Proportionate Flow Shop Scheduling with Two Competing Agents to Minimize Weighted Late Work and Weighted Number of Late Jobs

We investigate a competitive two-agent scheduling problem in the setting of proportionate flow shop, where the job processing times are machine-independent. The scheduling criterion of one agent is to minimize its total weighted late work, and the scheduling criterion of the other agent is to minimize its total weighted number of late jobs. The goal is to find the Pareto-optimal curve (i.e., the set of all Pareto-optimal points) and identify a corresponding Pareto-optimal schedule for each Pareto-optimal point. An exact pseudo-polynomial-time algorithm and an [Formula: see text]-approximate Pareto-optimal curve are designed to solve the problem, respectively.

Scheduling a proportionate flow shop of batching machines

In this paper we study a proportionate flow shop of batching machines with release dates and a fixed number $$m \ge 2$$ m ≥ 2 of machines. The scheduling problem has so far barely received any attention in the literature, but recently its importance has increased significantly, due to applications in the industrial scaling of modern bio-medicine production processes. We show that for any fixed number of machines, the makespan and the sum of completion times can be minimized in polynomial time. Furthermore, we show that the obtained algorithm can also be used to minimize the weighted total completion time, maximum lateness, total tardiness and (weighted) number of late jobs in polynomial time if all release dates are 0. Previously, polynomial time algorithms have only been known for two machines.

Proportionate Flow Shop Scheduling with Rejection

We consider the problem of scheduling [Formula: see text] jobs with rejection on a set of [Formula: see text] machines in a proportionate flow shop system where the job processing times are machine-independent. The goal is to find a schedule to minimize the scheduling cost of all accepted jobs plus the total penalty of all rejected jobs. Two variations of the scheduling cost are considered. The first is the maximum tardiness and the second is the total weighted completion time. For the first problem, we first show that it is [Formula: see text]-hard, then we construct a pseudo-polynomial time algorithm to solve it and an [Formula: see text] time for the case where the jobs have the same processing time. For the second problem, we first show that it is [Formula: see text]-hard, then we design [Formula: see text] time algorithms for the case where the jobs have the same weight and for the case where the jobs have the same processing time.