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This paper presents a cooperative distributed model for the control of product flow in a network of cooperative inventory systems (ISs). In each IS, a linear input/output equation describes the balance between product demand vs production, as well as the product flows among ISs. The peculiarity of the problem is that both the production and demand are stochastic and cannot be controlled. In addition, each IS has just deterministic information on its inventory level (i.e., the quantity of stored product) which is not shared in the network. Other information is available in each IS regarding the forecast of both its related production and demand. The goal of the proposed model, on the overall network, is to keep both the product stored in each IS and the product exchanged among ISs, around given values as planned a priori. The only available control is related to the product flow between neighboring ISs, which has to be locally computed. Section II describes the proposed approach, which is based on the dual decomposition of the problem, which enables reaching the optimal control. This problem can represent the abstraction of a series of problems, which are not just related to logistics. As examples, section III presents two case studies: a network of virtual power utilities; and the control of risk in the transport of dangerous goods by road.

Distributed Product Flow Control in a Network of Inventories With Stochastic Production and Demand