The Sharing Problem

Many important problems are concerned with the equitable distribution of resources. A new approach to resource distribution problems is presented as a network flow problem with a maximum objective function. The value of the smallest linear tradeoff function at the terminal points in a capacitated network is maximized. We develop a polynomially bounded algorithm and give computational experience. We illustrate the importance and usefulness of the sharing-problem model by considering the equitable distribution of coal during a prolonged coal strike.