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A Mathematical Programming Approach to Strategic Planning

Strategic Planning is often considered to be firmly in the domain of "soft" OR techniques such as Strategic Choice or Soft Systems Methodology. These are particularly appropriate in the early phases of Strategic Planning, i.e. in problem structuring, and where the planning relates to governmental or social issues.

In commerce and industry, however, there is a greater tendency to quantify issues, most obviously to draw up budgets and estimate the returns, and this makes "harder" techniques appropriate. The most widely used tools are, of course, spreadsheets, which are often complemented by sensitivity or risk analysis.

In some cases the planning may relate to many activities which are nominally separate but which are actually interconnected by financial or other constraints across the entire enterprise. For instance, there may be limits on:

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

In such a case, the spreadsheet can be used to check whether a master plan across the activities satisfies the constraints. But as options and constraints proliferate, it becomes increasingly hard to do this manually. This is where Mathematical Programming (MP) can play a valuable role. It does not supplant human judgement but is used as a tool to find combinations of plans which deserve further study.

This article is primarily concerned with strategic planning in the upstream oil industry, i.e. in planning the development of oilfields.

As well as the financial constraints which act across the enterprise, there are also constraints relating to the availability of development resources (e.g. numbers of wells which can be drilled in a year) and the infrastructure which is used to handle the oil produced (pipelines, separators, etc).

Although these are specific to the upstream oil industry, there were entirely analogous constraints in a strategic planning model which was developed for a large manufacturing company. In fact, the primary difference between the models lay in the complexity of the representation of the market for the manufactured product, as opposed to a straightforward price for a barrel of oil.

Nature of the Strategic Planning Problem

As far as an MP model is concerned, Strategic Planning involves deciding:

  • which out of a number of major projects should go ahead;
  • when they should be started;
  • which option should be pursued for a particular project.

For each project, forecasts are prepared of:

  • the streams of capital expenditure, operating expenditure and receipts;
  • the quantities of inputs required, e.g. new wells to be drilled, water for injection;
  • the quantities of outputs produced, e.g. oil, gas, water, extra pipeline capacity.

Typically there will be relationships between these, e.g. limits on the total capital expenditure or oil production in any year; cash flow requirements; limits on oil and gas separation and pipelines. Such relationships form the model of the system along with the objective, which is typically to maximise the Net Present Value.

Let us consider a very simple example. There are two fields, A and B, whose production capacity is as shown.

Production from the fields is delivered through a single pipeline whose transmission capacity is insufficient in years 7 and 8.

Slowing Down a Project

One special feature of oil resources planning is that, to a first approximation, production plans for a reservoir can be "slowed down". That is, if one has some combination of production plans which is otherwise ideal but which happens to exceed the production target in one year, it is possible to "slow down" the production plan for one reservoir for that year so that not all the production capacity is used. Nor is the production lost: "slowing down" does not affect the total quantity of oil which will be produced, only the point on the depletion curve where one happens to be at some particular time.

In fact, such a concept of "slowing down" a project is of wider applicability and was used in the model for the manufacturer. There it related to the development programme for a new product, whose launch would have to be postponed if fewer engineers were available to work on it. Whereas in the oil industry a barrel of oil which is delivered in 1998 is worth much the same as a barrel of oil delivered in 1997, this is not true of manufactured products. Market share is gained by being first with new features and if the launch of a product is delayed, the entire project may move from profit to loss.

Thus in addition to the decisions already described, a strategic planning model decides:

  • how much progress should be made on each project in each year.

It is this additional freedom to slow down a project which means that Mathematical Programming adds significant value to the decision-making process. Without it, it would be practicable to enumerate the combinations of options and select the best. Such solutions are, in any case, of limited value. To see why, consider what happens in our simple example if we are to satisfy the constraint on the transmission capacity of the pipeline.

The graph below shows what happens if we delay the start of development of Field B by 2, 4 or 6 years.

Although the peak in combined production lasts only two years, the shape of the production curves is such that we need to delay development of Field B by 6 years if we are to avoid exceeding the transmission capacity. Nor is it any better to delay Field A: the delay must also be 6 years and the Net Present Value is worse.

One way to improve the model would be to permit it to discard the excess production in years 7 and 8: it has less value than the cost of 6 years' delay to either Field A or Field B. But while this might be realistic here, it is not a good approach. There will be other occasions when the discarded resource has real value which we cannot afford to lose.

The alternative approach of explicitly permitting less than a full year's progress to be made in a year is much better. This is shown below.

With this, the optimal solution is for the development of Fields A and B both to start immediately. Less than the full production capacity is used in years 7 and 8. However, such production is not lost but can be drawn in future years before production from the fields becomes uneconomic.

Mathematical Programming can thus play a valuable role in Strategic Planning by helping to identify good combinations of plans, i.e. those which satisfy specified constraints. It is, however, only an aid to human decision-makers and complements other techniques rather than seeking to replace them.

Related articles include Mathematical Programming in the Oil Industry and Non-Linear Optimization Using Extensions to LP. To find other articles, refer to the MP in Action page.

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