The single machine ready time scheduling problem with fuzzy processing times

This paper studies a ready time scheduling problem with fuzzy job processing times. Firstly, we assume that the fuzzy processing time can be represented by a triangular fuzzy number. Then we apply the technique of chance constrained programming to construct a job completion likelihood profile from the job membership functions so that the likelihood of completing the queued jobs has a crisp mathematical representation. Some properties of the likelihood profile are subsequently discussed. Utilizing the fuzzy extension principle and the concept of job completion likelihood profile, the ready time scheduling model that maximizes the common ready time with crisp processing times is extended to one with fuzzy processing times. Optimal solutions for the scheduling model under several special conditions are developed, and a necessary condition that the optimal solution must satisfy when the jobs have different due dates and confidence levels is also established.