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Two-Stage Stochastic Programming for Transportation Network Design Problem

The transportation network design problem is a well-known optimization problem with many practical applications. This paper deals with demand-based applications, where the operational as well as many other decisions are often made under uncertainty. Capturing the uncertain demand by using scenario-based approach, we formulate the two-stage stochastic mixed-integer linear problem, where the decision, which is made under uncertainty, of the first-stage program, is followed by the second-stage decision that reacts to the observed demand. Such a program may reach solvability limitations of algorithms for large scale real world data, so we refer to the so-called hybrid algorithm that combines a traditional optimization algorithm and a suitable genetic algorithm. The obtained results are presented in an explanatory form with the use of a sequence of figures.

Genetic Algorithms for Scenario Generation in Stochastic Programming

Traditional deterministic max-min and min-min techniques are significantly limited by the size of scenario set. Therefore, this text introduces a general framework how to generate and modify suitable scenario sets by using genetic algorithms. As an example, the search of absolute lower and upper bounds by using GA is presented and further enhancements are discussed. The proposed technique is implemented in C++ and GAMS and then tested on real-data examples.

Waste processing facility location problem by stochastic programming: Models and solutions

The paper deals with the so-called waste processing facility location problem (FLP), which asks for establishing a set of operational waste processing units, optimal against the total expected cost. We minimize the waste management (WM) expenditure of the waste producers, which is derived from the related waste processing, transportation, and investment costs. We use a stochastic programming approach in recognition of the inherent uncertainties in this area. Two relevant models are presented and discussed in the paper. Initially, we extend the common transportation network flow model with on-and-off waste-processing capacities in selected nodes, representing the facility location. Subsequently, we model the randomly-varying production of waste by a scenario-based two-stage stochastic integer linear program. Finally, we employ selected pricing ideas from revenue management to model the behavior of the waste producers, who we assume to be environmentally friendly. The modeling ideas are illustrated on an example of limited size solved in GAMS. Computations on larger instances were realized with traditional and heuristic algorithms, implemented within MATLAB.

WS Network Design Problem with Nonlinear Pricing Solved by Hybrid Algorithm

The aim of the paper is to introduce a wait-and-see (WS) reformulation of the transportation network design problem with stochastic price-dependent demand. The demand is defined by hyperbolic dependency and its parameters are modeled by random variables. Then, a WS reformulation of the mixed integer nonlinear program (MINLP) is proposed. The obtained separable scenario-based model can be repeatedly solved as a finite set of MINLPs by means of integer programming techniques or some heuristics. However, the authors combine a traditional optimization algorithm and a suitable genetic algorithm to obtain a hybrid algorithm that is modified for the WS case. The implementation of this hybrid algorithm and test results, illustrated with figures, are also discussed in the paper.