Modified Algorithm for Scheduling Problem

Ayad M Ramadan

doi:10.32894/kujss.2010.41647

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 . Disjoint subsets N1 and N2 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 ( ) and the minimization maximum Tardiness ( ). 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 ( ), tardiness of early due date ( )’. This algorithm treats with a case that the set up time in rule is in increasing order. A counter example presented to show that the algorithm will fail if the set up time in 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 ( ) , ( ) and some solutions (efficient), we will choose the best one from the efficient solutions depending on his experiences.

Highlights

In the industrial context, scheduling problems are related to manufacturing resource planning (Rocha et al, 2008).There are many researches considering this type, but few machines or sequence-dependent setups
Preemptive scheduling problems are those in which the processing of a job can be temporarily interrupted (Potts & Mikhail, 2000)
Many practical scheduling problems involve processing several families of related jobs on common facilities, where a set-up time is incurred whenever there is a switch from processing a job in one family to a job in another family

Summary

Introduction

In the industrial context, scheduling problems are related to manufacturing resource planning (Rocha et al, 2008).There are many researches considering this type, but few machines or sequence-dependent setups. In scheduling one situation where benefits may result from batching occurs when machines require set-up if they are to process jobs that have different characteristics. Consider a mechanical parts manufacturing environment in which jobs have to be sequenced for processing on a multi-tool machine (Crauwels et al, 2005). There are different definitions of the notion of optimal solutions of a multi objective combinatorial optimization (MOCO) problem Van Wassenhove proposed an algorithm (Van Wassenhove and Gelders, 1980) to find all efficient solutions for problem (1). The objective is to find efficient solutions for (2) with set-up times

S ci and Tmax i N

Conclusions and suggestions range between