the valued outranking relation S(a, b)

Generation of two complete preorders:- ascending

- descending

Phase III: Exploitation of the valued outranking relation

Slide 43

Generation of the final ranking of the variants that is an intersection of two preorders

P U i it f T h lP U i it f T h lCASE STUDY IICASE STUDY II ELECTRE METHODELECTRE METHOD Poznan University of TechnologyPoznan University of Technology

OUTRANKING RELATIONOUTRANKING RELATION

CASE STUDY II CASE STUDY II -- ELECTRE METHODELECTRE METHOD

• OUTRANKING RELATION AS A GLOBAL MODEL OF PREFERENCES

MODEL OF PREFERENCESMODEL OF PREFERENCES

• FOUR – STATE DM’S PREFERENCE MODEL ( Roy, 1985; Vincke, 1990)

I INDIFFERENCE Q WEAK PREFERENCE P STRONG PREFERENCE— I – INDIFFERENCE, Q – WEAK PREFERENCE, P – STRONG PREFERENCE, J/ R – INCOMPARABILITY

— THREE THRESHOLDS: q – INDIFFERENCE, p – PREFERENCE , v – VETO

• WEIGHTS OF CRITERIA – MEASURE THE IMPORTANCE OF EACHCRITERION FOR THE DM

— USUALLY FROM 1 TO 10 POINTS; 1 POINT – NO IMPORTANT CRITERION,

Slide 44

10 POINTS – VERY IMPORTANT CRITERION



ELECTRE METHOD ELECTRE METHOD ––APPLIED METHODOLOGYAPPLIED METHODOLOGY

FOUR – STATE DM’S PREFERENCE MODEL

APPLIED METHODOLOGYAPPLIED METHODOLOGY

cj(a, b)b I a b Q a b P a b J aD(a b)

1QDj(a, b)

cj(a, b) Dj(a, b)

( ) ( )+ ( ( )) g(a)+p(g(a))0

g(a)+ν(g(a))

j( , ) j( , )

gj(a) gj(a)+qj(gj(a)) gj(a)+pj(gj(a)) gj(b)gj(a)+νj(gj(a))

Slide 45

P U i it f T h lP U i it f T h lELECTRE METHODELECTRE METHOD ––

CASE CASE STUDY II STUDY II –– SOLUTION PROCEDURESOLUTION PROCEDURE


BUILDING THE VALUED OUTRANKING RELATION


• CONCORDANCE COEFFICIENTS – IN WHAT DEGREE a IS AS GOOD AS b

≥+ (b),g))(( )( if 1 jagqag jjj

• CONCORDANCE INDEX – CONSTITUTES CONCORDANCE MATRIX

≤+=

1 and 0between function linear (b),g))(()( if 0),( jagpagbac jjjj

, where , for j = 1, 2,..., n

DISCORDANCE INDEX IN WHAT DEGREE IT IS NOT TRUE THAT

=

=n

jjj bacw

WbaC

1),(1),(

=

=n

jjwW

1

• DISCORDANCE INDEX – IN WHAT DEGREE IT IS NOT TRUE THAT a IS AS GOOD AS b

+≥+≤

= )),(()()(if1)),(()()( if 0

),( agagbgagpagbg

baD jjjj

jjjj

j ν

WHERE vj IS A VETO THRESHOLD, SUCH THAT ANY CREDIBILITY

+≥ figure see o,between twlinear )),(()()( if 1),( agagbgbaD jjjjj ν

Slide 46

jFOR THE OUTRANKING OF b BY a IS REFUSED IF

gj(b) ≥ gj(a)+νj(gj(a)),



Poznan University of TechnologyPoznan University of Technology• OUTRANKING RELATION

−

∀≤)(1

, ),,(),( if ),()(

jj

baDjbacbaDbaC

baS

−

⋅= ∏∈ ),(

),(1),(1

),(),(baJj j

j

bacbaD

baCbaS

where: J(a,b) is a set of criteria for which Dj (a,b) > cj (a,b)

EXPLOITATION OF THE OUTRANKING RELATION• QUALIFICATION ALGORITHM THAT LEADS TO TWO PREORDERS BASED• QUALIFICATION ALGORITHM THAT LEADS TO TWO PREORDERS BASED

ON THE OUTRANKING DEGREES S (a,b)• DEFINITION OF )b,a(Smax

Ab,a ∈

=λ

• ONLY THOSE VARIANTS ARE ANALYZED THAT ARE CLOSE ENOUGH TO λ – CUTTING LEVEL S(λ); DIFFERENCE λ – S(λ)

• CALCULATION OF QUALIFICATION COEFFICIENT Q(a) – DIFFERENCE

,

CALCULATION OF QUALIFICATION COEFFICIENT Q(a) DIFFERENCEBETWEEN THE NUMBER OF VARIANTS THAT a OUTRANKS AND THENUMBER OF VARIANTS BY WHICH a IS OUTRANKED

