High Multiplicity Scheduling with Switching Costs for few Products

TL;DR

This paper investigates a complex single-machine scheduling problem with switching costs and high multiplicity, demonstrating that even simple cases become challenging, and provides solutions for one and two products.

Contribution

It introduces a high multiplicity variant of the scheduling problem with switching costs and offers solutions for small cases, highlighting increased complexity.

Findings

High multiplicity and switching costs increase problem complexity.

Solutions are provided for cases with one and two products.

Even trivial instances become non-trivial under these conditions.

Abstract

We study a variant of the single machine capacitated lot-sizing problem with sequence-dependent setup costs and product-dependent inventory costs. We are given a single machine and a set of products associated with a constant demand rate, maximum loading rate and holding costs per time unit. Switching production from one product to another incurs sequencing costs based on the two products. In this work, we show that by considering the high multiplicity setting and switching costs, even trivial cases of the corresponding "normal" counterparts become non-trivial in terms of size and complexity. We present solutions for one and two products.