A Multivariate Complexity Analysis of the Material Consumption Scheduling Problem

by   Matthias Bentert, et al.

The NP-hard MATERIAL CONSUMPTION SCHEDULING Problem and closely related problems have been thoroughly studied since the 1980's. Roughly speaking, the problem deals with minimizing the makespan when scheduling jobs that consume non-renewable resources. We focus on the single-machine case without preemption: from time to time, the resources of the machine are (partially) replenished, thus allowing for meeting a necessary pre-condition for processing further jobs, each of which having individual resource demands. We initiate a systematic exploration of the parameterized (exact) complexity landscape of the problem, providing parameterized tractability as well as intractability results. Doing so, we mainly investigate how parameters related to the resource supplies influence the computational solvability. Thereby, we get a deepened understanding of the algorithmic complexity of this fundamental scheduling problem.


page 1

page 2

page 3

page 4


Parallel Machine Scheduling with a Single Resource per Job

We study the problem of scheduling jobs on parallel machines minimizing ...

Hardness of Interval Scheduling on Unrelated Machines

We provide new (parameterized) computational hardness results for Interv...

Single Machine Batch Scheduling to Minimize the Weighted Number of Tardy Jobs

The 1|B,r_j|∑ w_jU_j scheduling problem takes as input a batch setup tim...

Inapproximability Results for Scheduling with Interval and Resource Restrictions

In the restricted assignment problem, the input consists of a set of mac...

Parameterized Complexity of Problems in Coalitional Resource Games

Coalition formation is a key topic in multi-agent systems. Coalitions en...

Single-machine scheduling with an external resource

This paper studies the complexity of single-machine scheduling with an e...

A Fast Exact Algorithm for Airplane Refueling Problem

We consider the airplane refueling problem, where we have a fleet of air...