The goal of finding an efficient way to transport goods from an origin node to a destination node has received help from mathematicians at The Hong Kong Polytechnic University.
Built into their mathematical models are ways to balance multiple but conflicting criteria such as time and monetary cost via optimally distributing scarce resources subject to certain constraints.

Dr Yang and a book he wrote from the research.

Principal Investigator Dr Xiao-qi Yang said the constraints could be on demands, the integral nature of the decision variables / fixed charge and some externally imposed restrictions on traffic flows.
Oriented from the Wardrop’s single criterion user-optimal equilibrium conditions in 1952, which suggests road users travel on a path with minimum time delay, the study of traffic equilibrium has been the subject of research for more than half a century.
In real life, many road users are concerned not only with minimum time delay, but also with monetary cost and how pleasant it is to drive on a particular path, said Dr Yang. Thus, traffic flow along a path joining origin and destination nodes in a road network is greater than zero only if the resulting multiple criteria objective is efficient among all the paths that join the pair of nodes.
Dr Yang and his researchers devised the mathematical model using a new approach to the problem, namely vector variational inequality.
The integral nature of the decision variables / fixed charge results in non-convexity in the mathematical formulation, where the classical linear Lagrangian technique cannot be applied.
Motivated by these observations, the researchers studied a general non-convex multiple criteria optimisation problem and used a nonlinear Lagrangian technique which, he said, allowed better duality representation of the multiple criteria optimisation problems involved.
Advancement in non-convex multiple criteria optimisation, said Dr Yang, will have a significant impact on improving the current practice of design, operation, and management in many fields of business and engineering.

Principal Investigator
Dr Xiao-qi Yang : mayangxq@polyu.edu.hk