Solving a class of network models for dynamic flow control

Abstract

In modeling flows and controls in transportation, distribution, communication, manufacturing systems, etc., it is often convenient to represent the system as a store-and-forward network. In such networks it is common for time, space, attention, or other resources, to be shared between sets of neighbouring nodes. For example, neighbouring nodes may share storage space, machine time, operating time, etc. The allocation of this shared resource among nodes determines a set of ‘controls’ on the network arc flows. We develop a multi-period network model which describes such storage and forwarding, and the sharing of resources (controls) between subsets of nodes. To solve the model we develop algorithms which take advantage of the embedded network structure of the problem. Each of the algorithms is based on iterating between (a) solving a least-cost capacitated network flow problem with fixed capacities (controls) and (b) solving a set of simple small scale problems to update these controls. In a series of computational experiments we found that an (‘unoptimized’) implementation of the algorithms performed between 13 and 42 times faster than a good linear programming code, which is the natural alternative. Also, by decomposing the problem, the algorithms make solving larger scale problems tractable, and are suitable for implementation on parallel processors.