Multiprocessor Scheduling Part 10

Tham khảo tài liệu 'multiprocessor scheduling part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 260 Multiprocessor Scheduling Theory and Applications job k in stage i are the same because the corresponding processor in stage i 1 is idle at the Stage 1 Stage 2 Stage m Figure 1. A flexible flow line with no intermediate buffers Figure 2. A schema of processor blocking As noted earlier setup time can include the time for preparing the machine or the processor. In an FFLPB with sequence-dependent setup time FFLPB-SDST it is assumed that the setup time depends on both jobs to be processed the immediately preceding job and the corresponding stage. Thus a proper operation sequence on the processors has a significant effect on the makespan . cmax . As already assumed the processors in each stage are identical whereas the stages are different. Therefore it is assumed that the setup time also depends on the stage type. A schema of sequence-dependent setup time in the FFLPB is illustrated in Figure 4. Job q must be processed immediately before job k in stage i. Also job l must be processed immediately before job k in stage i 1. Siqk is equal to the processor setup time for job k if job q is the immediately preceding job in the sequence operation on the corresponding processor. Likewise S i 1 lk is equal to the processor setup time for job k if job l is the immediately preceding job. Job q is completed in stage i at time ciq and departs as time dq ciq to an available processor in stage i 1 excepting the one that is processing job k . As a result job k is started at time diq Siqk in stage i and departs at time dk d i 1 l to stage i 1. Likewise job l is completed in stage i 1 at time C i 1 l and departs at time d i 1 l C i 1 l to an available processor in the next stage. As a result job k started at time d i 1 l S i 1 lk in stage A New Mathematical Model for Flexible Flow Lines with Blocking Processor and Sequence-Dependent Setup Time 261 i 1 and completed at time C i 1 k. It is worth noting that the blocking processor or idle times cannot be used as setup time because

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