Minimizing makespan in a two-machine stochastic flowshop
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CitationAllahverdi, A. ve Aydilek, H. (2009). Minimizing makespan in a two-machine stochastic flowshop. Maltepe Üniversitesi. s. 79.
The two-machine flowshop scheduling problem is usually addressed where processing times are assumed to be deterministic for which Johnson’s algorithm can be used to solve the problem. For many scheduling environments, the assumption of deterministic processing times is not valid. Hence, the random variation in processing times has to be taken into account while searching for a solution. Some researchers addressed the flowshop problem where job processing times follow certain probability distributions. For some scheduling environments, it is hard to obtain exact probability distributions for random processing times, and therefore assuming a specific probability distribution is not realistic. Usually, solutions obtained after assuming a certain probability distribution are not even close to the optimal solution. It has been observed that, although the exact probability distribution of job processing times may not be known, upper and lower bounds on job processing times are easy to obtain in many cases. Hence, this information on the bounds of job processing times should be utilized in finding a solution for the scheduling problem. In this paper, we address the two-machine flowshop scheduling problem of minimizing makespan where jobs have random processing times which are bounded between a lower and an upper bound. The probability distributions of job processing times within intervals are not known. The only known information about job processing times are the lower and upper bounds. The decision about a solution of the problem has to be made based on these bounds. Different heuristics using the bounds are proposed, and the proposed heuristics are compared by using simulation. The simulation results have shown that the proposed heuristics perform well with an overall average error of less than one and half percent for all heuristics. One of the heuristics performs as the best with an overall average percentage error of less than one percent.
SourceInternational Conference of Mathematical Sciences
- Makale Koleksiyonu 
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