A Generalized Goal Programming Approach to the Minimal Interference, Multicriteria N × 1 Scheduling Problem

Abstract

Abstract The conventional approach to the modeling and solution of most scheduling problems involves the development of a mathematical model which (1) employs discrete variables (e.g., linear integer programs), and (2) includes only a single objective to be maximized or minimized (e.g., minimization of makespan). Unfortunately, models involving discrete variables are inherently combinatorially explosive (i.e., methods such as branch-and-bound will exhibit computation times which grow exponentially with problem size). Further, scheduling problems encountered in the real world invariably involve multiple conflicting objectives, and thus using a single-objective representation can lead to gross oversimplification. In this paper we address a specific class of scheduling problem encountered in several real-world applications that may be efficiently addressed as a linear multiobjective model having only continuous variables. The model and its solution are compared with those of a highly acclaimed recent approach, and they appear to provide significant improvements.