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Readily available processing hardware and "off-the-shelf" (OTS) simulation software has made "high fidelity" first principles models of both steady and transient states, for both axial and centrifugal industrial compressors, relatively easy to construct. These high-fidelity models are finding their way into "real-time. digital twin" performance monitors, front-end engineering design, and post-design – pre-construction compressor performance evaluation. The compressor models are useful for reliably demonstrating the compressor and – to some degree, based on the complexity of the model – process response to various operating conditions. Once the model is constructed, it is trivial to run a "what-if" analysis of compressor performance to answer questions related to (a) recommendations or validation of the recycle/vent valve size and actuation speed, (b) general piping layout and sizing around the compressor, (c) and hot gas bypass requirements, to name a few. This paper takes a practical approach in discussing the compressor and process parameters necessary for building these dynamic "high-fidelity" industrial-compressor models. We identify compressor inputs and compressor responses that are faithfully modeled by first-principle equations available in the simulation software and those that typically require a compromise between an "ab initio" and data-fitting approximation. We discuss the simulation's tendency to overstate pressure excursions during surge events and understate the compressor operation in the "stonewall" region. We also discuss using the simulator software's compressor-stage enthalpy calculations to predict and quantify the compressor train reverse rotation. We use our broad experience and understanding of the compressor operation and simulation and our experience with the AVEVA™ Dynamic-Simulation "OTS" simulation software as the basis for this discussion.

The article presents the results of the study of specific features of retail networks and ways of taking into account these features in the formation of a comprehensive model of management of product transportation in the network. The proposed comprehensive model takes into account such features of the retail network as multiproduct situation, indistinguishability of suppliers and consumers, availability of transit points, cost of storage at the transit point, capacity of warehouses and their load, transportation time and shelf life, priority of outlets and types of products, restrictions on capacity of transport. The proposed model allows solving multiproduct transport problems for trading networks of varying complexity, enabling decision makers to change the complexity of the model.

The article presents the research results on the use of discrete principle of Pontryagin 's maximum for solving the task of investment distribution over time, with the purpose to obtain maximal profit. The given problem is examined as a task of optimal discrete process control for investment decision-making. The investment strategy provides for price risks. In the course of realization of the above investment strategy specific features of enterprise activity are analyzed subject to the production plan. The developed mathematical model enables to build the relationships between the investment decision making system elements under the price risks. Based on the proposed strategy, an optimal investment plan is developed. [ABSTRACT FROM AUTHOR]