Mathematical programming methods

Bunch, P.R., Rowe, R.L., and Zentner, M.G. (1998) Large scale multi-facility planning using mathematical programming methods. AIChE Symposium Series, Proceedings of the Third International Conference of the Foundations of Computer-Aided Process Operations. Snowbird, Utah, USA, July 5-10, American Institute of Chemical Engineering, 94, p. 249. 

Supply chain operations planning at the tactical level determines the flow of goods over a specific time horizon. Mathematical programming methods yield time-dependent integrated sourcing, pro-... 

Operations research makes use of mathematical programming methods, a family of techniques for optimizing (minimizing or maximizing) a given algebraic objective function of a number of decision variables. The decision variables may either be independent of one another, or they may be related through constraints. 

Hybrid methods make use of both pinch analysis and mathematical programming methods, to exploit the strengths of both. These provide some user interaction and can also solve large problems. Studies on hybrid methods include Asante and Zhu (1996), Briones and Kokossis (1999) and Smith et al. (2010). See Sreepathi and Rangaiah (2014a) for a review of journal papers from 1993 to 2014 on HEN retrofitting methods and their applications. 

Studies on the specific features of MEIS made it possible to work out some modifications of mathematical programming methods that ensure effective application of the considered models. However, great difficulties are met even in the case when a problem solved can be reduced to a CP problem. For example, when applying MEIS of typ>e (8)-(13) they are 1) implicit setting of the constraints on monotony of characteristic functions (inequality (10)) and 2) large (up to 10-12 orders of magnitude) scatter in the values of sought variables, which happens in the analysis of environmental problems. 

Antsiferov, E.G. (1991). Application of mathematical programming methods to the analysis of thermodynamic systems Abstract of doctoral thesis, Computing Centre of AS USSR, Moscow (in Russian). 

Karlsson S. (2001). Optimization of a Sequential-Simulated Moving-Bed Separation Process with Mathematical Programming Methods. Ph.D. Thesis, Abo Akademi University. 

This methodology has been developed within the framework of mathematical programming methods involving an efficient dynamic analysis capability where a vehicle structure is modeled by rigid bodies connected by plastic hinges to model large structural deformations. 

The commonly used mathematical programming method for solving IP, MILP, and MINLP is the branch and bound method which uses a tree structure to define the problem and the associated binary variables. The following example shows the tree structure for the problem. 

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