Parametric Study On Single Machine Early/Tardy Problem Under Fuzzy Environment

Abstract

This paper presents a solution algorithm for solving the single machine early/tardy problem having fuzzy parameters in the constraints. There are several cost structures: job-independent, job-dependent and symmetric, and job-dependent and asymmetric. The last problem is shown to be NP-hard and it will be studied here. Some basic stability notions are defined and characterized for the problem of concern. These notions are the set of feasible parameters, the solvability set and the stability set of the first kind. A parametric study is carried out for the problem of concern. Finally, an illustrative numerical example is given to clarify the theory and the solution algorithm.