Energy efficiency is rarely reflected in the scheduling problem statements, and the cost of energy has become even more relevant due to the consequences of the energy crisis. It typically adds another dimension to the scheduling problem [MOD] and/or introduces nonlinearity into the problem [BUK]. We will study state-aware resource models with time-dependent energy costs. Exploiting the Time-Of-Use (TOU) tariffs to reduce energy costs (the price can even fall to negative values, see [OTE]) and using the power-saving states to lower the energy consumption of the machines are two crucial aspects of energy-aware scheduling. The effect of the optimization becomes much more significant when both aspects are considered jointly. The benefits of such a synergy were demonstrated in [BEN]. The problem becomes even more interesting when the company possesses volatile energy sources (like solar panels) and energy accumulators (like batteries or boilers).

Classical scheduling models of resources are too simplistic to be used for energy optimization since their description does not capture the processing modes of the machines or system dynamics that need to be considered to achieve the actual energy savings. Therefore, we will propose and investigate the properties of discrete (e.g., state diagrams) and continuous (e.g., differential equations) state-aware resource models in the scheduling theory. Furthermore, we will investigate the jobs with time-dependent processing costs, as these naturally arise from the formulations of problems assuming TOU, and maximum consumption diagrams. We will study the effects of these extensions on the computational complexity of the problems, algorithm design, and their experimental scalability.

Incorporating the dynamics of the machines into scheduling problems is a promising research area, as it can significantly decrease energy consumption due to a more accurate system model. We would formulate the problem using MIP or CP and solve it using general solvers or a custom exact algorithm with convex relaxations. If the performance of such algorithms will not be sufficient, we will resort to using heuristics, matheuristics or metaheuristics to solve industrial-sized problems.

About the group: The Industrial Informatics Department, led by Zdenek Hanzalek, is oriented towards scheduling, combinatorial optimization, and automated cars. The group collaborates strongly with high-tech companies (CEZ – Czech Energy Group, Porsche Engineering Services, EATON, Skoda Auto, ST Microelectronics, Volkswagen, DHL, …).

[BEN] Benedikt, O. - Modos, I. - Hanzalek, Z.: Power of Pre-Processing: Production Scheduling with Variable Energy Pricing and Power-Saving States, Constraints, Vol. 25, Iss. 3-4, Nov 2020, Pages 300–318.

[MOD] Modos, I. - Šůcha, P. - Hanzálek, Z.: Algorithms for robust production scheduling with energy consumption limits, Computers & Industrial Engineering, Vol. 112, Oct 2017, Pages 391-408

[BUK] Bukata, L. - Šůcha, P. - Hanzálek, Z. - Burget, P.: Energy Optimization of Robotic Cells, IEEE Transactions on Industrial Informatics, Vol. 13, Issue 1, Feb 2017, Pages 92-102

[OTE] https://www.ote-cr.cz/en/short-term-markets/electricity/intra-day-marke…