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The traffic assignment problem associated with a given transportation network is the process of distributing zone-to-zone trips on links of the network. A number of methods have been proposed to solve this problem, but none have been found to be entirely satisfactory. This paper is concerned with the nonlinear mathematical model of the problem, where the link-traveling costs are increasing functions of the link flows and no explicit capacity constraint is imposed on individual links. An efficient algorithm is developed, using a node-arc formulation of the problem. It is an adaptation of the convex-simplex method that takes advantage of the very special network structure of the traffic assignment problem formulated in this way. Numerical results obtained with a moderate size street network are presented. [ABSTRACT FROM AUTHOR]

This paper develops a dynamic programming model for selecting an optimal combination of transportation modes over a multiperiod planning horizon. The formulation explicitly incorporates uncertainty regarding future requirements or demands for a number of commodity classes. In addition to determining the optimal modes to employ, the model assigns individual commodity classes to various modes, determines which supply points serve which destinations, and reroutes carriers from destinations to alternative sources where they will be most effective. The model is formulated as an optimal discrete time stochastic control problem where cost is quadratic and dynamic equations linear in the state and control variables. This model may be solved in closed form by an efficient dynamic programming algorithm that permits the treatment of relatively large scale systems. A iso developed is an alternative, generally suboptimal method of solution, based upon wiving a sequence of convex programming problems over time. This technique may be employed for a more general class of problems. In both methods the use of 'shadow prices' that arise is discussed. [ABSTRACT FROM AUTHOR]

An algorithm for the determination of the economic design of X-charts based on Duncan's model is described in this paper. This algorithm consists of solving an implicit equation in design variables n (sample size) and k (control limit factor) and an explicit equation for h (sampling interval). The use of this algorithm not only yields the exact optimum but also provides valuable information so that the sensitivity of the optimum loss-cost (L*) can be evaluated. Loss-cost contours are used to discuss the nature of the loss-cost surface and the effect of the design variables. The effect of two parameters, the delay factor (e), and the average time for an assignable cause to occur (1/lambda), on the optimum design is evaluated. Numerical examples are used for illustrations. [ABSTRACT FROM AUTHOR]