Modified Algorithm for Scheduling Problem

Abstract

The problem of scheduling n jobs on a single machine is considered, where the jobs are divided into two classes and a machine set up is necessary between jobs of different classes. Jobs i (i= 1,…, n) becomes available for processing at time zero, requires a positive processing time i P. Disjoint subsets N 1 and N 2 define the partition of jobs into two classes. If two jobs in the same class are sequenced in adjacent positions, then no set up time between these jobs in necessary. We address the bicriterion (multi objective) scheduling problem, the two criteria are the minimization of flow time ( N i i c) and the minimization maximum Tardiness (max T). We characterized the set of all efficient points and the optimal solution. A modified algorithm presented to find efficient solutions for the problem with set up times. A relation found between number of efficient solutions and range of 'tardiness of shortest processing time (SPT T), tardiness of early due date (EDD T)'. This algorithm treats with a case that the set up time in  SPT rule is in increasing order. A counter example presented to show that the algorithm will fail if the set up time in  SPT rule is in decreasing order. Our task is to present the decision makers with all possible solutions and let them make the final selection. The decision maker has two objectives in mind ( N i i c) , (max T) and some solutions (efficient), we will choose the best one from the efficient solutions depending on his experiences.