Multi-machine earliness and tardiness scheduling problem: an interconnected neural network approach

Abstract

This paper addresses the problem of scheduling a set of independent jobs with sequence-dependent setups and distinct due dates on non-uniform multi-machines to minimize the total weighted earliness and tardiness, and explores the use of artificial neural networks as a valid alternative to the traditional scheduling approaches. The objective is to propose a dynamical gradient neural network, which employs a penalty function approach with time varying coefficients for the solution of the problem which is known to be NP-hard. After the appropriate energy function was constructed, the dynamics are defined by steepest gradient descent on the energy function. The proposed neural network system is composed of two maximum neural networks, three piecewise linear and one log-sigmoid network all of which interact with each other. The motivation for using maximum networks is to reduce the network complexity and to obtain a simplified energy function. To overcome the tradeoff problem encountered in using the penalty function approach, a time varying penalty coefficient methodology is proposed to be used during simulation experiments. Simulation results of the proposed approach on a scheduling problem indicate that the proposed coupled network yields an optimal solution which makes it attractive for applications of larger sized problems.