A survey of algorithms for the single machine total weighted tardiness scheduling problem
Discrete Applied Mathematics - Southampton conference on combinatorial optimization, April 1987
Computers and Operations Research
A Multiple-Criterion Model for Machine Scheduling
Journal of Scheduling
Scheduling Problems with Two Competing Agents
Operations Research
Revisiting Branch and Bound Search Strategies for Machine Scheduling Problems
Journal of Scheduling
Multicriteria Scheduling: Theory, Models and Algorithms
Multicriteria Scheduling: Theory, Models and Algorithms
Multi-agent scheduling on a single machine to minimize total weighted number of tardy jobs
Theoretical Computer Science
Mixed integer programming formulations for single machine scheduling problems
Computers and Industrial Engineering
Competitive Two-Agent Scheduling and Its Applications
Operations Research
A two-machine flowshop problem with two agents
Computers and Operations Research
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We consider two single machine bicriteria scheduling problems in which jobs belong to either of two different disjoint sets, each set having its own performance measure. The problem has been referred to as interfering job sets in the scheduling literature and also been called multi-agent scheduling where each agent's objective function is to be minimized. In the first problem (P1) we look at minimizing total completion time and number of tardy jobs for the two sets of jobs and present a forward SPT-EDD heuristic that attempts to generate the set of non-dominated solutions. The complexity of this specific problem is NP-hard; however some pseudo-polynomial algorithms have been suggested by earlier researchers and they have been used to compare the results from the proposed heuristic. In the second problem (P2) we look at minimizing total weighted completion time and maximum lateness. This is an established NP-hard problem for which we propose a forward WSPT-EDD heuristic that attempts to generate the set of supported points and compare our solution quality with MIP formulations. For both of these problems, we assume that all jobs are available at time zero and the jobs are not allowed to be preempted.