Planning and Control of Transportation Systems: Stochastic Optimization forRobust Planning in Transportation

摘要

We examine the role of stochastic optimization models in transportation, inparticular robust optimization methods in which system reliability and expected costs are balanced. We study stochastic programming duality and find that duality results for deterministic problems apply to stochastic problems. From this, we describe general subgradient methods to solve stochastic convex problems. We use this to solve our Average Plan Model. The average plan model, a stochastic extension of current deterministic optimization models, incorporates uncertainty into well known deterministic models. The objective is to find a solution that is average in the sense that it is closer to the solution of very high probability events, as opposed to infrequent events. We detail the conditions for optimality of the average plan model and we describe a methodology for its solution. We demonstrate the applicability of our average plan model and solution methodologies by applying them to two transportation problems. The first is a network design problem for the distribution of crops in Mexico and the second is an aircraft scheduling problem. We evaluate the solutions provided and contrast them with solutions generated under varying assumptions and policies.