Pareto optimization for the two-agent scheduling problems with linear non-increasing deterioration based on Internet of Things.

The Internet of Things (IoT) enables these objects to collect and exchange data and it is an important character of smart city. Multi-agent scheduling is one necessary part of Internet of Things. In this paper, we investigate the Pareto optimization scheduling on a single machine with two competing agents and linear non-increasing deterioration, which is Multi-agent scheduling problems often occurred in the Internet of Things. In the scheduling setting, each of the two competing agents wants to optimize its own objective which depends on the completion times of its jobs only. The assumption of linear non-increasing deterioration means that the actual processing time of a job will decrease linearly with the starting time. The objective functions in consideration are the maximum earliness cost and the total earliness. Two Pareto optimization scheduling problems are studied in this paper. In the first problem, each agent has the maximum earliness cost as its objective function. In the second problem, one agent has the maximum earliness cost as its objective function and the other agent has the total earliness as its objective function. The goal of a Pareto optimization scheduling problem is to find all Pareto optimal points and, for each Pareto optimal point, a corresponding Pareto optimal schedule. In the literature, the two corresponding constrained optimization scheduling problems are solved in polynomial time under the assumption that the inverse cost function of each job is available. In this paper, we extend these results to the setting without the availability assumption. Furthermore, by estimating the number of Pareto optimal points, we show that the above two Pareto optimization scheduling problems are solved in polynomial time. Hence, our results have much more theoretically meaningful constructs. Experimentation results show that the algorithms presented in this paper are efficient.