Efficient Heuristics for Total Completion Time and Maximum Lateness Bicriteria Scheduling Problems

This paper considers the bicriteria scheduling problem of minimizing the total completion time and maximum lateness with zero release dates. The problem is NP hard, though Early Due Date (EDD) and Shortest Processing Time (SPT) rules yielded optimal solutions for maximum lateness and total completion time, respectively if each criterion were to be considered singly. Thus, the values of each of the criteria for the two proposed heuristics; SII and PI were compared to the optimal solution of the sub problems. Results of computational experiment on job sizes varies from 5-100 jobs showed that the two proposed solution methods yielded results not significantly different from the optimal. This is because the two heuristic yielded results not significantly from the optimal sub-problems for the two performance measures at 95% significant level.

New Solution Methods for Single Machine Bicriteria Scheduling Problems: Minimizing the Total Flowtime and Maximum Tardiness with Zero Release Dates

This paper considers the bicriteria scheduling problem of minimizing the maximum tardiness and total flowtime on single machine with zero release dates. The problem is NP hard, though Early Due Date (EDD) and Shortest Processing Time (SPT) rules yielded optimal solutions for maximum tardiness and total flowtime, respectively if each criterion were to be considered singly. Thus, the values of each of the criteria for the two proposed heuristics; AA and SA were compared to the optimal solution of the sub problems. Results of computational experiment on job sizes varies from 5-150 jobs showed that the SA heuristic is preferred over AA. This is because the heuristic SA yielded maximum tardiness and total flowtime not significantly different from the EDD and SPT results, respectively at 99% significant level. Though AA yielded optimal for total flowtime, the maximum tardiness results is significantly different from the EDD results.

Bicriteria scheduling for due date assignment with total weighted tardiness

In the due date assignment, the bicriteria scheduling models are motivated by the trade-off between the due date assignment cost and a performance criterion of the scheduling system. The bicriteria scheduling models related to the maximum tardiness and the weighted number of tardy jobs have been studied in the literature. In this paper we consider a new model with criteria of the due date assignment cost and the total weighted tardiness. The main results are polynomial-time algorithms for the linear combination version, the constraint version, and the Pareto optimization version of bicriteria scheduling.