SYNTHESIS AND ANALYSIS OF SOME TRANSPORT PRICE POLICIES WITH A CHANCE-CONSTRAINED DEMAND CAPTURE MODEL.

Abstract : The 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 which 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 main assumptions of the model are the following: (a) over each route, each of the two competing firms has a group of 'hard core' customers which it will keep as long as it does not radically change its shipping price; (b) over each route there is a variable random demand of known distribution whose parameters may be price dependent, arising from a group of customers which assigns the bulk of its business to the firm charging the lowest price. The model we consider is a multi-route problem which involves both institutional and physical operating constraints. 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 relationship between our model and other notions in game theory and chance-constrained games.