Industrial applications nowadays are facing the complexity of the problem of finding an optimal energy supply composition. Heating and electricity needs vary throughout a year and need to be addressed. There is usually power available from the market, but a company has other investment options to consider, such as solar power, or utilization of local biomass. Fixed and proportional investment and operational costs must be compared to long-term cost-efficiency. The P-Graph framework is an effective tool in the design and synthesis of process networks, and is capable of showing optimal decisions. In the present work, a new P-Graph model was implemented to address the synthesis of the energy supply options of a manufacturing plant in Hungary. Compared to the original approach, a multi-periodic scheme was applied for heating and electricity demands. Also, the pelletizer and biogas plant investments are modeled in the P-Graph with a new technique that better reflects equipment capacities and flexible input ratios. The best solutions in this case study in terms of total costs are listed. It can be concluded that a long-term investment horizon is needed for the incorporation of sustainable energy sources into the system to be cost-efficient.

The P-Graph framework is an efficient tool that deals with the solution of Process Network Synthesis (PNS) problems. The model uses a bipartite graph of material and operating unit nodes, with arcs representing material flow. The framework includes combinatorial algorithms to identify solution structures, and an underlying linear model to be solved by the Accelerated Branch and Bound algorithmic method. An operating unit node in a P-Graph consumes its input materials and produces its products in a fixed ratio of operation volume. This makes it inadequate in modeling such real-world operations where input composition may vary, and may also be subject to specific constraints. Recent works address such cases by directly manipulating the generated mathematical model with linear programming constraints. In this work, a new general method is introduced which allows the modeling of operations with flexible input ratios and linear constraints in general, solely by tools provided by the P-Graph framework itself. This includes representing the operation with ordinary nodes and setting up their properties correctly. We also investigate how our method affects the solution structures for the PNS problem which is crucial for the performance of algorithms in the framework. The method is demonstrated in a case study where sustainable energy generation for a plant is present, and the different types of available biomass introduce a high level of flexibility, while consumption limitations may still apply.

A mathematical model is introduced to solve a mobile workforce management problem. In such a problem there are a number of tasks to be executed at different locations by various teams. For example, when an electricity utility company has to deal with planned system upgrades and damages caused by storms. The aim is to determine the schedule of the teams in such a way that the overall cost is minimal. The mobile workforce management problem involves scheduling. The following questions should be answered: when to perform a task, how to route vehicles—the vehicle routing problem—and the order the sites should be visited and by which teams. These problems are already complex in themselves. This paper proposes an integrated mathematical programming model formulation, which, by the assignment of its binary variables, can be easily included in heuristic algorithmic frameworks. In the problem specification, a wide range of parameters can be set. This includes absolute and expected time windows for tasks, packing and unpacking in case of team movement, resource utilization, relations between tasks such as precedence, mutual exclusion or parallel execution, and team-dependent travelling and execution times and costs. To make the model able to solve larger problems, an algorithmic framework is also implemented which can be used to find heuristic solutions in acceptable time. This latter solution method can be used as an alternative. Computational performance is examined through a series of test cases in which the most important factors are scaled.