MULTI CRITERIA DECISION MAKING - APPLICATIONS IN PROJECT MANAGEMENT AN INTRODUCTION TO THE ANALYTIC HIERARCHY PROCESS-AHP Vassilis C. Gerogiannis, PhD Assistant Professor, Department of Project Management Technological Education Institute of Larissa gerogian@teilar.gr

DO YOUR DECISION CONFERENCES TURN OUT LIKE THIS ? TOO BAD! WE WANT PROJECT B !! WE WANT PROJECT A !! COME ON IN THE WATER IS FINE! SEA OF INDECISION OR DOES THIS HAPPEN?

DO YOUR RECOMMENDATIONS TURN OUT LIKE THIS? BUT BOSS... THAT WAS MY BEST GUESS! GUESS AGAIN MAYBE YOU NEED A NEW APPROACH

Decision Making To make an effective decision making, one has to consider Details about problem for which the decision is required The people or stakeholders involved Their objectives and policies The influences affecting outcomes The time horizons, scenarios, and constraints

Analytic Hierarchy Process - AHP Introduced by Thomas Saaty in late 70’s. AHP, McGraw-Hill, 1980. A Multi Criteria Decision Making (MCDM) Technique. It structures any complex, multi-criterion, multi-person problem hierarchically. Identifies the strength with which one alternative dominates another with respect to a given criteria.

Advantages of AHP Multi-criterion, Multi-person. Can handle qualitative input. Decision making in presence of environmental, social and other influences. Can handle subjective judgements of individuals.

I THINK I ‘LL TRY THE ANALYTIC HIERARCHY PROCESS (AHP) !!!

AHP - Steps Define the problem and specify the objective. Structure the hierarchy from overall managerial perspective. Construct a pairwise comparison matrix of the relative contribution on each criteria. Obtain overall ranking of each decision alternative. Evaluation of consistency.

AHP - Inputs Relative importance of criteria. Preference on each criterion for each decision alternative. Construction of pairwise comparison matrix using the above two inputs.

AHP Output Prioritised ranking indicating the overall preference for each decision alternative.

AHP - Measurement Methodology Objective of measurement methodology is to establish priorities among alternatives within each stratum of hierarchy. This is accomplished through by asking participating stakeholders (e.g., managers) to evaluate each set of elements in a pairwise. This data constitutes the core element of AHP.

Pairwise Comparison Matrix A pairwise comparison matrix is constructed for each criteria based on the data collected. Pairwise comparison matrix for a criteria with 4 decision alternatives is given by:

9-Point Scale for Construction of Pairwise Comparison Matrix Intensity of Importance Definition 1 Equal importance 3 Weak importance of one over other 5 Strong Importance 7 Demonstrated Importance 9 Absolute Importance 2,4,6,8 Intermediate Values Reciprocals of the above If activity i has one of the above numbers assigned to it when compared with activity j, then j has the reciprocal value when compared with i. 1.1 – 1.9 When elements are close and nearly indistinguishable

Calculating Priorities Sum the values in each column of the pairwise comparison matrix. Divide each element in the pairwise comparison matrix by its column sum; the resulting matrix is called normalized pairwise comparison matrix. Compute the average of the elements in each row of the normalized matrix. This averages provide relative importance of each alternative.

Calculating Priorities Divide entry by column sum 1.83 3.5 6 Column Sum Relative Priority

OKAY, HERE’S AN EXAMPLE OF A DECISION PROBLEM THIS AHP STUFF SOUNDS INTERESTING. HOW ABOUT AN EXAMPLE OF HOW IT WORKS IN PRACTICE. OKAY, HERE’S AN EXAMPLE OF A DECISION PROBLEM

I SEE A NEW CAR IN YOUR FUTURE

Car Selection Problem XYZ corporation is planning to buy a new car for its transport section. The following four criteria has been identified for the selection of the car: Price Mileage per litre (MPL) Comfort Style Use AHP to select the best of three cars named A, B and C from the market.

The Problem “Hierarchy”

Pairwise Comparison Matrix for Comfort

Priorities of cars with respect to Comfort Pairwise Comparison Matrix Normalized Matrix Relative Priority

Pairwise Comparison for Other Criteria

Priority Vectors for Price, MPG and Style

Pairwise Comparison Matrix for the Criteria

Priorities for Four Criteria Price 0.398  MPG 0.085 Comfort 0.218 Style 0.299

Using AHP to Develop an Overall Priority Ranking The procedure used to compute the overall priorities for each decision alternative by using the priority for each criterion as a weight that reflects its importance. The overall priority for each decision alternative is obtained by summing the products of the criterion priority times the priority of its decision alternative. For example overall car A priority = .398 (.123) + .085 (.087) + 0.218 (.593) + .299 (.265)

Overall Priority Matrix for Car Alternative Priority Car A 0.265 Car B 0.421 Car C 0.314

Estimating the Consistency Step – 1. Multiply each value in the first column of the pairwise comparison matrix by corresponding relative priority matrix. Step – 2. Repeat Step – 1 for remaining columns. Step – 3. Add the vectors resulted from step-1 and 2. Step – 4. Divide each elements of the vector of weighed sums obtained in step 1-3 by the corresponding priority value. Step – 5. Compute the average of the values found in step –4. Let  be the average. Step – 6. Compute the consistency index (CI), which is defined as ( - n) / (n-1).

