MINLP model chapter

This chapter introduces the fundamentals of mixed-integer nonlinear optimization. Section 6.1 presents the motivation and the application areas of MINLP models. Section 6.2 presents the mathematical description of MINLP problems, discusses the challenges and computational complexity of MINLP models, and provides an overview of the existing MINLP algorithms. 

Today, there are more and more companies that continually look for competitive advantages in order to get a better position in the market. One way may be by aligning strategic/tactical decisions toward the optimization of an overall business performance metric. In this chapter, it is presented a novel approach to address this challenge. A MINLP model is developed, which addresses the network design and strategic marketing decisions of the SC in tandem. Then, this model is coupled with the financial formulation presented in Chap. 2, which allows the calculation of shareholders value by the discounted-free-cash-fiow method (DFCF). 

The intent of this chapter is to motivate and draw attention to the need of further research in this kind of decision problems, which are interfacing SC operations and marketing functions. A MINLP model simultaneously considering SC design/retrofitting, financial and marketing decisions is presented. A performance comparison with the traditional sequential decision approach is carried out, demonstrating the economic benefits that the holistic approach can provide. The aim is... 

The foregoing constraints constitute the full heat storage model. With the exception of constraints (11.3)—(11.5), all the constraints are linear. Constraints (11.3)—(11.5) entail nonconvex bilinear terms which render the overall model a nonconvex MINLP. However, the type of bilinearity exhibited by these constraints can be readily removed without compromising the accuracy of the model using the so called Glover transformation, which has been used extensively in the foregoing chapters of this book. This is demonstrated underneath using constraints (11.3). 

The objective function is nonlinear and nonconvex and hence despite the linear set of constraints the solution of the resulting optimization model is a local optimum. Note that the resulting model is of the MINLP type and can be solved with the algorithms described in the chapter of mixed-integer nonlinear optimization. Yee and Grossmann (1990) used the OA/ER/AP method to solve first the model and then they applied the NLP suboptimization problem for the fixed structure so as to determine the optimal flowrates of the split streams if these take place. 

Nonlinear problems— NLP and MINLP—can be further classified as convex or nonconvex, depending on the convexity of the objective function and feasible region. The understanding of the type of problem in terms of classification and convexity is very important in the utilization of modeling systems, since there are specific solvers and solution techniques for each type of problem, and depending on the problem, there may be local and global solutions. A more comprehensive study on mathanati-cal programming topics and continuous nonlinear optimization is out of the scope of this chapter. The interested reader is directed to references [4,6,7]. 

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