Optimization mixed integer linear program

One of the approaches that can be used in design is to carry out structural and parameter optimization of a superstructure. The structural optimization required can be carried out using mixed integer linear programming in the case of a linear problem or mixed integer nonlinear programming in the case of a nonlinear problem. Stochastic optimization can also be very effective for structural optimization problems. 

The SNP optimizer is based on (mixed-integer) linear programming (MILP) techniques. For a general introduction into MILP we refer to [11], An SAP APO user has no access to the mathematical MILP model. Instead, the modeling is done in notions of master data of example products, recipes, resources and transportation lanes. Each master data object corresponds to a set of constraints in the mathematical model used in the optimizer. For example, the definition of a location-product in combination with the bucket definition is translated into inventory balance constraints for describing the development of the stock level over time. Additional location-product properties have further influence on the mathematical model, e.g., whether there is a maximum stock-level for a product or whether it has a finite shelf-life. For further information on the master data expressiveness of SAP SCM we refer to [9],... 

The NLP solver used by GAMS in this example is CONOPT2, which implements a sparsity—exploiting GRG algorithm (see Section 8.7). The mixed-integer linear programming solver is IBM s Optimization Software Library (OSL). See Chapter 7 for a list of commercially available MILP solvers. 

In this chapter, we tackle the integration design and coordination of a multisite refinery network. The main feature of the chapter is the development of a simultaneous analysis strategy for process network integration through a mixed-integer linear program (MILP). The performance of the proposed model in this chapter is tested on several industrial-scale examples to illustrate the economic potential and trade-offs involved in the optimization of the network. 

This chapter explains the general representation of a petrochemical planning model which selects the optimal network from the overall petrochemical superstructure. The system is modeled as a mixed-integer linear programming (MILP) problem and illustrated via a numerical example. 

This chapter provides an introduction to the basic notions in Mixed-Integer Linear Optimization. Sections 5.1 and 5.2 present the motivation, formulation, and outline of methods. Section 5.3 discusses the key ideas in a branch and bound framework for mixed-integer linear programming problems. 

A large number of optimization models have continuous and integer variables which appear linearly, and hence separably, in the objective function and constraints. These mathematical models are denoted as Mixed-Integer Linear Programming MILP problems. In many applications of MILP models the integer variables are 0 - 1 variables (i.e., binary variables), and in this chapter we will focus on this sub-class of MILP problems. 

In this paper, we extend the work of [10] by simultaneously considering minimization of the total utility consumption, maximization of operational flexibility to source-stream temperatures, and even minimum number of matches as multiple design objectives. The flexible HEN synthesis problem is thus formulated as the one of multi-objective mixed-integer linear programming (MO-MILP). This formulation also assumes that the feasible region in the space of uncertain input parameters is convex, so that the optimal solution can thus be explored on the basis of the vertices... 

A process-synthesis problem can be formulated as a combination of tasks whose goal is the optimization of an economic objective function subject to constraints. Two types of mathematical techniques are the most used mixed-integer linear programming (MILP), and mixed-integer nonlinear programming (MINLP). 

The problem of portfolio selection is easily expressed numerically as a constrained optimization maximize economic criterion subject to constraint on available capital. This is a form of the knapsack problem, which can be formulated as a mixed-integer linear program (MILP), as long as the project sizes are fixed. (If not, then it becomes a mixed-integer nonlinear program.) In practice, numerical methods are very rarely used for portfolio selection, as many of the strategic factors considered are difficult to quantify and relate to the economic objective function. 

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