Estimating Consistency Compute the random index, RI, using ratio: RI = 1.98 (n-2)/n Accept the matrix if consistency ratio, CR, is less than 0.10, where CR is CR = CI / RI

Consistency of Comfort Matrix

Applications of AHP Marketing Make Versus Buy Decision Resource Allocation New Product Development Consumer Behaviour Project Management (Project Selection, Contractor Prequalification)

APPICATIONS OF AHP IN PROJECT MANAGEMENT

Project Selection Problem Screening models help managers pick winners from a pool of projects. Screening models are numeric or nonnumeric and should have: Realism Capability Flexibility Ease of use Cost effectiveness Comparability

Screening & Selection Issues Risk – unpredictability to the firm Commercial – market potential Internal operating – changes in firm operations Additional – image, patent, fit, etc. All models only partially reflect reality and have both objective and subjective factors imbedded

Approaches to Project Screening Checklist model Simplified scoring models Analytic hierarchy process Profile models Financial models

Checklist Model A checklist is a list of criteria applied to possible projects. Requires agreement on criteria Assumes all criteria are equally important Checklists are valuable for recording opinions and encouraging discussion

Simplified Scoring Models Each project receives a score that is the weighted sum of its grade on a list of criteria. Scoring models require: agreement on criteria agreement on weights for criteria a score assigned for each criteria Relative scores can be misleading!

Analytic Hierarchy Process A four step process: Construct a hierarchy of criteria and subcriteria Allocate weights to criteria Assign numerical values to evaluation dimensions Scores determined by summing the products of numeric evaluations and weights Unlike the simple scoring model, these scores can be compared!

Step 1& 2

Step 3 & 4

Contractor (Pre-)Qualification in a Project Bid Process Example taken from the article: “Application of the AHP in project management “ by Kamal M. Al-Subhi Al-Harbi, International Journal of Project Management Volume 19, Issue 1, January 2001, Pages 19-27

The Problem Hierarchy

15 QUESTIONS - PAIRWISE COMPARISONS

15 QUESTIONS - PAIRWISE COMPARISONS EXAMPLE ANSWERS

FINANCIAL STABILITY (FS) 0,293 QUALITY PERFORMANCE (QP) 0,156 EXPERIENCE (EXP) FINANCIAL STABILITY (FS) QUALITY PERFORMANCE (QP) MANPOWER RESOURCES (MPR) EQUIPMENT RESOURCES (ER) CURRENT WORKLOAD (CWL) 1,00 2,00 3,00 6,00 5,00 0,50 0,33 4,00 0,17 0,25 0,20 Priority Vector EXPERIENCE (EXP) 0,372 FINANCIAL STABILITY (FS) 0,293 QUALITY PERFORMANCE (QP) 0,156 MANPOWER RESOURCES (MPR) 0,053 EQUIPMENT RESOURCES (ER) 0,039 CURRENT WORKLOAD (CWL) 0,087

10 QUESTIONS - PAIRWISE COMPARISONS PER EACH CRITERION

10 QUESTIONS - PAIRWISE COMPARISONS PER EACH CRITERION EXAMPLE ANSWERS

Pairwise Comparisons for Experience B C D E 1,00 0,33 0,50 0,17 2,00 3,00 4,00 6,00 7,00 0,25 0,14

15 + 10x6 = 75 pair wise comparisons In total: 15 + 10x6 = 75 pair wise comparisons are required

Contractors are ranked according to their priorities as follows: Finally: EXPERIENCE (EXP) FINANCIAL STABILITY (FS) QUALITY PERFORMANCE (QP) MANPOWER RESOURCES (MPR) EQUIPMENT RESOURCES (ER) CURRENT WORKLOAD (CWL) A 0,086 0,425 0,269 0,151 0,084 0,144 B 0,249 0,089 0,074 0,273 0,264 0,537 C 0,152 0,178 0,462 0,449 0,556 0,173 D 0,457 0,268 0,164 0,081 0,057 E 0,055 0,040 0,032 0,045 0,038 0,062 x Priority Vector EXPERIENCE (EXP) 0,372 FINANCIAL STABILITY (FS) 0,293 QUALITY PERFORMANCE (QP) 0,156 MANPOWER RESOURCES (MPR) 0,053 EQUIPMENT RESOURCES (ER) 0,039 CURRENT WORKLOAD (CWL) 0,087 = Contractors are ranked according to their priorities as follows: D, C, A, B and E Overall Priority Vector A 0,22264602 B 0,20163657 C 0,2412353 D 0,28818864 E 0,04629346

IF YOU’RE HOOKED HERE’S SOME BOOKS FOR FURTHER READING I LIKE AHP Y Wind and T L Saaty, ‘Marketing Applications of Analytic Hierarchy Process,’ Management Science, Vol. 26, No. 7, July 1980. T L. Saaty, ‘How to make Decision: The Analytic Hierarchy Process, Interfaces, Vol. 24, No. 6, pp. 19-43, 1994. Some recent personal research: V. C. Gerogiannis, P. Fitsilis, D. Voulgaridou, K.A. Kirytopoulos & E. Sachini, “A Case Study for Project and Portfolio Management Information System Selection: a Group AHP-Scoring Model Approach”, International Journal of Project Organisation and Management, to be published in 2010.   P. Fitsilis, V. C. Gerogiannis & M. Tsinidou, “Evaluation of the Factors that Determine Quality in Higher Education. An Empirical Study”, Quality Assurance in Education, Emerald Group Publishing Limited, Vol. 18, Issue 3, pp. 227 - 244, 2010. I LIKE AHP AND WITH ALL THIS KNOWLEDGE YOU WILL BE ABLE TO...