Enterprises, such as energy management, supply chain management, transportation and disaster management are complex engineering systems. Decision makers struggle to reduce costs and increase efficiencies in the face of uncertainty and complicated interactions among a large number of agents. Traditional optimization approaches that rely on static mixed integer programming models cannot accurately capture the complexities of the dynamic enterprise and are limited by computational complexity.
We propose a novel approach to integrate rule-based systems with optimization to dynamically control modern enterprises. By allowing decision makers to model their complex enterprise with if-then rules, we will enable them to accurately reflect the real-life environment and to easily modify the rules to capture unexpected changes in the system. We will consider one of several potential application areas. One area is the transmission and distribution of electrical power, where rules or protocol are used to decide how to distribute power reserves to accommodate uncertainties in the power market (due to weather, power outage, demand, etc.). Another possible application area is transportation management, where vehicle routing and scheduling must respond to dynamic pick-up and delivery requests that consider traffic, truck maintenance, and personnel. We may also test our rule-based methodology with disaster management teams, including medical providers and fire departments, to design protocols for efficient responses to disasters.
Current approaches to optimizing enterprise systems are limited by their ability to accurately model a complex system, as well as the computational limitations to solve NP-hard problems. The intellectual merit of our approach lies in developing a mathematical scheme that converts rules of an enterprise to an automaton, which provides the dynamics of the rules. That allows us to solve an optimal control problem. We translate the solution back into the rules of the application via the automaton. This research will contribute to computer science, applied math and operations research communities by creating a new hybrid methodology. Our approach is transformative in that it can apply to virtually any enterprise, and provides the decision makers with rules in their own natural language. Its broad impact resides in the potential to provide a new hybrid methodology for combinatorial type enterprise problems, such as routing, sequencing and scheduling, that currently rely on mixed integer programs and heuristics. In our research and education missions, we are committed to fostering diversity and will recruit and mentor underrepresented students.
Modern enterprises are complex systems that are dynamically evolving as the environment around them changes. Due to their complex interdependencies, inherent uncertainties, dynamic adaptation, and multiple objectives, it is difficult to design and control these complex systems with traditional optimization and control models. However, these enterprise systems can be expressed by straightforward rules or protocols that can be easily changed by decision makers. Our research has developed a methodology and new technology to integrate rule-based complex systems with optimization to dynamically control modern enterprises. We have proven that it is possible to transform a rule-based system into a dynamical system, apply optimization procedures, and then map the solution back into the rules space. Because of the one-to-one relationship between first order logic and automata theory, we have been able to design rule-based feedback laws and rule-based predictors for enterprise systems. This provides the decision maker with optimal rules or policies to design and control their complex system. Many enterprise systems can benefit by having flexible rule-based models that can quickly adapt as streams of data indicate changes in the environment. Examples of such enterprise systems include: production, scheduling, inventory, demand forecasting, dispatching, and pricing. We have explored the application of our methodology in supply chain management and power systems with renewable energy sources. The problems that we are attacking are notoriously ill-posed: they do not have a mathematical closed-form expression, they do not have smoothness or differentiability properties, they are not convex, and they are not compact. Further, constraints are expressed purely by membership rules. This makes the problems intractable with current methodologies. Our methodology, on the other hand, provides a translation from rules to a formulation as an optimal control problem for which there exist efficient numerical methods. The primary figure illustrates our architecture replacing a classic forecaster and controller with a rule-based forecaster and controller providing a rule-based feedback loop. Our new computational techniques demonstrate the viability of our rule-based approach to efficiently approximate and optimize the dynamic behavior of large-scale enterprise systems that rely on rules for their operations. Our work is transformative because our algorithms can improve the efficiency of many classes of applications in industry, particularly applications in which the knowledge about the behavior of the system is empirical or phenomenological. It is also transformative because our new technology allows the users to take advantage of their expertise combined with the power of our method to extract optimal strategies that were previously unreachable.
