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One Machine Fuzzy Scheduling to Minimize Total Weighted Tardiness, Earliness, and Recourse Cost

In this article, we consider the problem of scheduling n jobs on one machine. Precise job processing times are unknown and represented as normalized triangular fuzzy numbers. We propose a two-stage fuzzy scheduling approach to solve the problem. The underlying idea is essentially identical to the stochastic programming with recourse. We solve the problem through two-stage decisions and reflect the influence of the fuzziness of processing times as recourse cost. The proposed approach is meaningful and effective, especially in situations where the spread of fuzzy processing times is relatively wider and higher recourse costs have to be paid to deal with the impression/uncertainty of processing times. The proposed approach has a computational advantage over the one-stage fuzzy scheduling approach; the latter is faced with the computational complexity of calculations and comparisons of non-normalized fuzzy numbers.