math.OCJan 10, 2026

Resource-constrained Project Scheduling with Time-of-Use Energy Tariffs and Machine States: A Logic-based Benders Decomposition Approach

Authors: Corentin Juvigny, Antonín Novák, Jan Mandík, Zdeněk Hanzálek

Organizations: Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague, Jugosl´avsk´ych partyz´an˚u 1580/3, 160 00, Prague 6, Czech Republic

Abstract

In this paper, we investigate the Resource-Constrained Project Scheduling Problem (RCPSP) with Time-of-Use (TOU) energy tariffs and machine states, a variant of RCPSP for production scheduling, where energy price is part of the criteria and one highly energy-demanding machine can be in one of the following three states: proc, idle, or off. The problem involves scheduling all tasks, respecting precedence constraints and resource limitations, while minimizing the combination of the overall makespan and the Total Energy Cost (TEC), which varies according to the TOU tariffs, which can take negative values. We propose two novel approaches to solve it: a monolithic Constraint Programming (CP) approach and a Logic-Based Benders Decomposition (LBBD) approach. The latter combines a master problem handling the energy cost solved using Integer Linear Programming (ILP) with a subproblem handling the RCPSP, resolved using CP. Both approaches outperform the monolithic compact ILP counterpart, but the LBBD significantly outperforms the monolithic CP in most cases, especially when the makespan criterion is not included in the objective function, solving to optimality instances with up to 480 tasks. Finally, we propose a way to generalize our LBBD approach to other problems sharing similar characteristics, and applied it to various problems, such as an RCPSP with blocking times & total weighted tardiness criterion, or a flexible job shop.

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