Joint replenishment meets scheduling

TL;DR

This paper studies a combined problem of joint replenishment and single machine scheduling with release dates, analyzing complexity and online competitiveness for minimizing costs and scheduling criteria.

Contribution

It introduces a new integrated model for joint replenishment and scheduling, providing complexity results and competitive analysis for online algorithms.

Findings

Complexity results for offline problem.

Competitive ratios for online variants.

Insights into cost and scheduling trade-offs.

Abstract

In this paper we consider a combination of the joint replenishment problem (JRP) and single machine scheduling with release dates. There is a single machine and one or more item types. Each job has a release date, a positive processing time, and it requires a subset of items. A job can be started at time $t$ only if all the required item types were replenished between the release date of the job and time point $t$. The ordering of item types for distinct jobs can be combined. The objective is to minimize the total ordering cost plus a scheduling criterion, such as total weighted completion time or maximum flow time, where the cost of ordering a subset of items simultaneously is the sum of a joint ordering cost, and an additional item ordering cost for each item type in the subset. We provide several complexity results for the offline problem, and competitive analysis for online variants with min-sum and min-max criteria, respectively.