The Optimal Allocation of Resources to a Variable Timetable

In this note we describe a programming method for allocating resources to a variable timetable. It is illustrated in terms of a restricted version of a general programming model for resource allocation to a CPA network, but it can be used for more general versions of the CPA model, and for the scheduling of ships, aeroplanes, buses and so on. It makes use of the standard trans-shipment transportation problem framework, although in practice the assignment matrix need not be constructed. A highly efficient initial solution is obtained first, then optimized via a primal method of dealing with the "either-or" constraints which arise because of the variability in the timetable.