Philipp. Sci. Lett. 2018 11 (2) 061-070
available online: July 25, 2018
Email Address: firstname.lastname@example.org
Date Received: May 17, 2018
Date Revised: June 23, 2018
Date Accepted: July 05, 2018
When is the Pareto choice from a finite set invariant to variations in weight and values of multiple performance criteria?
by Jose B. Cruz, Jr.1,* and Elvin Michael R. Almario2
1National Academy of Science and Technology,
Engineering Sciences and Technology Division, Bicutan, Taguig City, Philippines2Malayan Colleges Laguna, Pulo Diezmo Road, Cabuyao, Laguna 4025, Philippines
A simple procedure is described for selecting one option from a finite set or list of n options. Each option is associated with m performance criteria, features, or attributes. A weighted sum of the values of the normalized criteria is calculated for each option and the option with the largest weighted sum is selected. If the list contains Pareto-optimal options the winning option is Pareto optimal. It is shown that the winning option is invariant in spite of variations in the weights provided that these remain in a specified subspace of the multi-dimensional space of the weights that includes the chosen weights. Moreover, the winning option is invariant in spite of variations in the values of the multiple criteria provided that the variations remain in specified subspaces of the criteria space that includes the original criteria values. These invariance properties are reported for the first time in this paper. The entire process is called the invariance method. An upper bound for the maximum number of pairwise comparisons to identify all the k Pareto-optimal options in a finite set of n options, is derived. For each pair of n and k, where n is greater than or equal to k, there is a list such that the upper bound is reached.