EQUIVALENT JOB FOR JOB BLOCK IN DETERMINATION OF OPTIMAL DUE DATE AND MINIMIZATION OF LATENESS COST FUNCTION IN SPECIAL CLASS OF N-JOBS 3-MACHINES SEQUENCING PROBLEM.

Abstract

This research study on sequencing problem with the introduction of equivalent job for job block in special class of n-jobs on 3-machines sequencing problem in which some conditions are imposed on the processing times. The purpose of this research is to find the processing time of equivalent job for jobs in block, determine optimal value of processing time multiple, due-date assignment and optimal sequence of jobs so as to minimize squared value of lateness cost func tion. A heuristic method has been developed based on lemma,theorem and corollary proved for minimization of objective function. Here the squared value of lateness is used as performance measure in obtaining optimal sequence. The result of study is a formula to find the processing time of an equivalent job for jobs in block on each machine has been obtained, the processing time multiple shown to be constant and independent of the sequence of jobs,due-date assigned and optimal sequence is obtained by arranging jobs based on the processing time of the last machine according to shortest processing time rule. Moreover an algorithm has been developed and numerical example is provided to support the theoretical development.