Scheduling a Proportionate Flow Shop of Batching Machines

TL;DR

This paper introduces polynomial-time algorithms for scheduling in a proportionate flow shop of batching machines, optimizing various performance metrics, which was previously only solved for two machines.

Contribution

It extends polynomial-time scheduling algorithms to any fixed number of machines in a proportionate flow shop with batching, including multiple optimization criteria.

Findings

Polynomial algorithms for makespan and total completion time.

Extension to minimize weighted total completion time, lateness, tardiness, and late jobs.

Applicable for any fixed number of machines with zero release dates.

Abstract

In this paper we study a proportionate flow shop of batching machines with release dates and a fixed number $m \geq 2$ 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.