multiple criteria decision makingmaking/ aiding/ aiding...
TRANSCRIPT
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
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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
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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
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INTRODUCTION INTRODUCTION / MOTIVATION/ MOTIVATIONDECISION DECISION MAKINGMAKING/ AIDING/ AIDING PROCESS BASED ON MCDM/APROCESS BASED ON MCDM/A
Poznan University of TechnologyPoznan University of Technology
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
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COMPROMISESOLUTIONS
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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
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COMPROMISE SOLUTIONSCOMPROMISE SOLUTIONSCOMPROMISE SOLUTIONSCOMPROMISE SOLUTIONS
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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%)
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MANAGEMENT – 76%, EMPLOYEES – 54%, CUSTOMERS – 52%)
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INTRODUCTION / MOTIVATIONINTRODUCTION / MOTIVATIONWHY TO USE MCDWHY TO USE MCDM/AM/A IN IN ……??
Poznan University of TechnologyPoznan University of Technology
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…”
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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
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Multidimensional analysis of different companies
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MCDMCDM/A M/A METHODOLOGYMETHODOLOGYHISTORICAL BACKGROUNDHISTORICAL BACKGROUND
Poznan University of TechnologyPoznan University of Technology
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
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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∈
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A CONSISTENT FAMILY OF CRITERIA F
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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
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EVOLVING, BEING MODIFIED IN THE DECISION PROCESS
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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
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MCDMCDM/AM/A METHODOLOGYMETHODOLOGYMCDMCDM/AM/A METHODSMETHODS
Poznan University of TechnologyPoznan University of Technology
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
( )
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MCDMCDM/AM/A METHODOLOGYMETHODOLOGYMCDMCDM/AM/A METHODSMETHODS
Poznan University of TechnologyPoznan University of Technology
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)
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MCDAMCDA/M/M METHODOLOGYMETHODOLOGYMCDAMCDA/M/M METHODSMETHODS
Poznan University of TechnologyPoznan University of Technology
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.
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MCDAMCDA/M/M METHODOLOGYMETHODOLOGYMCDAMCDA/M/M METHODSMETHODS
Poznan University of TechnologyPoznan University of Technology
OUTRANKING RELATION S IS A SUM OF THE INDIFFERENCE I AND PREFERENCE P RELATIONS
IPS ∪=
► SOME ACTIONS ARE INCOMPARABLE
bSaaSbIFFaIbbSaaSbIFFaPb
∧−∧
bSaaSbIFFbabSaaSbIFFaIb−∧−
∧?
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CASE CASE STUDY STUDY II –– SINGLE CRITERION & BISINGLE CRITERION & BI--CRITERIA CRITERIA OPTIMIZATION OF THE DISTRIBUTION SYSTEMOPTIMIZATION OF THE DISTRIBUTION SYSTEM
Poznan University of TechnologyPoznan University of Technology
•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 =
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RIDING TIME 9 – 12 HOURS (AVG. 9.5 HOURS)
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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
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CASE CASE STUDY STUDY II –– TWO MATHEMATICAL MODELSTWO MATHEMATICAL MODELSPoznan University of TechnologyPoznan University of Technology
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
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CASE CASE STUDY STUDY II –– TWO MATHEMATICAL MODELSTWO MATHEMATICAL MODELSPoznan University of TechnologyPoznan University of Technology
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
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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
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CASE STUDY ICASE STUDY I -- COMPUTATIONAL EXPERIMENTSCOMPUTATIONAL EXPERIMENTS
Poznan University of TechnologyPoznan University of Technology
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
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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
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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
