Approximate and exact approaches to energy-aware job shop scheduling with dynamic energy tariffs and power purchase agreements

With the goal of strategically analyzing energy tariff structures and operationally establishing energy-aware production schedules, we develop approximate and exact methods for generating energy-efficient Pareto schedules in job shop environments. Energy costs are influenced by dynamic market prices and available fixed tariff contracts. In this context, power purchase agreements (PPAs) have recently emerged to support renewable energy generation, guaranteeing a fixed price for a specified amount of renewable energy sold to industrial customers. To integrate energy-related aspects, we extend the job shop setting by machine states, energy sources, carbon emissions, energy consumption, and time-dynamic energy tariffs. We develop a time-indexed mathematical programming formulation integrated into the ϵ-constraint method to achieve Pareto efficiency concerning production makespan and energy costs minimization. Our research addresses the challenges of integrating energy market characteristics with production scheduling, tackling nonlinearity and time dynamics while managing NP-hardness of energy-aware job shops. Key contributions include developing a model-based methodology for optimizing energy-aware schedules, integrating this approach within an algorithmic framework for determining Pareto schedules, and creating a decision-making workflow for analyzing energy tariffs. In particular, this facilitates an analysis of the largely unexplored PPA tariff. Using 2023 energy price data from the European Network of Transmission System Operators for Electricity (ENTSO-E), we provide extensive numerical experimentation to analyze trade-offs related to schedule determination, energy price data, PPA and tariff specifications, and working time restrictions. This provides insights into the interplay between tariff selection and production scheduling, relevant to the strategic financing and operational management of energy-aware production systems.