Chance Constrained Models for Transport Pricing and Scheduling under Competition

This paper is concerned with the development of a model for planning shipping prices over various routes of a transportation network. It is assumed that over each route a “railroad” (or other transport firm) competes directly with one other shipping firm (e.g., another railroad, a trucker) for the volume of business that is to be shipped over the route. We allow the possibility that the railroad's competition will come from different firms over different routes. The model we consider is a multiroute problem that involves both institutional and physical operating constraints. Each firm's demand depends linearly upon its own and its opponent's price. Since each competing firm sets its price policy independently and before the variable demand is known, some of these constraints cannot be guaranteed to hold with certainty. Thus they are best expressed as chance constraints. The objective of the “railroad” is to maximize its profit subject to the constraints of the model. The solution of the model synthesizes a pricing policy for the “railroad”; we also indicate how variations of the model can be employed in a sensitivity analysis of the suggested policy and discuss the relation between our model and other notions in game theory and chance-constrained games. An example is outlined, and the implications for a welfare-economic pricing policy considered.