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Showing 3 results for Linear Approximation

Yahia Zare Mehrjerdi,
Volume 24, Issue 4 (12-2013)

Stochastic Approach to Vehicle Routing Problem: Development and Theories Abstract In this article, a chance constrained (CCP) formulation of the Vehicle Routing Problem (VRP) is proposed. The reality is that once we convert some special form of probabilistic constraint into their equivalent deterministic form then a nonlinear constraint generates. Knowing that reliable computer software for large scaled complex nonlinear programming problem with 0-1 type decision variables for stochastic vehicle routing problem (SVRP) is not easily available merely then the value of an approximation technique becomes imperative. In this article, theorems which build a foundation for moving toward the development of an approximate methodology for solving SVRP are stated and proved. Key Words: Vehicle Routing Problem, Chance Constrained Programming, Linear approximation, Optimization.
Yahia Zare Mehrjerdi,
Volume 25, Issue 3 (7-2014)

Abstract It is the purpose of this article to introduce a linear approximation technique for solving a fractional chance constrained programming (CC) problem. For this purpose, a fuzzy goal programming model of the equivalent deterministic form of the fractional chance constrained programming is provided and then the process of defuzzification and linearization of the problem is started. A sample problem is presented for clarification purposes.
Reza Ramezanian, Maryam Afkham,
Volume 31, Issue 2 (6-2020)

A non-linear bi-level problem is suggested in this paper for wildfire self-evacuation planning, the upper problem of which includes binary variables and the lower problem includes continuous variables. In this model, the upper problem selects a number of links and adds them to the available evacuation network. It, moreover, predicts the traffic balance, and the time window of the links in the lower problem. A part of the objective function in the bi-level problem is non-linear which is linearized with a linear approximation method that does not require binary variables. Then the linear bi-level model is reformulated as a non- linear single level problem. This model is linearized and transferred into Mixed Integer Programing. The model is then used for the real case study of the Beechworth fire in 2009. The resulted outputs of the model are beneficial in planning design schemes for emergency evacuation to use the maximum potential of the available transportation network.

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