Department of Management Science & Engineering

Number 11/Spring 2003

Investment Science Newsletter

By Professor David G. Luenberger

Investment Science Home

Back to Newsletter





Strategy And The State Framework

This Newsletter is intended to help perpetuate the informal Investment Science community. Some of you receive this Newsletter because you took the two-day course on Investment Science for Industry. Others have indicated an interest through the web or by personal contact. We welcome comments and feedback.

A special feature of every Newsletter is a short technical article on some aspect of Investment Science. This issue's subject is "Strategy and the State Framework." The article is motivated primarily by issues of business strategy, such as how to allocate resources to an R&D project or to a development program which may encompass a single product or a family of related products. The issue may be that of finding a strategy for manufacturing (at home or abroad, alone or with partners, all at once or in stages). The issue may be one of determining a good strategy for marketing and pricing, for selecting product lines, for designing sales channels, or for improving inventory and supply chain operations. Indeed, strategy issues occur at most levels in a business, and clear and simple methods for determining good strategies and explaining their virtues is an essential element of business management. The method outlined in this article is comprehensive and adaptable to almost all strategy issues. Furthermore, combined with the principles of Investment Science, it produces strategies that are financially sound.

The key element of the approach presented in this article is that of the state concept. This is easy to understand, easy to explain, economical in terms of its definition, and intuitive. It is an alternative to decision tree methods, which although very useful for simple problems, can become unwieldy for many realistic problems.

Short Course

The two-day course Investment Science for Industry is described on the website There has been a number of requests to have this course offered again soon, and we are making plans to do so. If you have an interest in this, either individually or to be offered in your company, please let us know by responding as indicated in the website in the Resources section.

Strategy And The State Framework

I. Introduction

One of the most powerful concepts for strategy development is that of a state. It is vastly more efficient than decision trees and more complete than ad hoc strategy diagrams. The state completely describes the relevant aspects of a strategy situation. At any one time, it summarizes the information about past actions, events, and observations required for immediate decision making. Over a time horizon, the state framework provides the structure required for design of strategy.

Pictorially, the state evolves step-by-step (or stage-by-stage) as in the figure at the top of the next page. The state at any one stage is influenced by the state
at the previous stage and by actions, events, and observations at the current stage. This process continues stage-by-stage. There is a fixed formula for how these influences translate directly into new state values or probabilistically affect the state.

Example. (Development Effort) Consider a company developing a new product variation. The issue is how much financial resource should be allocated during each six-month period. Investing heavily leads to fast time to market and hence higher revenue, but also to less efficient use of resources and hence additional cost relative to a conservative approach. What is the best rate of development?

We suppose that progress advances by 0%, 20%, 40%, or 60% each period, corresponding to whether $0, $1 million, $3 million, or $7 million is allocated that period. If the product is completed in 2, 3, 4, or 5 periods, the total discounted net revenue obtained from the product is expected to be, correspondingly, 10, 9, 7, or 4 millions of dollars.

The situation can be described by a single state variable at each period, denoting development progress and a single action variable corresponding to the amount invested that period. The single state variable has the 6 potential values 0, 20, 40, 60, 80, and 100, all being percentages of completion.

II. Defining States

Typically, state variables can be classified according to six types:

1. Internal progress variables. These variables describe project progress (for example, a percent of product development or an estimate of the quality of the final product).

2. Resource status variables. These variables define the physical and human resources available to the firm. These variables also define actions that must be carried forward as directly affecting
future times. For example, in designing an oil field extraction plan, an early decision to drill at site A instead of site B must be carried along as a state variable to all future phases.

3. Market variables. These variables describe the market in which the company must operate. They may be current market prices or estimates of future market prices.

4. Competitive variables. These variables describe the status of competition.

5. Regulation and standards variables. These variables describe the status of possible government action (such as tax policy or environmental requirements) or industry standards.

6. Financial variables. Often only total discounted cash flow is required and hence no state is needed. In cases where there is a financial constraint, a state variable keeps track of the constraint.

In most applications the state will not include variables for all of these categories. Good analysis involves the selection of a few variables that are critical to strategy design. When first approaching a strategy creation situation, however, both the novice and the expert strategy designer may usefully define perhaps a dozen state variables. Through intuition, experience, and detailed probing this number can usually be reduced to about a half-dozen.

