Bi-criteria single machine scheduling problem with a learning effect: Aneja–Nair method to obtain the set of optimal sequences

Abstract

In this paper, we consider the bi-criteria single machine scheduling problem of n jobs with a learning effect. The two objectives considered are the total completion time (TC) and total absolute differences in completion times (TADC). The objective is to find a sequence that performs well with respect to both the objectives: the total completion time and the total absolute differences in completion times. In an earlier study, a method of solving bi-criteria transportation problem is presented. In this paper, we use the methodology of solving bi-criteria transportation problem, to our bi-criteria single machine scheduling problem with a learning effect, and obtain the set of optimal sequences,. Numerical examples are presented for illustrating the applicability and ease of understanding.