Making Decisions – Vol. XI: ORESTE

            ORESTE is a prioritization and decision-making tool that evaluates alternatives according to their deviations from a hypothetical ideal solution.  The acronym, translated from French, stands for “organization, storage, and synthesis of relational data.”  The method establishes a hierarchy of criteria that is then used to determine a hierarchy of alternatives.
            In this installment, a relatively-simple analysis is used to demonstrate the ORESTE method.  The hypothetical machine purchase of previous installments is revisited, maintaining continuity that facilitates comparison of methods.  A potential pitfall of the method and recovery options are also discussed.

The ORESTE Method
            The example used to demonstrate the ORESTE method is the same as that presented in Vol. III:  Analytic Hierarchy Process and Vol. X: Fuller Triangle.  For convenience, the performance matrix is reproduced in Exhibit 1.  In this installment, criteria and alternatives are identified by the first letter of each:  C, P, S for criteria and J, W, A for alternatives.  Presentation in this fashion reflects readers’ familiarity with the example, gained in previous installments, while continuing to provide greater clarity than arbitrary alphanumeric identifiers.  This may not be feasible in a larger analysis; however, experience gained prior to such an undertaking should obviate this practice.
            As in previous analyses, productivity and service life are deemed more important than cost, and productivity is also deemed more important than service life.  This hierarchy is presented as PROD > SVC > COST.  In terms of preference rankings, this gives rP = 1, rS = 2, and rC = 3.
            The alternatives are ranked in order of preference with respect to each criterion.  Replacing the values in the performance matrix with the rank order values yields the position matrix, P, shown in Exhibit 2.  Note that Wiley and Acme offer identical service life, resulting in equal rank, each being the average.

            Next, the block distance of each position is calculated.  In two-dimensional Cartesian space, the block distance between two points is |x1 – x2| + |y1 – y2|.  Also called “city block distance,” the distance traversed between two locations, when only travel parallel to the axes is permitted, is determined.  However, ORESTE is not conducted in Cartesian space, but in “decision space.”
            The ORESTE decision space has an arbitrary origin, 0.  Block distances of each position from the origin, d(0, Aij), are determined as

where dij is the distance from the origin of the position of the ith alternative with respect to the jth criterion, pij is the position of the ith alternative with respect to the jth criterion, rcj is the preference rank of the jth criterion, and r is a scaling factor.  The derivation of r is beyond the scope of this presentation; suffice to say that r = 3 is typically used, as it is herein.  Substitution of these values yields the distance matrix, D, shown in Exhibit 3.

            The distance of each position is ranked from least to greatest; ties (i.e. equal distances) are assigned average rankings.  The ordinal rankings replace the cardinal distances for each position in the matrix to determine the final alternative ranking.  The ranking matrix, R, shown in Exhibit 4, includes a summation column for this purpose.  Each alternative ranking score equals the sum of its criterion position rankings:  Ra = ∑ raj, where Ra is the total ranking score of alternative a and raj is the rank of alternative a with respect to the jth criterion.  The lowest total ranking score corresponds to the preferred alternative.
            It is interesting that the preference ranks obtained by the ORESTE method do not align with those from AHP and FT.  Two key influences are responsible for this deviation.  First, the degree to which an alternative is preferred with respect to any criterion (the magnitude of preferences) is not fully accounted for in scores based on ordinal rankings alone.  Second, whereas the other methods tend to resolve ties at earlier stages of analysis, those in the final ranking matrix in the ORESTE method allow small changes in scoring totals to shift the results.

Speaking of Ties…
            The ORESTE method is often demonstrated with no ties in the position matrix.  However, equal performance of alternatives on one or more metric is not an unusual occurrence.  The significance of a tie depends on it persisting to the final ranking and the rank at which it occurs.  When only one alternative is to be pursued, a tie that occurs below the highest rank requires no further attention.  A tie for the most-preferred alternative, however, requires further analysis.  A few options are discussed below, though it must be noted that these should be used with caution.
            The most obvious option is to abandon the ORESTE method when ties are discovered.  If it is one of several MCA tools in use, this may be advisable.  Doing so eliminates the additional computation and justifications required to rank alternatives.  The final results may still be less clarifying than desired, further incentivizing decision-makers to forego ORESTE analysis for a particular decision.
            Consider the equal service life of the Wiley and Acme machines; with an alternative method of calculating block distances, this tie persists to the final ranking where purchase of either machine is deemed equally desirable and preferred to a purchase from Jones.  This provides little insight beyond that gained from reviewing the performance matrix prior to analysis; no definitive conclusion is reached.
            One approach to breaking such a tie is to intentionally introduce bias into the analysis.  As examples, let’s say that decision-makers perceived one of the suppliers to be more responsive than the other during the proposal process or they have successful project history with one, but the other is a new supplier.  Instead of assigning both an average position of 1.5 on the SVC metric, the favored supplier would be rated 1 and the other 2.
            If Acme is given the advantage in the tie-breaker of our example, the analysis changes to that shown in the composite matrix of Exhibit 5.  In this scenario, the results align with those of AHP and FT, where Acme is favored over Wiley, and Jones is the least-desirable supplier.  In a small analysis like this, the impact such a bias introduction will have on final results is predictable.  This leaves the analysis susceptible to manipulation with weak justifications for modifications to the position matrix.  Thus, the practice should be employed only in larger analyses, where the influence of such a tie-breaker is less obvious, and then only with open acknowledgement that the results are less definitive than other analyses may provide.

