An extension of the general lot-sizing and scheduling problem (GLSP) with time-dependent energy prices

The demand for electrical power in industrial production processes often leads to increasing energy costs for companies. In the course of a more sustainable power generation in the future, companies are faced with time-dependent energy prices, which have the potential to influence energy costs significantly. In order to manufacture the products at minimal decision-relevant total costs, planning approaches for production scheduling have to consider energy costs. To date, time-dependent energy prices are only considered in few production planning approaches in the field of job-shop scheduling and in some individual planning approaches in the field of simultaneous lot-sizing and scheduling. Up to now, a general model formulation for the consideration of time-dependent energy prices in lot-sizing and scheduling and an investigation of appropriate conditions for an energy-oriented production planning is missing. In this contribution, the energy-oriented general lot-sizing and scheduling problem is introduced as an extension of the respected general lot-sizing and scheduling problem. The cost saving potential is analyzed by considering energy in the lot-sizing and scheduling problem compared to classical planning approaches and appropriate frame conditions are investigated within a structured parameter analysis. In the numerical study, this leads to a total cost saving potential about 1.04% and an energy cost saving potential about 9.69%. In particular, a high volatility of the energy prices and a direct transfer of this volatility in form of short periods of constant energy prices increase this cost saving potential.