Scheduling Hybrid Flowshop with Parallel Batching Machines and Task Compatibilities

C'est un résumé qui a été présenté à la conférence MAPSP07, en une partie nommé IntroductionInternational audienceWe consider a two-stage hybrid flowshop scheduling problem where each of n tasks is to be processed first at stage 1 and then at stage 2. The first stage contains m_1 identical parallel discrete machines and the second stage contains m_2 identical parallel batching machines. Each discrete machine can process no more than one task at time and each batching machine can process up to k tasks simultaneously in batch. The processing time of task j on any machine of stage one requires p_j time units and on any machine of stage two requiers q_j time units, which is given by the interval [a_j,b_j]. On the second stage the tasks are processed in batch and all tasks of the same batch start and finish together with the additional constraint that the tasks of the same batch have to be compatible. A compatibility is a symmetric binary relation in which a pair (i,j) of tasks is compatible if they share a similar processing time on the second machine (i.e, $[a_i, b_i] \cap [a_j, b_j] \neq \emptyset$). The batch processing time on the batching machine is determined as the maximum initial value a_j of compatible tasks. The objective is to find a schedule such that the completion time of the latest batch is minimized