This is pretty much a mantra in project management, but what does it mean. It means that the person who set the parameters of the project, who worked out beforehand all the difficulties the project would face, either did a good job or a poor job. If you were the project manager, then the parameters were set just right. If you were the project owner, the parameters were set too slack and not enough pressure was put on the project team to perform.
If the project was very simple, buy and install equipment, put up a building just like one we did last year, then time and budget can be precisely calculated. The handover to the project team is typically a paper plan describing outcome, timeframe and budget, and may include a high level CPM plan. If the project is not simple, and may be hostage to the weather or there is development involved, then a range of budget is appropriate. This is done now in a simple way - the project owner can pay overruns out of petty cash or keeps a contingent sum hidden in reserve. This method is very crude - when should the reserve be released, will it just send good money after bad. If it is a building project with a highly predictable outcome, then a delay of six months on an asset with 40 years life is no big deal, and a yield falling from six percent to five and three quarters is tolerable if most of the money is already spent. Development projects have a much wilder swing in outcome, ranging from three times cost to outright failure.
For many development projects we should be moving towards a model of the project that recognises risks and variable outcomes, so "On time and under budget" means that, for the particular circumstances encountered, the project was well run. An active model of the project, linking cost, time, risks and outcome, allows every participant to understand what the project is about, and what the value of the outcome is to the project owner. The project manager and the project owner can decide together on the particular settings to be used in running the project, the "preferred outcome".
Unfortunately, some project managers even on the client side have a cost plus view of the world, so a plan showing a range of budget depending on risk and outcome turns into a plan whose budget is the highest figure given, irrespective of risk and outcome. The fixed and low budget was a useful bludgeon to keep the project on track and the project manager motivated, except that as soon as it was obvious the budget would be exceeded, the motivation may have turned into how big the variation could be. Rather than hiding the flexibility of the budget, a way has to be found of motivating the project manager not to overspend on the outcome. This is complicated by the fact that some project managers will underplan, it being more fun to fix up the inevitable problems on the fly. Part of this underplanning has been the inability of the planning tools to represent the interaction of complex factors. A Constraint Reasoning model does not have the limitations of CPM or spreadsheets, so an active CRM model reduces the possibility of underplanning.
CRM can make the Project Manager's job easier on difficult projects, while at the same time making it harder to hide lack of planning and forethought in crucial areas.