On two single machine scheduling problems with fuzzy processing times and fuzzy due dates

Two single machines scheduling problems with fuzzy processing times and fuzzy due dates are considered. In both we define the fuzzy tardiness of a job in a given sequence as a fuzzy maximum of zero and the difference between the fuzzy completion time and the fuzzy due date of this job. In the first problem we minimize the maximal expected value of a fuzzy tardiness and in the second we minimize the expected value of a maximal fuzzy tardiness. The problems look similar but we show that they have quite different computational complexity. The first problem can be solved by a polynomial algorithm if we only can calculate easily the fuzzy tardiness. We propose such an algorithm assuming that all processing times and all due dates are fuzzy numbers of the L–R type with power shape functions. We prove that the second problem is NP-hard.