Robust Optimization Method for Online Flowshop Problem with Uncertain Processing Times and Preemption Penalties Mohammad Bayat * and Mohammad Mahdavi Mazdeh Department of Industrial Engineering, Iran University of Science and Technology; mohammadbayat@iust.ac.ir Abstract The flowshop scheduling problem has been one of the most attractive research issues. Deterministic flowshop problem is widely studied; whereas it is uncertain processing times has remained a challenge. In this paper, a robust heuristic method for this problem is presented, which is applicable whenever the lower and upper bounds of each job are available. The proposed method is capable of handling the perturbation which exists amongst the processing times. Therefore, the proposed robust method could guarantee that a small deviation of the processing times does not afect the feasibility. The performance of the proposed method is explored using some numerical examples. Keywords: Flowshop Scheduling, Online Flowshop, Online Scheduling, Preemptive Flowshop, Robust Optimization, Uncertain Processing Times *Author for correspondence 1. Introduction he scheduling problem aims to address the best sequence for processing of jobs such to cause the best value for the objective function. However, it is not possible to use classic models to for scheduling the jobs in stochas- tic and dynamic environments because unwanted and unpredicted events might possibly happen in these envi- ronments. he real environments are actually dynamic in many cases. his means that planning may be done based on conditions which do not remain constant till the end and they may experience some changes. Moreover, many of these changes are possibly beyond control of the deci- sion maker and the decision maker could be unaware of its all details until its occurrence. Complexities of plan- ning in such an environment are thus much more than the static environment. In other words, there are some events which must be considered in these cases including unspeciied completion time of the jobs, asynchronous and online arrival of the jobs, as well as preemption probability and penalties of the jobs. So, it can be said that the scheduling in such an environment must be capable to make the best decision immediately ater occurrence of an unpredicted event (i.e. arrival of a new job) and to give the optimal sequence according to that event. As a result, the problem under study here involves a dynamic FlowShop Scheduling (FSS). Scheduling problem has been well studied and numer- ous solution strategies have been provided for various environments such as job shop and lowshop. he two-ma- chine lowshop problem with makespan objective function and deterministic processing time can be solved optimally by Johnson’s rule 1 . Considering three or more machines for this problem would result in an NP-hard problem 2 . hus, several heuristic algorithms have been suggested for solving such problems in various studies. Some of these articles have been reviewed by Framinan et al. 3 . Hejazi and Saghaian reviewed 176 articles on lowshop problems with makespan objective function and various heuristic methods 4 . Indian Journal of Science and Technology, Vol 7(7), 1026–1038, July 2014 ISSN (Print): 0974-6846 ISSN (Online) : 0974-5645