Resource Leveling: Complexity of a UET two-processor scheduling variant and related problems

TL;DR

This paper investigates a resource leveling variant of a two-processor scheduling problem, focusing on minimizing resource overload costs under deadline constraints, and explores the computational complexity of related problems.

Contribution

It introduces a polynomial algorithm for the resource leveling problem with deadline constraints and analyzes the complexity of related problems, extending existing scheduling methods.

Findings

Polynomial algorithm for resource leveling with deadlines

Complexity classification of related resource leveling problems

Comparison with classical scheduling problem complexities

Abstract

This paper mainly focuses on a resource leveling variant of a two-processor scheduling problem. The latter problem is to schedule a set of dependent UET jobs on two identical processors with minimum makespan. It is known to be polynomial-time solvable. In the variant we consider, the resource constraint on processors is relaxed and the objective is no longer to minimize makespan. Instead, a deadline is imposed on the makespan and the objective is to minimize the total resource use exceeding a threshold resource level of two. This resource leveling criterion is known as the total overload cost. Sophisticated matching arguments allow us to provide a polynomial algorithm computing the optimal solution as a function of the makespan deadline. It extends a solving method from the literature for the two-processor scheduling problem. Moreover, the complexity of related resource leveling problems sharing the same objective is studied. These results lead to polynomial or pseudo-polynomial algorithms or NP-hardness proofs, allowing for an interesting comparison with classical machine scheduling problems.