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    Minimizing average job completion time in a two-stage assembly flowshop with setup times
    (Maltepe Üniversitesi, 2009) Allahverdi, Ali; Al-Anzi, Fawaz S.
    The two-stage assembly flowshop problem consist of two stages where there are m machines at the first stage while there is only a single assembly machine at the second stage. There are n jobs to be scheduled and each job has m + 1 operations. For each job, the first m operations are conducted at the first stage by m machines in parallel and a final operation in the second stage by the assembly machine. The last operation at the second stage may start only after all m operations at the first stage are completed. The two-stage assembly scheduling problem has many applications in industry, and hence, has received an increasing attention of researchers recently. We address the two-stage assembly scheduling problem with the objective of minimizing average job completion time. This objective is particularly important in real life situations where reducing inventory or holding cost is of primary concern. Setup times are treated as separate from processing times. This problem is NP-hard since its special case, when setup times are ignored and m = 1 (which is a regular two-machine flowshop problem), is NP-hard. Therefore, we present a dominance relation and present three heuristics. The heuristics are evaluated based on randomly generated data. One of the proposed heuristics is known to be the best heuristic for the case of zero setup times while another heuristic is know to perform well for such problems. A new version of the latter heuristic is proposed and shown to perform much better than the other two heuristics.
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    Minimizing makespan in a two-machine stochastic flowshop
    (Maltepe Üniversitesi, 2009) Allahverdi, Ali; Aydilek, H.
    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.
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    Multiple-criteria assembly flowshop scheduling problem
    (Maltepe Üniversitesi, 2009) Al-Anzi, Fawaz S.; Allahverdi, Ali
    Different performance measures are considered in the scheduling research. These performance measures may be classified as completion time related or due date related. Makespan (Cmax), a completion time related performance measure, is one of the most widely used performance measures. Minimizing makespan is important in situations where a simultaneously received batch of jobs is required to be completed as soon as possible. For example, a multi-item order submitted by a single customer needs to be delivered as soon as possible. The makespan criterion also increases the utilization of resources. Minimizing maximum lateness (Lmax) is a widely used due date related measure. This objective is particularly important in situations where there is a penalty to complete a job beyond its due date and the penalty increases with the gap between the two. We consider a two-stage assembly flowshop scheduling problem with the objective of minimizing a weighted sum of makespan and maximum lateness. The problem is known to be NP-hard, and therefore, we propose heuristics to solve the problem. The proposed heuristics are Tabu search (Tabu), particle swarm optimization (PSO), and self-adaptive differential evolution (SDE). An extensive computational experiment is conducted to compare the performance of the proposed heuristics. The computational experiment reveals that both PSO and SDE are much superior to Tabu. Moreover, it is statistically shown that PSO perform better than and SDE. The computation time of both PSO and SDE are close to each other and it is less than 45 seconds for the largest size problem considered.