Minimizing the number of tardy job units under release time constraints

Minimizing the number of tardy job units under release time constraints

We study two single-machine scheduling problems: Minimizing the weighted and unweighted number of tardy units, when release times are present. Fast strongly polynomial algorithms are given for both problems: For problems with n jobs, we give algorithms which require O(n log n) and O(n2) steps, for the unweighted and weighted problems respectively. Our results also imply an extension of the fami...

Minimizing the Number of Tardy Jobs in the Single Machine Scheduling Problem under Bimodal Flexible and Periodic Availability Constraints

In single machine scheduling problems with availability constraints, machines are not available for one or more periods of time. In this paper, we consider a single machine scheduling problem with flexible and periodic availability constraints. In this problem, the maximum continuous working time for each machine increases in a stepwise manner with two different values allowed. Also, the durati...

Minimizing the Number of Tardy Jobs

Minimizing the Number of Tardy Jobs with Chance Constraints and Linearly Associated Stochastically Ordered Processing Times

We consider the single-machine sequencing model with stochastic processing times and the problem of minimizing the number of stochastically tardy jobs. In general, this problem is NP-hard. Recently, however, van den Akker and Hoogeveen found some special cases that could be solved in polynomial time. We generalize their findings by providing a polynomial solution for any stochastically ordered ...

Minimizing the Number of Tardy Jobs in a Permutation Flowshop Scheduling Problem with Setup Times and Time Lags Constraints

This paper studies the permutation flowshop scheduling problem with sequence dependent setup times and time lags constraints minimizing the number of tardy jobs. Dependent setup times are defined as the work to prepare the machines between two successive jobs. Time lags are defined as intervals of time that must exist between every couple of successive operations of the same job. Two mathematic...