Project portfolio optimisation and scheduling using temporal tolerances

Abstract

In financial portfolio optimisation, there is a hitherto agreed definition of the value of a particular series of investments, this being financial returns. When one considers applying the machinery of portfolio optimisation in Defence, the objective is to select and schedule a subgroup of projects. Such projects are drawn from a larger pool, typically extant and new projects. There is no fiscal “return, ” as projects are public goods. Each project must be assigned a value depending on its potential start time. Ideally each project has two attributes, a vector of starting-time dependent values and a vector of costs which commence from the project starting time. The optimised portfolio ensemble must meet time-dependent budget constraints. The optimisation formalism is that of a multiple knapsack problem and the methods of integer programming apply. In practice forming starting-time project values is contentious. Unlike financial portfolio theory, there is no agreed approach to value determination, as there is no analogy to currency. It is this issue that drives the approach developed here. The starting-time values for projects are elicited through a specific pre-defined time-dependent functional form of value. The parameters of this functional form are then derived by asking what is the ideal project starting-time and how tolerant is the subject matter expert of that time? By doing this, one introduces an agreed currency for projects, deviance from this ideal time. This pre-defined functional form of the starting-time values, is called in this paper a temporal tolerance function. In this paper the multi-knapsack problem is explored with temporal tolerance starting-time value functions. In Section 1 the issue of determining the value of the public good's military capability is discussed. In Section 2 then describe the multiple-knapsack problem and introduce a number of temporal tolerance functions. In Section 3 computational experiments are conducted with such functions to determine portfolio structure properties, such as optimised value and time deviance as tolerance levels change. Finally in Section 4 the paper is summarised and the general problem understanding the statistics of project selection, as a function of cost structure and value function structure is discussed.