Solving Three Objectives Single-Machine Scheduling Problem Using Fuzzy Multi-Objective Linear Programming

Abstract

In this paper, three criteria scheduling problem of n jobs on a single machine is considered. Each of these n jobs is to be processed without interruption and becomes available for processing at time zero. The problem is to minimize three objectives simultaneously, which are the completion time, maximum tardiness, and maximum earliness. Here, we develop a fuzzy multi-objective linear programming (FMOLP) model for solving multi-objective scheduling problem in a fuzzy environment by using piecewise linear membership function (PLMF). A numerical example demonstrates the feasibility of applying the proposed model to scheduling problem, and yields a compromised solution to help the decision maker’s overall levels of satisfaction. The algorithm is tested to show the ability of applying this model to three criteria.