Minimizing total tardiness on one machine is NP-hard
Mathematics of Operations Research
A note on scheduling on a single processor with speed dependent on a number of executed jobs
Information Processing Letters
A Multiple-Criterion Model for Machine Scheduling
Journal of Scheduling
Scheduling Problems with Two Competing Agents
Operations Research
A note on the scheduling with two families of jobs
Journal of Scheduling
Multi-agent scheduling on a single machine to minimize total weighted number of tardy jobs
Theoretical Computer Science
Some scheduling problems with sum-of-processing-times-based and job-position-based learning effects
Information Sciences: an International Journal
A new approach to the learning effect: Beyond the learning curve restrictions
Computers and Operations Research
Computers and Industrial Engineering
Some scheduling problems with general position-dependent and time-dependent learning effects
Information Sciences: an International Journal
Solution algorithms for the makespan minimization problem with the general learning model
Computers and Industrial Engineering
Single-machine and flowshop scheduling with a general learning effect model
Computers and Industrial Engineering
Scheduling problems with deteriorating jobs and learning effects including proportional setup times
Computers and Industrial Engineering
Genetic algorithms for a two-agent single-machine problem with release time
Applied Soft Computing
Uniform parallel-machine scheduling to minimize makespan with position-based learning curves
Computers and Industrial Engineering
A tabu method for a two-agent single-machine scheduling with deterioration jobs
Computers and Operations Research
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In traditional scheduling, job processing times are assumed to be known and fixed over the entire process. However, repeated processing of similar tasks improves workers' skills. In fact, scheduling with learning effects has received considerable attention recently. On the other hand, it is assumed that there is a common objective for all the jobs. In many management situations, multiple agents pursuing different objectives compete on the usage of a common processing resource. In this paper, we studied a single-machine two-agent scheduling problem with learning effects where the objective is to minimize the total tardiness of jobs from the first agent given that no tardy job is allowed for the second agent. A branch-and-bound algorithm incorporated several properties and a lower bound is developed to search for the optimal solution. In addition, two heuristic algorithms are also proposed to search for the near-optimal solutions. A computational experiment is conducted to evaluate the performance of the proposed algorithms.