Price and frequency competition in freight transportation

Abstract

This paper develops a simple analytical model of price and frequency competition among freight carriers. In the model, the full price faced by a shipper (a goods producer) includes the actual shipping price plus an inventory holding cost, which is inversely proportional to the frequency of shipments offered by the freight carrier. Taking brand loyalty on the part of shippers into account, competing freight carriers maximize profit by setting prices, frequencies and vehicle carrying capacities. Assuming tractable functional forms, long-and short-run comparative-static results are derived to show how the choice variables are affected by the model's parameters. The paper also provides an efficiency analysis, comparing the equilibrium to the social optimum, and it attempts to explain the phenomenon of excess capacity in the freight industry.

A differential Stackelberg game for pricing on a freight transportation network with one dominant shipper and multiple oligopolistic carriers

“…When c;t z r;ij approaches in nity, the approximation becomes increasingly accurate. Then, we can reformulate the model (24) to (36) as a nonlinear programming model with linear constraints as follows: (42) (47) ' c;t z ij 0; $ c;t z r;ij 0; h c;t z r;ij 0:…”

“…-Step 1: Set the iteration counter K = 0, choose an initial solution S 0 = (p t 0 z j ; q t 0 z i ; ' c;t 0 z ij ; h c;t 0 z r;ij ; $ c;t 0 z r;ij ) which is the optimal solution of the model (24) to (37), ignore Constraint (36). Also, set the initial values for penalty parameters vector, 0 ; -Step 2: Solve the model (39) to (48) and set S K+1 = (p t z j ; q t z i ; ' c;t z ij ; h c;t z r;ij ; $ c;t z r;ij ); -Step 3.…”

“…Mozafari and Karimi [23] investigated pricing decisions for truckload carriers in a duopoly market, considering two scenarios of non-cooperative and cooperative games. Price and frequency competitions between freight carriers were formulated by Shah and Bruckner [24] using game theoretic models. Naimi Sadigh et al [25] examined channel pricing problem comparing two scenarios of centralized and decentralized structures using game theory.…”

European freight rolling stock fleet size in 2050 in light of the Transport White Paper 2011

“…loaded tonne km per annum/hours in service, hours available but not used/empty running, round trips per annum). It is hoped that changes in operational patterns and higher frequency between trains will lead to an increase in productivity (Jackson et al, 2014;Shah & Brueckner, 2012;Tsamboulas, Vrenken, & Lekka, 2007;Woroniuk et al, 2013). At present this is rarely achieved since this operational pattern is expected to lead to the wholesale integration of freight and passenger rail services.…”

Optimal rescheduling for the mixed passenger and freight line

“…In some papers [9,10] only the idea of operational management is offered, which improves the transfer and handling of freight trains, with direct examination of the profit or the loss. A similar problem is formulated for the area of road freight haulage [11]. There are a limited number of publications, which show the decisive role of the energy resources in the formation of operating costs, which depend on the mode of operation.…”