• DESCENDING & ASCENDING PREORDERS – DISTILLATIONS

Slide 47

DESCENDING & ASCENDING PREORDERS DISTILLATIONS— DESCCENDING – SELECTION FROM THE BEST TO THE WORST (HIGHEST Q(a) )— ASCENDING – SELECTION FROM THE WORST TO THE BEST (LOWEST Q(a) )


ELECTRE METHOD ELECTRE METHOD ––APPLIED METHODOLOGYAPPLIED METHODOLOGY Poznan University of TechnologyPoznan University of Technology

FINAL RANKING IS THE INTERSECTION OF THE PREOEDERS 3 SITUATIONS MAY OCCUR I P J/R

APPLIED METHODOLOGYAPPLIED METHODOLOGY

– 3 SITUATIONS MAY OCCUR – I , P, J/R

QUALIFICATIONS RULES:

• aSb IF IN ONE PREORDER a IS AHEAD OF b AND IN THE SECONDPREORDER a IS AS GOOD AS b

• aIb IF BOTH VARIANTS BELONG TO THE SAME CLASS IN EACHPREORDER

Jb OR Rb IF IS AHEAD OF b IN ONE PREORDER AND BEHIND• aJb OR aRb IF a IS AHEAD OF b IN ONE PREORDER AND BEHINDb IN THE SECOND ONE

FINAL RANKING HAS A GRAPHICAL CHARACTER

Slide 48


CASE CASE STUDY II STUDY II –– SOLUTION PROCEDURESOLUTION PROCEDURETHE DM’S MODEL OF PREFERENCES Poznan University of TechnologyPoznan University of Technology

NO. CRITERIA UNIT PREFERENCESq p v w kp

THE DM’S MODEL OF PREFERENCES

qj pj vj wj kpj

1 MARKET EXPERIENCE YEARS 2 5 30 4,0 MAX2 FIXED ASSETS

TURNOVER — 1,5 4 15 1,5 MAX3 TRANSPORTATION

COSTS MLN ZL 0,15 0,50 5,0 10 MINCOSTS MLN ZL 0,15 0,50 5,0 10 MIN4 DELIVERY TIME HOURS 0 12 48 7,5 MIN 5 SALES/EMPLOYEE THOUS. ZL 12 50 150 3,5 MAX6 MARKET SHARE [%] 0,1 0,5 2,5 8,0 MAX7 FLEET QUALITY

& SUITABILITY POINT 0,5 2,0 5,0 9,0 MAX& SUITABILITY POINT 0,5 2,0 5,0 9,0 MAX8 SERVICE COMPLEXITY

& FLEXIBILITY POINT 0,5 2,0 5,0 6,0 MAX9 QUALITY OF HUMAN

Slide 49

9 QUALITY OF HUMAN RESOURCES POINT 0,5 2,0 5,0 5,0 MAX



RESULTSRESULTS

ASCENDING PREORDERDESCENDING PREORDER

Slide 50



RESULTSRESULTS –– OUTRANKING MATRIXOUTRANKING MATRIX

Slide 51


CASE CASE STUDY II STUDY II –– SOLUTION PROCEDURESOLUTION PROCEDURE


RESULTSRESULTS –– FINAL RANKINGFINAL RANKING

Slide 52


CASE CASE STUDY II STUDY II –– FINAL RECOMMENDATIONSFINAL RECOMMENDATIONSPoznan University of TechnologyPoznan University of Technology

IN THE ANALYZED CASE THE RANKING WINNERS ARE:SPOL & ERDSPOL & ERD

THE WINNERS ARE CHARACTERIZED BY THE FOLLOWINGCHARACTERISTICS

SPOL – VERY HIGH LEVEL OF SERVICE, MARKET SHARE& FLEET QUALITY

ERD – LOW TRANSPORTATION COSTS & SHORT ERD LOW TRANSPORTATION COSTS & SHORTDELIVERY TIME

IN MANY CASES INDIFFERENCE AND INCOMPARABILITY OF VARIANTS IS OBSERVED IN THE FINAL RANKING EG :OF VARIANTS IS OBSERVED IN THE FINAL RANKING, EG.:

INDIFFERENCE OF POLBI & RIDPOL (TWO VARIANTS IN THE SAME BOX)

INCOMPARABILITY OF ERD & HARTKAT (TWO VARIANTSWITH NO CONNECTION BETWEEN EACH OTHER)

SPOL IS RECOMMENDED (SEE THE OUTRANKING MATRIX)

Slide 53

SPOL IS RECOMMENDED (SEE THE OUTRANKING MATRIX)


FINAL FINAL CONCLUSIONSCONCLUSIONSPoznan University of TechnologyPoznan University of Technology