Considerations of computational ease dictate that most state variables are allowed to take on only a small number of possible values. Some variables, such as "research success or failure," will have only two possible values. Others, such as, "product quality being high, medium, or low" take on a small number. Some variables, such as "market price," may have many potential values.

III. Influence Variables

The influence variables are the actions, events, and observations that effect the state variables at the current stage.

1. Actions. As a general rule actions are controlled by the entity carrying out the strategy. Actions are a consequence of decisions. Typically, actions depend on the most recent state and the current values of other influence variables. Examples of action include deployment of resources, gathering of information, delay or termination of the project, or major change of project direction.

2. Events. Events are those factors that cannot be controlled, and are most often treated as random. Examples include market prices or expectations of future market prices, government actions, standards, competitor actions, and physical outcomes (such as machine breakdowns or research successes).

3. Observations. Observations are often interchangeable with events. The difference is that the (unknown) result of the observation is not available without conscious effort. Examples are test results in oil exploration, results of market surveys, and test market results.

State variables and influence variables often have similar names. For example, market price is a state and also an influence. The difference is that the (state) market price from the previous period as well as a current price change (influence) determines the current market price (state). Thus influences are often incremental while states are absolute.

IV. Computational Ease

Overall computational difficulty is proportional to the product P of the numbers of possible values of all of the state variables. That is, it is the number of all combinations of state values. Hence if there are six variables and the number of possible values are 100, 10, 2, 3, 10, 2, respectively, then P = 100 x 10 x 2 x 3 x 10 x 2 = 120,000. A P of this order means that the problem is fairly complex, but not unreasonably so.

By contrast, the number of final nodes in a decision tree usually grows geometrically as Kn where n is the number of stages. The quantity K depends on the number of action, event, and status combinations, and hence even modest strategy problems have millions or hundreds of millions of final nodes. Often the number K is about equal to the number of state combinations P. Hence the number of final nodes in a 5 stage tree with the same K as in the previous paragraph would be 120,0005 which is over 2 x 1025, or billions of times larger than the number of grains of sand on Earth.

V. Results

Once constructed, the state system can be used to find an optimal strategy and display various aspects of any given strategy. Typically, an important criterion is a measure of financial value. Here all the concepts and techniques of Investment Science, as represented for example in this Newsletter series, are applicable. For example, private uncertainties will be discounted at the risk-free rate, and market uncertainties at the growth rate of the market.

In addition, various statistics, sensitivities, and special valuations can be displayed. Here is a list of possible uses.

1. Strategy evaluation.
This is perhaps the most useful application in practical situations. The strategy team suggests strategies that are operationally feasible and these are evaluated according to many criteria. Often, excellent strategies are obtained this way, together with a good intuitive understanding of the advantages and disadvantages of various contending strategies.

2. Optimization.
Given a particular criterion, such as total discounted cash flow, the optimal strategy can be computed using dynamic programming. This strategy can then be simplified if necessary to produce an operationally feasible policy.

3. Sensitivity.
The sensitivity of various measures to variations in some of the parameters of the model can be computed and displayed.

4. Scenario evaluation.
A scenario is a predetermined sequence of some of the state variables or of the events and observations.

For example, one might project a rate of price decrease after a product is introduced, rather than allowing the price sequence to be random. This type of analysis can show how robust a particular strategy is to scenarios of concern.

5. Scenario averaging.
As a short cut to a full probabilistic model of uncertainties, where say a price changes randomly from period to period, one may define a small set of typical scenarios and then evaluate strategies against an average of these scenarios. That is, the scenarios are assigned probabilities and the single strategy is evaluated according to its average performance against these. This approach is most valuable when the most critical element of a strategy is the current action (or decision).

There are variations of these themes. A good state model combined with various methods of analysis and optimization can produce excellent strategies together with intuitive rationales for their benefits. Investment Science concepts are essential to providing the correct strategy performance measures.

As a simple exercise, you may wish to find the optimal solution to the example given in the early part of this article. One way to do it is to use dynamic programming. At first, assume that the appropriate discount rate is 0%. Then see what happens if the discount rate is positive. A solution will be posted on the website next month.