In "Multicriteria Optimization Method for Network-Level Bridge Management" (Transportation Research Record 1561), V. Ravirala, D.A. Grivas, A. Madan, and B.C. Schultz discussed a study whose goal was "to develop and implement a comprehensive decision process for establishing a bridge capital program." They described "an optimization method that assists decision makers in analyzing multiple goal-oriented scenarios for bridge capital programs." They concluded that this goal-oriented method is applicable to both small and medium bridges or to the spans of larger bridges.

BACKGROUND

As they age, bridges require costly repair and maintenance; therefore, "it is crucial to develop a bridge maintenance, rehabilitation, and reconstruction (MR&R) program that optimizes over the long term the use of limited resources." Typically, bridge programs are designed by means of comprehensive Bridge Management Systems (BMSs) that "use advanced information and assessment technologies, robust algorithms, and sophisticated computational tools."

Overall, "an integrated (capital and maintenance) multiyear bridge program is developed by conducting a network-level analysis of present condition, deterioration process, treatment needs, and program goals." Research has shown that optimization methods such as dynamic, linear, and integer programming can be helpful in the network-level decision-making process of bridge management. Because transportation managers incorporate a variety of objectives into their work, the multicriteria optimization techniques in BMSs are constantly changing both to recognize and to assist this sophisticated planning and programming of capital and maintenance projects.

SCOPE

This study considered the inventory, inspection, treatments, costs, and sample state transition data of a case study of 747 small and medium bridges in the New York State Thruway Authority (NYSTA). Most were built between 1954 and 1960 and were now deteriorating. The capital program for these bridges was developed using the goal-oriented optimization method, in which "the condition ratings of nine important structural elements within each bridge [were] used to rate four major components" (wearing surface, structural deck, superstructure, and substructure). Condition ratings from one (hazardous condition) to seven (excellent condition) were given to individual elements and to components, spans, and the bridge as a whole.

Capital program decisions were based on the condition needs of those components, and the bridge condition was characterized by defining the bridge states. Increment models were used to select workable treatment options for each state, as well as predict the time over which state increments (or transitions) occur. These state increment models were developed into a multicriteria optimization method that incorporated goal programming techniques to keep treatment costs low while getting the best possible result for capital invested in reaching condition goals.

MODELING

Assessing the current and future condition of bridges involved defining bridge states and state increments. A state is defined as "a combination of specific levels of variables (called the state variables) that completely describe the bridge condition." Bridge states are defined by bridge type, component type, and component condition rating. This study classified bridges into four types: steel stringer or girder, steel truss, concrete with integral deck, and concrete with separate deck.

As noted earlier, four components made up the structural elements of each bridge: wearing surface, structural deck, superstructure, and substructure. This grouping by components was necessary because a single condition rating did not adequately describe the entire bridge condition. In addition, capital program decisions are based largely on the needs of major components, and these components vary according to treatment types and costs and deterioration characteristics.

State increments are "based on the concept of defining controls that transform the bridge condition from one state to another." A control is defined as "a conjunction of treatments planned and the resulting change in state as a function of time. The state increment process changes states with a random amount of time between changes." Instead of being a one-time effort, MR&R options are thus planned as controls with corresponding short-term plans or a sequence of treatments. Over time, the bridge deteriorates or improves with treatment, thus changing the value of at least one state variable and resulting in state increments (or transitions). Each transition involves the current state, a sequence of treatments, variability in transition time, and the resulting future state. Because the transition time is variable, the goal became determining the probability density function of the transition time.

Identifying appropriate treatments for bridge components at various condition ratings was essential in determining the best time and condition for treating the bridge. Treatment of the Thruway bridges involved two general criteria. First, a "do nothing" option for each component. (This did not mean that no treatments should be applied, but rather that "specific" or other treatments should not be applied. For example, for the wearing surface component, the treatment options were do nothing, apply a thin overlay, or mill and inlay.) Second, the scope of each treatment had to be general enough to match the broad definitions of condition ratings and to apply to all bridge types.

Along with these criteria, condition-treatment matching rules were used to decide treatment options for each bridge state; the rules were possible component condition ratings at which different treatments could be applied. Both superstructure and bridge replacement decisions are based on the condition of several components. If the decision to replace is based on the condition of multiple components, it requires modeling component interactions.

In this state increment method, the prediction process involves estimating the probability density function for the transition time of each state/control condition. Of the three bridge-state variables, only component condition rating will change because it deteriorates or improves with treatment. Both bridge and component type cannot change unless a new bridge design is reconstructed. Because the overall bridge condition involves the condition of the four major components, the future condition of all four is predicted.

Transition times for each state/control combination were based on a range of the number of years it takes for a component to deteriorate from one component rating to the next lower rating. Transition times were based on the bridge's historical condition; in this case, researchers analyzed data for the Thruway bridges from 1978 to 1992. Minimum, typical, and maximum transition times were also assigned, with the transition time for improvement assumed to be between 0.5 and 1.5 years, the time expected to apply the treatment. These minimum, typical, and maximum transition times for each state/control combination were used to determine the probability density functions for the transition times.

GOAL-ORIENTED METHOD

The goal-oriented method for the bridge capital program involved a four-step procedure. The first step was a project-level analysis that used the state increment method to characterize condition, identify treatment, estimate cost, and predict performance. The second step was identifying the multiyear program objectives, goals, and constraints. The third step formulated a goal program for constrained optimization, and the fourth step was a variational analysis of feasible scenarios that satisfied goals. Determining capital investment and average condition rating for each year in the analysis period were two significant goals in this study.

The case study incorporated five scenarios, each with primary and secondary objectives, as well as condition goals for the first five and last five years of the ten-year capital program. Primary objectives included meeting condition goals and minimizing costs, and secondary goals involved minimizing costs. Condition goals for the first five years were improving and maintaining conditions; condition goals for the last five years were improving conditions, maintaining conditions, and maintaining improved conditions.

CONCLUSIONS