Feasibility of Linear Programming Model Employing Discrete Aumann-Shapley Values in Highway Cost Allocation

摘要

The objective of Highway Cost Allocation (HCA) is to divide a highway cost among all vehicle classes based on their requirement for pavement thickness, measured in terms of number of 18,0001b Equivalent Single Axle Load (ESAL) applications and roadway capacity (lanes). Considering vehicle classes as players and groups of vehicle classes as a coalition, the cost of the grand coalition (including all players) is allocated using a linear programming (LP) model with constraints defining a region of feasible allocations. The optimal allocation will satisfy properties of completeness, marginality and rationality. The purpose of this paper is to study the feasibility aspect of a new LP based HCA methodology that was designed to integrate traffic capacity and pavement thickness requirements by using concept of discrete Aumann-Shapley (A-S) values. This new method suggested formulation of the Right-Hand Sides (RHS) of the LP model by combining discrete A-S values of cost per ESAL and cost per Lane with associated ESALs and traffic lane requirements of vehicle classes in respective coalitions. Results of the study in this paper are indicative of the fact that the approach of using discrete A-S values for structuring RHS in an LP model could lead to infeasibility.