Optimal Two-Part Pricing and Capacity Allocation with Multiple User Classes and Elastic Arrivals at Constrained Transportation Facilities

Abstract

This paper focuses on the joint determination of optimal two-part prices and optimal capacity allocation at transportation facilities with elastic arrivals of multiple user classes. The model considers a general cost function and a two-part tariff comprised of an entrance fee and a dwell charge for use of the facility. Examples of this type of decision problems include: parking lots, airline seat allocation, and area congestion pricing schemes, among others. The results indicate that, in general, the optimal prices for the major pricing rules (i.e., profit maximization or welfare maximization) have three main components: one that captures the contributions of the willingness to pay and marginal costs, i.e., the classic solution; one that reflects the role of capacity constraint; and another that captures the role of elastic arrivals. Both welfare maximizing and second best prices have an additional term that accounts for the effect on consumer surplus produced by the dwell charges through the arrival rates. The models developed demonstrate the existence of a new dimension, namely cross-effects among the optimal prices and the underlying demand functions. The theoretical analyses in the paper were complemented with numerical calculations to provide a context for the discussion.