Resource-constrained scheduling with optional recycling operations

• A new variant of resource-constrained scheduling problem is introduced.
• The concept of optional operations is proposed.
• Complexity status of the problem is discussed.

This paper introduces a scheduling problem with a variant of resource constraint that stems from a relocation project. We also propose the concept of optional recycling operations, in which recycling operations are separated from the processing of jobs and recycling operations are exercised only when necessary. An integer program is proposed to formulate the problem and facilitate complexity classification. We propose a pseudo-polynomial time dynamic program, and then classify the complexity status of several restricted cases.