Process scheduling under uncertainty using multiparametric programming

In this article, the problem of process scheduling under uncertainty was studied using multiparametric programming method. Based on the uncertainty type (prices, demands, and processing times), the scheduling formulation results in different parametric problems including multiparametric mixed integer linear (mpMILP), quadratic (mpMIQP), and general nonlinear programming (mpMINLP) problem. This article analyzes the solution characteristics and proposes a novel solution framework for specific mpMILP/mpMIQP problems addressing a wide variety of scheduling problems under different types of uncertainty, which are modeled as coefficient in objective function, as coefficient of integer variable and right hand side vector of the constraints. The main idea of the proposed framework is to decompose the problem into a series of smaller subproblems, each of them producing the parametric information around a given parameter value. The parametric solution of every subproblem is retrieved by solving a series of multiparametric linear programming (mpLP) and mixed integer linear/nonlinear programming problems (MILP/MINLP). Several examples were solved to analyze the complexity and the effectiveness of the proposed method.

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