An Approach for Solving RoughMulti-Objective De Novo Programming Problems

Abstract

In this paper, a multi-objective De Novo programming (MODNP) problem is considered where all of its coefficients in the objective function and constraints are rough intervals (RIs) containing the unit price and the right hand side available budget. In order to solve this problem, we will construct two MODNP problems with interval coefficients. One of these problems is an MODNP where all of its coefficients are upper approximations of RIs and the other is an MODNP where all of its coefficients are lower approximations of RIs. Through these two MODNPs, two newly solutions (finally and rather satisfactory) are defined. All four linear programming models are solved by a regular simplex method which yields an efficient solution of the original MODNP problem. A numerical example is given to demonstrate the results.