Linear mixed-integer

Since scope economies are especially hard to quantify, a separate class of optimization models solely dealing with plant loading decisions can be found. For example, Mazzola and Schantz (1997) propose a non-linear mixed integer program that combines a fixed cost charge for each plant-product allocation, a fixed capacity consumption to reflect plant setup and a non-linear capacity-consumption function of the total product portfolio allocated to the plant. To develop the capacity consumption function the authors build product families with similar processing requirements and consider effects from intra- and inter-product family interactions. Based on a linear relaxation the authors explore both tabu-search heuristics and branch-and-bound algorithms to obtain solutions. 

Problem Type Linear, mixed-integer, nonlinear, dynamic, and mixed-integer nonlinear programs Method Generalized benders decomposition, outer approximation and variants, genertilized cross decomposition... 

Given the unit selling prices of products A, B, and C as 12, 9, and 7 respectively, formulate a linear mixed integer program to determine the optimal production schedule that will maximize the total profit. 

The model above which contains many parameters and constraints is a large-scale, stochastic linear mixed integer convex programming model. What follows is the explanation and illustration for components of the model. 

The above model contains many parameters and constraints, which makes it a large-scale and complex stochastic linear mixed integer programming model. The components of the model are described and explained as follows ... 

The above model is a large-scale fiizzy random linear mixed integer programming model with many parameter and restrictions. The explanation of the components is as follows ... 

Dyken SV, Bakken BH, Slqelbred HI (2010) Linear mixed-integer models for biomass supply chains with transport, storage and processing. Energy 35 1338-1350... 

Grossmann, I. E., Mixed-Integer Non-Linear Programming Techniques for the Synthesis of Engineering Systems, Res. Eng. Design, 1 205, 1990. 

In this way the problem is reformulated as an MILP (Mixed Integer Linear Programming) problem. Readers who are interested in the problem of discrete sizing are referred to the paper of Voudoris and Grossmann (1992). 

When a linear programming problem is extended to include integer (binary) variables, it becomes a mixed integer linear programming problem (MILP). Correspondingly,... 

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. 

Mixed Integer Linear Programming If the objective and constraint functions are all linear, then (3-84) becomes a mixed integer linear programming problem given by... 

In order to make the problem solvable, a linearized process model has been derived. This enables the use of standard Mixed Integer Linear Programming (MILP) techniques, for which robust solvers are commercially available. In order to ensure the validity of the linearization approach, the process model was verified with a significant amount of real data, collected from production databases and production (shift) reports. 

A mixed-integer linear programming approximation can be derived following a problem specific approach. 

Both the mixing process and the approximation of the product profiles establish nonconvex nonlinearities. The inclusion of these nonlinearities in the model leads to a relatively precise determination of the product profiles but do not affect the feasibility of the production schedules. A linear representation of both equations will decrease the precision of the objective but it will also eliminate the nonlinearities yielding a mixed-integer linear programming model which is expected to be less expensive to solve. 

A continuous-time mixed integer linear programming model for... 

I. E. (1997) A mixed-integer linear programming model for shortterm scheduling of single-stage multiproduct batch plants with parallel lines. Ind. Eng. 

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