The decentralized profit maximization of interconnected production systems Part I. The theory of price coordination

The problem of the decentralized profit maximization of interconnected production systems is considered under the assumption that the problem may be posed as a separable static optimization of the set points of the system. In particular, the paper reviews the validity of decomposing the optimization problem by associating ‘ prices ’ with the interconnection product streams and investigates the unfortunate occurrence of duality gaps which makes the price method unreliable. The paper concludes by emphasizing the restrictive nature of currently known conditions to guarantee that duality gaps do not occur.