On the optimal coordination of profit maximizing divisions using auctions and price theory

This dissertation argues that auctions can optimally coordinate subproblems arising from decentralized approaches to chemical engineering problems by viewing interactions between the subproblems as demands for limited resources. Auctions do this by finding prices over plant resources, like purity and heat content, which process units need in order to maximize their individual profits. A proof is presented that when auctions terminate with equilibrium prices --prices which balance the supply and demand of resources--the decisions that maximize individual profits maximize the overall profit of the entire system as well. There are, however, cases where equilibrium prices do not exist. One such instance occurs when some subproblems are described by linear programs. This dissertation describes why this problem exists, and it proves that a type of pseudo-equilibrium can be restored using a form of nonlinear pricing called augmented pricing . A more serious form of equilibrium failure occurs when one tries to coordinate divisions in chemical plants. Standard decomposition techniques like Lagrangean substitution have difficulty with these types of problems because the obvious way of defining interprocess resources is flawed. The difficulty can be overcome by defining resources properly. This leads to a new type of resource called slack resources --the absolute difference between what upstream and downstream divisions want the states of the interprocess streams to be. Slack resources restore the concept of equilibrium resource prices which in turn allows divisions in chemical plants to be optimally coordinated. Prices over slack resources provide a dollar measurement of the costs of divisional interaction. They can be used to design control systems which maximize dollar performance by balancing the costs of controller error and controller action throughout the plant. These cost-oriented control systems outperform generically designed control systems because the relative importance of the controllers is incorporated implicitly via the slack prices. Slack resource ideas can also be applied beyond process streams. Using the concept of courtesy constraints and generalized slack resources , plant divisions can express their preferences over anything in a chemical plant.