The network maintenance problem

In this research, we describe an optimization problem motivated by the need to maintain infrastructure net-works over time. We consider infrastructure networks in which product is transported between distinct origin-destination pairs, and at the same time the infrastructure assets need to be maintained by resources moving in the network. In order to perform maintenance the assets have to be shut down from time to time thus reducing the system capacity for those time periods. The objective is to maximize the total transported product by aligning the maintenance activities appropriately. This problem combines flow maximization with maintenance scheduling capturing some important aspects of the motivating practical problem: (1) the interaction between utilization of network assets such as nodes and arcs and their maintenance demands, (2) the limited resources available to perform the maintenance, and (3) the time for moving the maintenance resources between different locations in the network. Depending on the application context, there are a number of natural ways to reflect these in a mathematical model, and this gives rise to a rich and challenging optimization problem which we call the network maintenance problem. We formally introduce the problem, and present a mixed integer programming formulation. Next, we consider the case of a single commodity and a single maintenance resource when the network is a single path. We describe a polynomial time algorithm which, under some simplifying assumptions, solve the single path case to optimality. The problem becomes more challenging when the simplifying assumptions are dropped.