Even if the problem is too complex to rely on the decision proposed by the solution of a model, we should not underestimate the value of model building per se. The model building process itself is a valuable activity as it requires the following ingredients:
- Gathering data. Quite often, complex organizations do not pursue a disciplined approach to data management. Important data are missed, some are duplicated with possible inconsistencies, some are not shared between different offices, and errors are not discovered because no one really uses that information. The need to collect data to build a model may force an improvement of the related processes. Furthermore, model building can help in transforming a huge amount of useless data, into useful and shared information.
- Structuring the problem. This requires sharing information and understanding the multiple dimensions of a problem, as well as the points of view of other stakeholders. This is important in large organizations, where conflicting views are the rule rather than the exception, and entities within a firm pursue hidden agendas without agreeing on a shared understanding. It is always important to keep in mind that any quantitative analysis is doomed to failure if some relevant actor is not involved and motivated.
If model building and model solving result in a solution to the business problem, the solution itself must be implemented, monitored, and adapted when required by new circumstances. Fostering the culture and the discipline needed to monitor a solution and to assess the improvement in key performance indices is again valuable per se.
We close this section by remarking that quantitative analysis can play an important role in the following circumstances:
- When an objective support for decisions is needed. Rationalizing the analysis may ease potential conflicts between stakeholders.
- When the decision process leading to a recommendation must be explicitly documented. Because of uncertainty, even the best decision may result in a bad outcome. If you can back your decision with serious analysis, chances are that you will be able to save your neck.
- When the relationship between variables is too complex to be analyzed intuitively; in such a case, intuition can lead to wrong decisions because we are not able to fully grasp the impact of decisions.
- When the number of decision variables is too large to be managed even by the best human experts.
- When there are many difficult constraints and even finding a feasible (let alone optimal) solution is very hard. One example is train timetabling, which is a daunting task because of the number of shared resources (trains, crews, rails) and the constraints on their use, such as rules constraining how personnel shifts are scheduled.
- When tradeoffs between conflicting criteria must be assessed objectively (e.g., customer service vs. inventory holding cost).
Problems
1.1 Consider again the growth option problem of Section 1.2.2. We want to check the impact of less extreme assumptions about the conditional probabilities for the second movie, but we are unsure which values we should use. So, we assume that the conditional probability of a second success, after a first success, is 0.5 + α, for some unknown value of α; this is also the probability of a second flop, after a first flop. The analysis in Section 1.2.2 shows that if α = 0.5, we should produce the first movie. What is the limit value of α below which we should change our mind?
1.2 Consider the optimal mix model of Section 1.1.2. How could we extend the model to cope with
- Third-party suppliers offering items at given cost?
- The possibility of overtime work at some resource centers?
Leave a Reply