A Note on Linearized Reformulations for a Class of Bilevel Linear Integer Problems
We consider reformulations of a class of bilevel linear integer programs as equivalent linear mixed-integer programs (linear MIPs). Themost common technique to reformulate such programs as a single-level problem is to replace the lower-level linear optimization problem by Karush–Kuhn–Tucker (KKT) optimality conditions. Employing the strong duality (SD) property of linear programs is an alternative method to perform such transformations. In this note, we describe two SD-based reformulations where the key idea is to exploit the binary expansion of upper-level integer variables. We compare the performance of an offthe- shelfMIP solver with the SD-based reformulations against the KKT-based one and show that the SD-based approaches can lead to orders of magnitude reduction in computational times for certain classes of instances
This paper proposes a risk-aware approach to tactical supply chain planning based on integration of mathematical programming and simulation. A prototype planning system implementing this ap-proach is described. The prototype is developed using Anylogic simulation software and an open source mixed integer optimization tool – GNU Linear Programming Kit (GLPK)
This paper describes an approach to supply chain network optimization for a petrochemical enterprise. The state-task network is used for supply chain representation. A framework for comprehensive economic and environmental assessment based on life cycle assessment is proposed. The software implementation of proposed methodology is described.
This paper describes a prototype distribution network planning tool based on an iterative approach using a combination of mixed-integer linear programming and simulation. The prototype is implemented using an open-source optimization package GLPK and Anylogic software.
The problem of management of the nonlinear object which is exposed to impact of uncontrollable indignations, is considered in a key of differential game. Synthesis of optimum managements is made with application of transformation of the nonlinear equation of initial object in the differential equation with the parameters depending on a condition. The square-law functional of quality allows to formulate synthesis conditions in the form of need of search of solutions of the equation of Rikkati. The solution of the equation of Rikkati with the parameters depending on a condition, is in a symbolical view with application of algebraic methods that allows to generalize a number of earlier published theoretical results, to receive rather constructive decisions in a number of statements of problems of management.
The article is based upon the fact that the growing demand for master data management systems has not yet produced a commonly accepted metodology for their design and development/ The article offers two mathematical models? that allow a master data management systems designer a way to formally describe their system before development and verify the system quality by measurements? unique to master data management systems.