Most organisations engage in some form of planning. It involves making projections of what might happen and considering the actions which might be taken to influence outcomes. The projections often include numerical estimates which make it possible to compare one scenario against another. Businesses usually transform these estimates to financial costs and benefits and to measures such as Net Present Value.

The most widely used tool for planning is, of course, the spreadsheet. It can be used both for the analysis of an individual scenario and for sensitivity and risk analysis. In some cases the activity to be planned may itself be highly complex and involve many inter-related decisions, e.g. the operation of an oil refinery. In other cases each individual activity may be nominally separate but there may be interconnections across the entire enterprise. For instance, there may be limits on:

• cash flow;
• profitability;
• research and development resource.

In such cases, the planning problem may go beyond what can be analysed directly in a spreadsheet. It is as options and constraints proliferate that a systematic approach to analysis comes into its own. This is where mathematical optimization can play a valuable role. It does not supplant human judgement but serves as a tool to find good solutions which are worthy of further analysis.

Planning and scheduling problems are not really distinct but shade into one another. They are aspects of a larger problem which is broken down into parts so that it can be analysed. These parts form a hierarchy, with decisions from one level cascading down to become fixed data for the next. The timescale for planning problems is longer, between, say, 10 years for strategic planning and 3 months for operational planning. Problems concerned with the next month or two are more often described as scheduling and this terminology applies down to a timescale of a day. Below this one is into the world of process control, with real-time control operating on a timescale of seconds.

Just as the timescale of planning and scheduling problems varies, so does the focus. Over 5 - 10 years the focus tends to be global while over 1 - 2 years it is regional and over 3 - 6 months local. Conversely, the level of detail tends to increase as the timescale decreases, as models need to capture aspects of behaviour which are important over the shorter timescale.

More information about planning problems can be found in A Mathematical Programming Approach to Strategic Planning, Planning and Scheduling in Oil Refineries and Prize-Winning Planning at Harris Semiconductors.