ABSTRACT
Planning over the total project duration may be simplified by considering the project to be composed of stages (or phases). The planning problem then becomes a multistage optimal control problem or multistage decision problem. Various optimal control tools are available to assist, including Pontryagin’s maximum principle, dynamic programming and mathematical programming. Controls are chosen for each stage to give a globally optimum solution
over the whole project. The controls considered in this chapter relate to resources and resource production rates only, that is the lower level problems in the context of Chapter 5. The work method is assumed given or fixed. The synthesis problem involving work method as controls is very difficult; in the comparative area of structural optimisation, only Michell structure results have evolved. States are chosen as cumulative resource (or money) usage and cumulative
production. The single objective case is given. Stages may be chosen to match the type of work, convenient time period
divisions in the project, or in an arbitrary sense. Hold or approval points might be used to distinguish stages. Breaking down the project into stages is equivalent to discretising the project duration interval. This chapter is dealing with planning over the whole project duration
using stages. Replanning is also carried out according to stages or at discrete points in time, but this follows from the nature of what replanning is. Parts of this chapter follow Carmichael (2004).