MCDM/A METHODOLOGY CAN BE UTILIZED IN REAL LIFE SITUATIONS TO SOLVE COMPLEX TRANSPORTATION/ LOGISTICS PROBLEMS

• IT HELPS THE DM TO FIND A COMPROMISE SOLUTION• IT ASSURES THAT INTERSTS OF DIFFERENT STAKEHOLDERS CAN BE CONSIDERED• IT GUARANTEES THAT DIFFERENT MODELS OF PREFERENCES MAY BE TAKEN INTO• IT GUARANTEES THAT DIFFERENT MODELS OF PREFERENCES MAY BE TAKEN INTO

ACCOUNT MCDM/A METHODOLOGY GUARANTEES A CLEAR DISINCTION OF THE MAJOR

PLAYERS OF THE DECISION MAKING PROCESSPLAYERS OF THE DECISION MAKING PROCESS DECISION MAKER (MANAGERS, PUBLIC AUTHORITIES, CUSTOMERS) STAKEHOLDERS ANALYST (EXPERT/CONSULTANT - AUTHOR) ANALYST (EXPERT/CONSULTANT - AUTHOR)

→ CONSTRUCTION OF THE DECISION MODELS (MATHEMATICALPROGRAMING PROBLEMS IN CASES I & II AND RANKING PROBLEM IN CASE III)

→ SELECTION OF THE DECISION TOOLS (SOLVER PREMIUM PLUS IN CASE(I, PROGRAM PEOPLE + LBS IN CASE II, AHP & ELECTRE METHODS IN CASE III)

IN ALL CASE STUDIES APPLICATION OF MCDM/A METHODOLOGY GENERATED IMPROVEMENTS AGAINST THE EXISTING SITUATION

Slide 54



BASED ON THE B. ROY’S SUGGESTIONS (B. ROY – 1985) THE SOLUTION PROCEDURE HAS BEEN DIVIDED INTO THE FOLLOWING STEPS:PROCEDURE HAS BEEN DIVIDED INTO THE FOLLOWING STEPS: VERBAL DESCRIPTION OF THE DECISION PROBLEM; RECOGNITION OF THE CATEGORY

OF THE DECISION PROBLEM ( CHOICE PROBLEM – CASE I AND RANKING PROBLEM IN CASE II);CASE II);

MATHEMATICAL FORMULATION OF THE DECISION PROBLEM– DEFINITION OF THE SET OF VARIANTS (INDIRECT, THROUGH CONSTRAINTS; DEFINITION OF

THE SET OF FEASIBLE SOLUTIONS IN CASES I ; COMPLETE LIST OF VARIANTS IN CASE II)– CONSTRUCTION OF THE CONSISTENT FAMILY OF CRITERIA (4 CRITERIA IN CASE I; 9 CRITERIA

IN CASE II) MODELLING AND AGGREGATION OF THE DM’S PREFERENCES (WEIGHTS AND

THRESHOLDS PAIRWISE COMPARISONS ASPIRATIONS TRADE OFFS ANALYSIS )THRESHOLDS, PAIRWISE COMPARISONS, ASPIRATIONS, TRADE-OFFS ANALYSIS ) SOLVING THE DECISION PROBLEM – COMPUTATIONAL EXPERIMENTS (OPTIMAL

ASSIGNMENT OF DUTIES TO EMPLOYEES IN CASE I AND EVALUATION OF URBAN TRANSPORTATION SYSTEMS IN CASE II)TRANSPORTATION SYSTEMS IN CASE II)

VERIFICATION OF RESULTS – SENSITIVITY ANALYSIS; „WHAT …IF SCENARIOS” PRACTICAL IMPLEMENATION

Slide 55



OTHER APPLICATIONS OF MCDM/A IN TRANSPORTATION/LOGISTICS FLEET SELECTION PROBLEM (OPEN BIDS FOR TRAMS & BUSES) – EURO 2006 FACILITY LOCATION PROBLEMS (IFORS 2011 – LOGISTICS CENTERS; FAN

ZONES – UEFA 2012 SOCCER COMPETITIONS)ZONES UEFA 2012 SOCCER COMPETITIONS) PORTFOLIO OPTIMIZATION PROBLEMS (PRODUCTS, SERVICES)-

TRANSPORTATION RESEARCH 2006TECHNICAL DIAGNOSTICS & SORTING VEHICLES INTO PREDEFINED CLASSES TECHNICAL DIAGNOSTICS & SORTING VEHICLES INTO PREDEFINED CLASSES (EJOR 2010)

CREW ASSIGNMENT & SCHEDULING (JAT 2008) VEHICLE ASSIGNMENT, ROUTING & SCHEDULING FLEET REPLACEMENT STRATEGIES (TRANSPORTATION RESEARCH 2009) FLEET COMPOSITION PROBLEM (JAT 2010; EWGT 2011)( ; ) PROJECT EVALUATION; DESIGN OF TRANSPORTATION / LOGISTICS

SOLUTIONS (WCTRS 2007, 2011)

Slide 56

Documents

MULTIPLE CRITERIA DECISION MAKINGMAKING/ AIDING/ AIDING …sydney.edu.au/business/__data/assets/pdf_file/0004/105745/jacekz... · multiple criteria decision makingmaking/ aiding