Efficient interpretive ranking process incorporating implicit and transitive dominance relationships

Abstract

Interpretive ranking process (IRP) is a multi-criteria decision making method based on paired comparison in an interpretive manner. Due to paired comparisons, the number of interpretations to be made for n ranking variables are $n(n-1)/2$ to establish dominance with respect to each reference variable or criterion. IRP is a knowledge intensive method and thus a large number of comparisons poses a limitation on the number of rankling as well as reference variables to be considered in the design of the decision problem. This paper is intended to make the process of comparison more efficient so that this limitation on number of variables can be relaxed to handle comparatively large size problems as well. The number of interpretive comparisons can be drastically reduced by considering both implicit and transitive dominance relationships. It provides a critical review of IRP steps and suggests improvements to make it more efficient. It then illustrates the modified IRP method on a couple of already published examples (including an example on post-disaster management) and summarizes the reduction in interpretive comparisons that indirectly gives a measure of increase in its efficiency.

Appendices

Appendix I

1.1 Example 1: Ranking of actors with respect to processes (Sushil 2009a)

1.1.1 Exhibit I.1: Ranking and reference variables

Variables
Ranking variables—Actors
A1–CEO of ABB (Parent Company)
A2–ABB India’s management
A3–ABB India’s employees
A4–Government of India
Reference variables—Processes
P1–Technology and business strategy alignment
P2–Mergers and acquisitions
P3–Backward integration
P4–Offering technological solution to customer

1.1.2 Exhibit I.2: Cross-interaction matrix ‘Actor $\times$ Process’

Contextual Relationship : Roles of actors in various processes

• (a) Binary Matrix

(b) :

Interpretive Matrix

1.1.3 Exhibit I.3: Interpretive logic—knowledge base-ranking of actors w.r.t. processes

Paired comparison	Interaction with process	Interpretive logic
A1 Dominating A2	P1	Vision/global Strategy have more influence than domestic strategy on Technology and Business Strategy Alignment
	P2	Provision of resources for M&A is more important than Post M&A integration
A2 Dominating A3	P4	Understanding Customer needs for developing solutions is more important than simply developing technological solutions
A4 dominating A1	P2	Regulation for M&A influence the M&A Process more than provisions of resources

1.1.4 Exhibit I.4: Pair-wise dominance of actors for different processes

• (a) Dominating Interaction Matrix of Actors for Process P1

  

• (b) Dominating Interaction Matrix of Actors for Process P2

  

• (c) Dominating Interaction Matrix of Actors for Process P3

  

• (d) Dominating Interaction Matrix of Actors for Process P4

  

1.1.5 Exhibit I.5: Dominance matrix—ranking of actors w.r.t. processes

Appendix II

1.1 Example 2: Ranking of actions w.r.t. performance areas (Sushil 2009a)

1.1.1 Exhibit II.1: Ranking and reference variables

Variables
Ranking variables—Actions
A1*–Technology management as core function
A2*–Core competence building agenda
A3*–Backward integration strategy
A4*–Develop in-house R&D
Reference variables—Performance areas
P1*–Sustainable competitive advantage
P2*–Customer satisfaction
P3*–Dependence on imported technology

1.1.2 Exhibit II.2: Cross-interaction matrix ‘Action $\times$ Performance’

Contextual Relationship: Influence of actions on various performance areas

(a) :

Binary Matrix

• (b) Interpretive Matrix

1.1.3 Exhibit II.3: Pair-wise dominance of actions for different performance areas

• (a) Dominating Interaction Matrix of Actions for Performance Area P1*

  

• (b) Dominating Interaction Matrix of Actions for Performance Area P2*

  

• (c) Dominating Interaction Matrix of Actions for Performance Area P3*

  

1.1.4 Exhibit II.4: Dominance matrix—ranking of actions w.r.t. performance

Appendix III

1.1 Example 3: Ranking of flexibility initiatives w.e.f. to benefits and costs (Sushil 2017a)

Exhibit III.1: Ranking and reference variables

Variables
Ranking Variables—Flexibility Initiatives
F1–Variable capacity
F2–Multi-skilling
F3–Flexi-time/Flexi-place
Reference Variables—Benefits
B1–Low inventory
B2–Ability to handle unprecedented job requirements
B3–Reduction in manpower cost
B4–Work-life balance
Reference Variables—Costs
C1–Training cost
C2–Coordination cost
C3–Cost of technology
C4–Complex job allocation

1. Source: Sushil (2017a)

1.1.1 Exhibit III.2: Cross-interaction Matrix—Flexibility Initiatives $\times$ Criteria (Benefits/Costs)

Contextual Relationship: Flexibility initiatives generating benefits and incurring costs

• (a) Binary Matrix

• (b) Interpretive Matrix

1.1.2 Exhibit III.3: Pair-wise dominance of flexibility initiatives for different benefits and costs

• (a) Dominating Interaction Matrix of Flexibility Initiatives for Benefit B1

  

• (b) Dominating Interaction Matrix of Flexibility Initiatives for Benefit B2

  

• (c) Dominating Interaction Matrix of Flexibility Initiatives for Benefit B3

  

• (d) Dominating Interaction Matrix of Flexibility Initiatives for Benefit B4

  

• (e) Dominating Interaction Matrix of Flexibility Initiatives for Cost C1

  

• (f) Dominating Interaction Matrix of Flexibility Initiatives for Cost C2

  

• (g) Dominating Interaction Matrix of Flexibility Initiatives for Cost C3

  

• (h) Dominating Interaction Matrix of Flexibility Initiatives for Cost C4

  

1.1.3 Exhibit III.4: Dominance matrix—ranking of flexibility initiatives w.r.t benefits and costs

Appendix IV

1.1 Example 4: Ranking of post-disaster actions w.r.t. intended performance (Sushil 2017b)

1.1.1 Exhibit IV.1: Ranking and reference variables

Variables
Ranking Variables—Action (Post-disaster, on-site)
A1*–Improvisation for rescue (Volunteers)
A2*–Communication with all modes (Local administration)
A3*–Activate medical support (Local bodies/Hospitals)
A4*–Channelize supplies (NGOs/Government bodies)
A5*–Sending professional rescue teams (Military/NGOs)
A6*–Committed supervision (Executives/Political leadership)
A7*–Clearing the site (Trained Professionals)
Reference Variables—Performance (Intended)
P1*–Loss of life
P2*–Loss of property
P3*–Timeframe for rescue/relief
P4*–Relief from injuries
P5*–Timely reach of aid

1.1.2 Exhibit IV.2: Cross-interaction matrix: Action (A*) $\times$ Performance (P*)

Contextual Relationship: Influence of actions on various performance areas

• (a) Binary Matrix

  

• (b) Interpretive Matrix

  

1.1.3 Exhibit IV.3: Pair-wise dominance of post-disaster actions for different performance areas

Dominating Interaction Matrix of Post-Disaster Actions for Performance P1*

Dominating Interaction Matrix of Post-Disaster Actions for Performance P2*

Dominating Interaction Matrix of Post-Disaster Actions for Performance P3*

Dominating Interaction Matrix of Post-Disaster Actions for Performance P4*

Dominating Interaction Matrix of Post-Disaster Actions for Performance P5*

1.1.4 Exhibit IV.4: Dominance matrix—ranking of post disaster actions w.r.t. intended performance