| Abstract: | The budget problem of selecting projects (or activities) with known values (or payoffs) and associated costs, subject to a prescribed maximum budget, is akin to the knapsack problem, which is well documented in the literature. The optimal solution to maximise the total value of selected projects for a given budget constraint can readily be obtained. In practice, budgets are often somewhat flexible, or subject to possible changes, so that an optimal solution for a given budget value may not remain optimal when the budget is modified. It is, therefore, sensible in many situations to consider a budget range, instead of a single budget value. In addition to their original objective of maximising the total value of selected projects, decision makers are often concerned to get ‘value for money’, indicated by the ratio of payoff to cost. This paper examines how these questions can be tackled through the introduction of a stability index, to guide project selection within a defined budget range, and the use of a portfolio diagram, to help in the ranking of projects with respect to the stated twin objectives. |
