On Pareto Set for a Bi-criterion Scheduling Problem Under Fuzziness

Abstract

In this paper a bi-criterion fuzzy scheduling problem was presented and the problem under consideration is total fuzzy completion time and maximum earliness, where the processing times and the due dates are triangular fuzzy numbers. Each of jobs is to be processed without interruption on a single machine and becomes available for processing at time zero. A new definition of fuzzy numbers was given namely m-strongly positive fuzzy numbers, through this definition we found an interval which restricts the range of the fuzzy lower bound and presented a relation between the fuzzy lower bound and the fuzzy optimal solution with number of efficient solutions. Also we found the exact solution of the problem through finding the Pareto set.

Keywords

• keywords: scheduling problem
• bi-criterion problems
• pareto set
• fuzzy processing times
• fuzzy due dates