The production schedule has a direct impact on the periodic utilization and energy consumption of equipment units. Meanwhile, for companies operating small power plants, the available renewable solar or wind energy changes continuously during the day, as does the hourly market price of the energy that can be purchased. Fortunately, the flexibility of production, possible schedules, or alternative recipes allow not only the minimization of costs but also the maximum use of renewable resources. The novelty of the P-graph-based method proposed here is the integration of three component problems into a single optimization model, namely the production scheduling by discrete event formulation, the management of flexible recipes by process synthesis, and the maximal renewable energy utilization according to discrete-time energy production and market price forecasts by representing them with temporarily available resources. The challenge of formalizing the optimization problem lies in synchronizing the time model of production scheduling with the resolution of market price and renewable energy production forecasts. The results show that the flexibility to alter both the sequence and schedule of operations by the integrated optimization model plays a critical role in optimizing energy usage.

Optimal clean process design requires strict constraints to enforce waste and byproduct management, all of which can be formulated in the language of mathematical programming. However, waste management and the utilization of by-products are often carried out in locations or periods other than the production process. The paper describes all modeling steps by P-graphs sufficient to represent raw material availability and production capacities in multiple time periods at multiple sites, as well as transportation and storage capacities of process materials and wastes. These steps are integrated into a single comprehensive model generation algorithm. For easier understanding, each model generation step is illustrated by a case study of planning a multi-site multi-period furniture production process alongside the recent challenges of energy supply and waste management. Finally, the case study of furniture production is analyzed under various circumstances to highlight the power of the proposed tools in daily production and transportation planning. Accordingly, the proposed method provides such alternative 5 best manufacturing and logistics plans that, in the event of a complete failure or overloading of one of the production capacities at either locations, there is still an alternative plan within a 3% profit decrease.