Competitive multi-agent scheduling with an iterative selection rule

In this work we address a class of deterministic scheduling problems in which k agents compete for the usage of a single machine. The agents have their own objective functions and submit their tasks in successive steps to an external coordination subject, who sequences them by selecting the shortest task in each step. We look at the problem in two different settings and consider different combinations of cost functions. In a centralized perspective, generalizing previous results for the case with k=2 agents, we characterize the set of Pareto efficient solutions as for a classical multicriteria optimization problems. On one hand we determine the number of Pareto efficient solutions and on the other hand we study the computational complexity of the associated decision problem. Then, we consider the problem from a single agent perspective. In particular, we provide a worst-case analysis on the performance of two natural heuristic algorithms, SPT and WSPT, that suggest to an agent how to sequence its own tasks when its objective is makespan, sum of completion times, or sum of weighted completion times.