Brill 1979

Citation

Brill, E. D. Jr. 1979. The use of optimization models in public-sector planning. Management Science, 25(5), 413-422.

Summary

Brill proposed that optimization, instead of being considered the end product, should be considered as a tool to facilitate the planning process. He contends that is many situations, it is not true that optimization can produce the one-true-and-right answer. This is because pure optimization 1) does not consider equity, and 2) it is often difficult to put empirical values on costs and benefits.

Brill presents three ways that optimization can be constructively incorporated into the planning process, as an aid to human creativity and decision making. First, simulation and optimization can be used jointly. In this case, an optimization model is used to determine a solution, and a simulation is performed to evaluate that solution. This has been put to use in designing outpatient healthcare facilities. Secondly, optimization can be paired with analytical models. This method has been applied to the timing of police car schedules. In this case, the optimization model was solved multiple times while changing constraints. The solutions were then analyzed using a time-dependent queuing model. Finally, planners can use a toolbox of models. This entails using multiple models to “develop, evaluate, and elaborate alternative solutions.”

Brill described how optimization models can be used in the planning process to spark the creativity of the analyst, and help develop innovative solutions. This occurs when there is human-machine interaction. In this situation, the computer would produce a first solution, which the analyst would then evaluate, with the intention of identifying “attractive features” and making model refinements. Running the model through computer optimization again will create a cycle in which the computer assists the person in arriving at the best answer.

For this process to work, optimization results must satisfy two criteria: 1) they must meet minimal constraints, and 2) they must be different. The author proposed that difference be quantified in an objective function, where the goal is to minimize the sum of the variables that are non-zero in the original design. In the first iteration, all non-zero values go to zero, and the model is re-solved. This is the “maximum difference.” In subsequent iterations, Lagrange multipliers are used to produce “more different” solutions, based on the relative effect of changes in problem constraints.

Discussion

I agree with Brill that optimization tools are more effective in planning when coupled with human judgment. I think that the human aspect allows for more subjective and “political” concerns, which a computer is unable to know, to be incorporated into the model.

Brill acknowledged that his approach for maximizing difference was in the early development and implementation stages when this article was published. One question that I have is how many Lagrange multipliers would need to be determined in order to accurately assess the trade-off of changes in constraints? Does it depend on the type of problem (linear, piece-wise, etc.)?