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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
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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
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(Max)
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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
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CASE STUDY ICASE STUDY I –– COMPUTATIONAL EXPERIMENTSCOMPUTATIONAL EXPERIMENTSPoznan University of TechnologyPoznan University of Technology
SOFTWARE LBS (LIGHT BEAM SEARCH)
Slide 28
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CASE STUDY CASE STUDY I I –– COMPUTATIONAL EXPERIMENTSCOMPUTATIONAL EXPERIMENTSPoznan University of TechnologyPoznan University of Technology
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
P U i it f T h lP U i it f T h l
CASE STUDY CASE STUDY I I –– COMPUTATIONAL EXPERIMENTSCOMPUTATIONAL EXPERIMENTSPoznan University of TechnologyPoznan University of Technology
SET OF 20 SELECTED (FILTERED) SOLUTIONS( )
(LP)(EP)
(PZP)(KRP)
Slide 30
P U i it f T h lP U i it f T h l
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
P U i it f T h lP U i it f T h l
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
Poznan University of TechnologyPoznan University of Technology
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
P U i it f T h lP U i it f T h l
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
P U i it f T h lP U i it f T h l
CASE CASE STUDY II STUDY II –– PROBLEM DESCRIPTIONPROBLEM DESCRIPTIONPoznan University of TechnologyPoznan University of Technology
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
P U i it f T h lP U i it f T h l
CASE CASE STUDY II STUDY II –– PROBLEM DESCRIPTIONPROBLEM DESCRIPTIONPoznan University of TechnologyPoznan University of Technology
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
P U i it f T h lP U i it f T h l
CASE CASE STUDY II STUDY II –– PROBLEM DESCRIPTIONPROBLEM DESCRIPTIONPoznan University of TechnologyPoznan University of Technology
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
P U i it f T h lP U i it f T h l
CASE CASE STUDY II STUDY II –– PROBLEM DESCRIPTIONPROBLEM DESCRIPTIONPoznan University of TechnologyPoznan University of Technology
• 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
)
P U i it f T h lP U i it f T h l
CASE CASE STUDY II STUDY II –– PROBLEM DESCRIPTIONPROBLEM DESCRIPTIONPoznan University of TechnologyPoznan University of Technology
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
P U i it f T h lP U i it f T h l
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
P U i it f T h lP U i it f T h l
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
P U i it f T h lP U i it f T h l
CASE CASE STUDY II STUDY II –– SOLUTION PROCEDURESOLUTION PROCEDUREPoznan University of TechnologyPoznan University of Technology
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
P U i it f T h lP U i it f T h l
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
P U i it f T h lP U i it f T h l
CASE CASE STUDY II STUDY II –– SOLUTION PROCEDURESOLUTION PROCEDUREPoznan University of TechnologyPoznan University of Technology
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
Poznan University of TechnologyPoznan University of Technology
BUILDING THE VALUED OUTRANKING RELATION
ELECTRE METHOD ELECTRE METHOD ––APPLIED METHODOLOGYAPPLIED METHODOLOGY
• 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)),
P U i it f T h lP U i it f T h l
ELECTRE METHOD ELECTRE METHOD ––APPLIED METHODOLOGYAPPLIED METHODOLOGY
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) )
P U i it f T h lP U i it f T h l
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
P U i it f T h lP U i it f T h l
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
P U i it f T h lP U i it f T h l
CASE CASE STUDY II STUDY II –– SOLUTION PROCEDURESOLUTION PROCEDUREPoznan University of TechnologyPoznan University of Technology
RESULTSRESULTS
ASCENDING PREORDERDESCENDING PREORDER
Slide 50
P U i it f T h lP U i it f T h l
CASE CASE STUDY II STUDY II –– SOLUTION PROCEDURESOLUTION PROCEDUREPoznan University of TechnologyPoznan University of Technology
RESULTSRESULTS –– OUTRANKING MATRIXOUTRANKING MATRIX
Slide 51
P U i it f T h lP U i it f T h l
CASE CASE STUDY II STUDY II –– SOLUTION PROCEDURESOLUTION PROCEDURE
Poznan University of TechnologyPoznan University of Technology
RESULTSRESULTS –– FINAL RANKINGFINAL RANKING
Slide 52
P U i it f T h lP U i it f T h l
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)
P U i it f T h lP U i it f T h l
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
P U i it f T h lP U i it f T h l
FINAL FINAL CONCLUSIONSCONCLUSIONSPoznan University of TechnologyPoznan University of Technology
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
P U i it f T h lP U i it f T h l
FINAL FINAL CONCLUSIONSCONCLUSIONSPoznan University of TechnologyPoznan University of Technology
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