            The “intentional bias” approach reduces the reliability of the ORESTE method.  A more-accurate representation of the importance of a relationship with a supplier, or any attribute of an alternative, is achieved by adding it to the performance matrix.  Whether initially overlooked, or deemed too inconsequential to warrant additional computations, the potential impact of any relevant criterion should not be discounted.  The reversal of preferences in our example demonstrates the potential impact of shortcuts in analysis.
            To extend the example, let’s say a fourth criterion represents decision-makers’ confidence in the supplier’s ability to successfully deliver the project as specified.  We’ll call it the “X-factor” to reflect its qualitative nature.  An advantage of ORESTE is that qualitative assessments need not be converted to quantitative metrics.  On this assessment, Jones, Wiley, and Acme are rated very high, high, and moderate, respectively.  Given that “X-factor” was previously used to break a tie with respect to service life, it is now ranked above SVC in importance.  Thus, PROD > X > SVC > COST; rP = 1, rX = 2, rS = 3, rC = 4.
            The expanded analysis is summarized in the composite matrix shown in Exhibit 6.  That Acme is the preferred supplier in the final ranking is no surprise, as the expanded analysis merely formalized a previously revealed preference.  What may be surprising, however, is that Jones is now ranked second.  Very high confidence in successful project delivery substantially narrowed the gap between Jones and the ultimate “winner,” but it could not overcome Acme’s superior machine performance.
            Results of the expanded analysis are not directly comparable to those previously obtained by AHP and Fuller Triangle methods.  For such comparisons to be valid, those analyses must also be expanded to include the “X-factor” evaluations.  A Fuller Triangle analysis with X-factor yields a tie between Wiley and Acme in the final ranking, reminding us that an important decision may require iterative analysis or multiple tools to develop sufficient confidence in the final selection.

ORESTE II
            The second phase of the ORESTE method, sometimes called ORESTE II, uses threshold values to determine a “complete” ranking.  These thresholds differentiate between preference and indifference (β), between indifference and incomparability (C*), and between preference and incomparability (γ).  Its purpose is to refine “weak order” rankings found in the first phase by accounting for strengths of preferences.
            The second phase is often omitted, as is done here.  It does not clarify the decision in the present example and could create unnecessary confusion.  Therefore, a detailed discussion of ORESTE II is postponed until it can be done in a context to which it adds value.

A Final Tip
            In our example, the order of presentation of criteria does not coincide with their relative priorities.  The performance matrix could be rearranged such that the priority ranking of each criterion equals its subscript when using Cj notation to identify them.  This is only a matter of convenience to reduce the potential of errors, particularly in larger matrices.  It is an additional step, performed only if it serves analysts’ or decision-makers’ preferred style of information organization and presentation.


            For additional guidance or assistance with decision-making or other Operations challenges, feel free to leave a comment, contact JayWink Solutions, or schedule an appointment.

            For a directory of “Making Decisions” volumes on “The Third Degree,” see Vol. I:  Introduction and Terminology (8Apr2020).

References
[Link] “Preference relations on actions and criteria in multicriteria decision making.”  Marc Roubens.  European Journal of Operational Research; May 1982.
[Link] Multiple Criteria Decision Analysis:  State of the Art Surveys, 2ed.  Salvatore Greco, Matthias Ehrgott, and José Rui Figueira (eds).  Springer; 2016.
[Link] New Methods and Applications in Multiple Attribute Decision Making (MADM).  Alireza Alinezhad and Javad Khalili.  Springer; 2019.
[Link] “The Issue of Multicriteria Decision-Making:  Model Example of Business Partner Risk Assessment.”  Jaromir Vrbka and Vojtech Stehel.  Proceedings of the 13th International Management Conference; January 2020.
[Link] “Multicriteria Decision-Making Methods.”  M. Pavan and R Todeschini.  In Comprehensive Chemometrics, 2ed ; S. Brown, R. Tauler, and B. Walczak (eds).  Elsevier, 2020.
[Link] “Solution proposal for completed preference structure in ORESTE method.”  Mehmet Akif Yerlikaya, Kürşat Yildiz, and Büşra Nur Keskin.  Scientific Reports; March 2023.

Jody W. Phelps, MSc, PMP®, MBA
Principal Consultant
JayWink Solutions, LLC
[email protected]