A STUDY ON APPLIED NETWORK EQUILIBRIUM MODELS

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Many models have been proposed so far to determine optimal transportation systems operations or strategic plans which take into account both supplier and user behavior. These problems have the common structure of a hierarchical decision-making process : A single decision-making unit which may represent a supplier of transportation services or controlling agency tries to make optimal decisions with respect to the transportation system, which may restrict the feasible constraints set for user of that transportation system and influence user behavior or demands. Algebraically, the decision making problem mentioned above is typically described as bilevel programming problem or Stackelberg problem. We call such a generalized transportation problem an applied network equilibrium analysis in a sense that it always recognizes that the lower problem consists of user equilibrium models in transportation networks.The main research results are summarized as follows :(1) It is evident from the empi … More rical analysis of cost structure for railway and bus industries in Japan that scale economy exists in mass transportation systems. This might make the Ramsey pricing rule useful for determining prices for newly introducing mass transportation systems and the determination of subsidy for them.(2) The applications of the conventional Ramsey rule is unrealistic and insufficient in that network congestion effects on pricing have been neglected.(3) That rule is very simple, but, possible to provide prohibitive prices in some cases when fixed costs burden for transit system providers are very high. The govemment subsidy is of importance to lower prices of transportation and achieve welfare maximization.(4) If network congestion effects are taken into account, Ramsey price equilibrium model can be formulated as a Stackelberg's leader-follower problem. For this problem, the nonlinear sensitivity analysis for the restricted variational inequality problem is effective.(5) In order to solve a bilevel programming problem, both of Nash equilibrium and Stackelbereg equilibrium concepts are available, however, the algorithm based on Stackelbereg equilibrium gives an efficient computation procedure than that of Nash. Less