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Fuzzy job sequencing for a flow shop. (English) Zbl 0762.90039
Summary: In job sequencing for a flow shop, processing times are frequently not known exactly and only estimated intervals are given. Fuzzy numbers are ideally suited to represent these intervals. In this work, the Campbell, Dudek and Smith (CDS) job sequencing algorithm [see H. G. Campbell, R. A. Dudek and M. L. Smith, Manage Sci., Appl. 16, B630–B637 (1970)] is modified to accept trapezoidal fuzzy processing times. Deterministic sequences result, but the sequence performance measurements of makespan and job mean flow time are fuzzy, having been calculated using fuzzy arithmetic. The use of possibility theory and the fuzzy integral enables the schedular to meaningfully interpret these fuzzy results. Deterministic approximations to this fuzzy approach are also investigated.

MSC:
90B35 Deterministic scheduling theory in operations research
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
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