5.1: Introduction
Infrastructure managers must make decisions on a regular basis. They must make decisions about allocating time and other organizational resources. For infrastructure components, managers must make decisions about maintenance and rehabilitation in each planning period. In many cases, the decision about procedures to apply to a particular infrastructure component may be to ‘do-nothing,’ but it is prudent for a manager to make such a decision consciously rather than simply from lack of oversight. With continuing deterioration, some maintenance or rehabilitation will be needed to prevent failure of the component.
This chapter discusses the use of optimization approaches to aid infrastructure management decision making. No previous experience with formal optimization approaches is assumed. Our intent is not to cover all the different approaches to optimization, but to illustrate how optimization might be used for infrastructure management. We don’t expect readers to become experts in optimization from reading this chapter. However, a manager may not ever develop their own optimization problem formulations. However, many asset management software programs include optimization sub-routines, and a manager using such programs should understand their approach. Also, optimization provides a useful conceptual approach to aid structuring decision making, even if formal optimization procedures are not used.
Optimization has been used in numerous applications that are not discussed in this chapter. In particular, optimization is used to aid production planning, vehicle routing, inventory controls, and engineering design. Optimization is also used for the estimation of parameter values. Regression models, as discussed in Chapter 4 on Deterioration Models, is a form of optimization. Just as one example, the package delivery company UPS uses optimization to suggest vehicle routes for their deliveries. The route planning minimizes driving costs in terms of time and fuel use. With route planning technology introduced in 2004, UPS has saved a million gallons of fuel each year (UPS 2016).
All optimization problems have some common features. The user is interested in searching for maximum (or minimum) values for an objective function. For infrastructure management, the objective might be to maximize the average condition of components or to minimize money spent on maintenance and rehabilitation. There are a set of decision variables obtained in finding an optimization solution. For infrastructure management, the most common decision variables are actions performed on particular components, such as rehabilitation options for different roadway sections. There are a set of constraints imposed on the decision variables. For example, there may be an available budget for infrastructure management, a minimum allowable component condition, or a requirement that one and only one rehabilitation option is chosen for each component in a single year. Finally, there is some solution process (usually called a solution algorithm) to obtain optimal values of the decision variables. In practice, management problems are sufficiently large that software packages are used to obtain such solutions.
Engineers and scientists first encounter optimization as part of the study of calculus. In particular, maximum values of a function with a single variable can be obtained by setting the first derivative to zero and insuring that the second derivative of the function is positive:
\[ \frac{d f(x)}{d x}=0, \frac{d^{2} f(x)}{d x^{2}}>0 \]
There may be a single value of x that maximizes the equation, or there may be multiple values.