An exact algorithm is developed for the chance-constrained multi-area reserve sizing problem in presence of transmission network constraints. The can be cast as a two-stage stochastic mixed integer linear program using sample approximation. Due to complicated structure problem, existing methods attempt find feasible solution based on heuristics. Existing mixed-integer algorithms that applied di...

Direct methods, comprising limit and shakedown analysis, are a branch of computational mechanics. They play significant role in mechanical civil engineering design. The concept direct methods aims to determine the ultimate load carrying capacity structures beyond elastic range. In practical problems, lead nonlinear convex optimization problems with large number variables constraints. If strengt...

this paper addresses a new version of the exible ow line prob- lem, i.e., the budget constrained one, in order to determine the required num- ber of processors at each station along with the selection of the most eco- nomical process routes for products. since a number of parameters, such as due dates, the amount of available budgets and the cost of opting particular routes, are imprecise (fuzz...

Lean manufacturing is a strategic concern for companies which conduct mass production and it has become even more significant for those producing in a project-oriented way by modularization.  In this paper, a bi-objective optimization model is proposed to design and plan a supply chain up to the final assembly centre. The delivery time and the quality in the procurement and low fluctuation of t...