Development of an optimal durability-based highway cost allocation model

This dissertation presents an integrated approach to modeling one of the most critical problems in modern transportation planning. The problem is the so-called highway cost allocation problem involving the equitable allocation of the joint total cost among all vehicle classes sharing a transportation facility such as a highway. It closely resembles problems which typically operate under the premise that the total project cost must be divided among the participants equitably and exactly, that is, with no profit or loss to the project agency. In an effort to capture the incentives for cooperation and to provide a formal mathematical framework to deal with the intuitive notion of equity, the highway cost allocation problem is cast as an n-person cooperative cost game. The cornerstone of this cost game is a durability-based cost function which assesses the destructive effects of increased legal traffic loadings on pavements using the concept of equivalent single axle loads (ESALs). This function is used to determine the cost of the optimal long-term construction and maintenance strategy for each subset of the set of distinct vehicle classes sharing the highway. Using these optimal durability-based costs, a highway cost allocation problem can then be defined as the problem of finding an equitable cost allocation for each vehicle class such that the total cost of providing the highway for all users is completely financed by the users themselves (completeness), and such that no group of vehicle classes pays more than the cost of providing an exclusive highway for the group (rationality). It is shown via an implicit function approach that, under reasonable assumptions, these two conditions mathematically define a nonempty, bounded, convex polyhedron known as the core, consisting of an infinite number of feasible but nondominated cost allocation solutions, from which one must be selected. A meaningful criterion of equity termed the Marginal to Rational Max-Min Ratio (MRMR) Nucleolus involving a fractional max-min linear programming problem is developed to select such an equitable cost allocation from the core. An integrated framework is developed and computerized using this concept, applied to selected Texas pavements, and compared to existing joint cost allocation procedures.