In this paper a single machine scheduling problem to minimize tardy jobs is considered. To increase the reality of the problem, deterioration and learning effect is added to. Beside, according to Inherent uncertainty in processing times, they are considered to be normally distributed. To find an appropriate solution, four existing models are extended and the results are compared to validate them.

This paper deals with single machine scheduling problems where some job characteristics are uncertain. This uncertainty is described through a finite set S of well-defined scenarios. We denote by pj , d s j and w s j , respectively, the processing time, the due date and the weight of job j under scenario s ∈ S. Consider a scheduling problem, denoted by α|β|γ according to Graham et al. notation ...

Gafarov et al. [6] have recently presented an O(n) time dynamic programming algorithm for a single machine scheduling problem to maximize the total job tardiness. We reduce this problem in O(n log n) time to a problem of unconstrained minimization of a function of 0-1 variables, called half-product, for which a simple O(n) time dynamic programming algorithm is known in the literature.

We consider the problem of common due-date to of simultaneously available jobs and sequencing them on a that a number of the jobs are tardy. The optimal combination of the common due-date and job sequence that minimizes the total absolute lateness. A simple to achieve this. Effectively three independent procedures : one to the nnT,nn<>1 sequence; a second to the optimal due date and a third to ...

Robust scheduling aims at the construction of a schedule that is protected against uncertain events. A stable schedule is a robust schedule that changes only little when variations in the input parameters arise. This paper presents a model for single-machine scheduling with stability objective and a common deadline. We propose a branch-andbound algorithm for solving an approximate formulation o...