How do you formulate a problem?


One of the most difficult, demanding, and decisive managerial tasks is to formulate problems in such a way that they can have a satisfactory solution. This task is difficult because desired outcomes and binding constraints are many and vary widely across space and time. Another source of difficulty if that the definition of problems is highly political in nature.

In economics or in operation management, a well-defined problem typically takes the form of an objective function in which we want to maximize (minimize) a desirable (undesirable) outcome, using some resources, and within the boundaries defined by a set of constraints we must satisfy. For instance, you might already be familiar with the following formulation: “maximize profit under the following constraints:…”. These constraints are usually expressed in terms of available factors of production, but they can also refer to demands of other stakeholders which the organization must satisfy to secure their support. Such problems are highly convenient because they can be solved with linear programming.

However, many problems are not framed is such a way for several reasons. First, it may be extremely difficult to agree on the outcome to prioritize (Simon, 1964). This is indeed a highly sensitive and political decision resulting from power struggles. For instance, the choice between “maximizing profit under a constraint of maximum level of greenhouse gas emissions” and “minimizing greenhouse gas emissions under a constraint of minimum level of profit” is not factual and objective: it is driven by values, negotiated between stakeholders, and far from neutral in terms of societal outcomes. A second reason for which all problems cannot be defined in linear programming terms is that objective functions are often complex and non-linear: which variables affect the outcome and thus should be included in the objective function? Are there interactions between these variables? A third reason is that constraints can be extremely difficult to list exhaustively and are also highly political in nature: whose expectations do you acknowledge? Finally, and perhaps more importantly, linear programming is as reliable as the estimates used in the underlying equations, and everything that matters cannot be given a monetary value: how do you estimate the value of employees’ health? Of an endangered species?

Therefore, a common way to frame problems in practice is instead to ask “what would happen if we do this instead of that?”. In other words, one or several alternative courses of action are suggested and compared in terms of their quantitative and qualitative outcomes. The advantage of this approach is that it does not require agreeing ex ante about a hierarchy of goals and constraints. A second advantage is that it does not require listing exhaustively all the variables potentially relevant to the decision at hand. And a third advantage is that it allows the integration of criteria which are difficult to assess.

While we will see examples of both kinds of problem formulation, most of the decisions we will study fall in the second category. Such a solution-driven rather than problem-driven approach cannot pretend to completeness, and therefore it does not yield optimal solutions the way linear programming does. But it is doable, flexible, and allows for continuous incremental improvement through multiple iterations. Decision alternatives are indeed not frozen: they are progressively shaped, revised, refined, improved or dropped as new alternatives are considered. Moreover, the basic decision alternatives discussed later in this chapter can also be combined to form more complex courses of actions.


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References

Simon, H. A. (1964). On the Concept of Organizational Goal. Administrative Science Quarterly, 9(1), 1–22.