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In the field of industrial engineering and business logistics, project planning with resource constraints has become a critical challenge when incorporating dynamic variables such as time-of-use (TOU) electricity tariffs. This problem, known as RCPSP with variable energy costs, seeks to simultaneously minimize the total project duration (makespan) and energy expenditure, even allowing certain electricity prices to be negative during periods of low demand. Traditionally, it was addressed with integer linear programming, but more powerful approaches such as logic-based Benders decomposition (LBBD) have proven to be far more efficient, solving instances with hundreds of tasks. The key lies in separating the problem into a master problem that optimizes electricity cost using integer linear programming and a subproblem that handles precedence and resource constraints using constraint programming. This hybrid architecture leverages the strengths of each technique and can be generalized to other contexts, such as flexible workshops or time blockages.
For companies seeking to implement advanced planning solutions, having custom applications that incorporate these algorithms is decisive. At Q2BSTUDIO, we develop custom software that integrates artificial intelligence and combinatorial optimization techniques to address complex scheduling problems. Our teams design AI agents capable of learning consumption patterns and proposing production schedules that reduce costs without compromising deadlines. Furthermore, we deploy these systems on AI for businesses in secure cloud environments (AWS and Azure cloud services), ensuring scalability and data protection through comprehensive cybersecurity. Integration with business intelligence tools, such as Power BI, allows real-time visualization of the impact of decisions on energy cost and productivity. In this way, we transform mathematical theory into real competitive advantages for our clients.
