Research Issues and Practical Considerations in Utilizing Decision Analysis

Herein we showed how the problem of choosing among speedup options in a serial project can be characterized and solved using decision analysis. To do this we considered a core problem having two events for each task and two crash options for each decision. We saw that the problem with lead-times is significantly more complex than the one without lead-times in that the decisions expand from "speedup/don't speedup" to "when to make such decisions." The problem has some fundamental properties that we discussed, including lead-time slack and the cost impact of changes in lead-time, as well as indirect costs. The purpose of the chapter is not only to consider a solution of the serial problem, but also to lay a foundation for future work in this area.

As for future work, much needs to be done. While the core problem and the corresponding decision analysis can be readily extended to situations with more than two events for each task and with more than two options for each decision, the corresponding complexity of the decision tree increases quickly. Also, as the number of tasks increase, the size of the tree grows exponentially. Thus, decision analysis can quickly become unwieldy for even modest-sized problems.

One avenue of future research is to find methods for reducing the size of the decision tree prior to analysis. It may be possible to do some form of decision tree reduction by developing domination conditions (conditions that eliminate segments of the decision tree).

Of course, in practice other issues may mandate generalizing the problem to incorporate other aspects such as stochastic lead-times, resources, and risk aversion. And finally there is the question of how to deal with nonserial projects (having parallel paths). Here again we can, in concept, utilize the decision analysis approach, but the complexity of the analysis may make this prohibitive. On this latter point, one possible approach is to reduce a project to a serial path using an approach analogous to classical PERT. However, just as in classical PERT, such an approach may yield suboptimal answers since it ignores other paths that are critical with a nonzero probability.

Given such limitations of decision analysis, future research should include the possible utilization of other approaches such as stochastic optimization, dynamic programming, and heuristic methods.