Linear programming mixed integer programs

Chemical-industry related literature addressing value chain management focuses on production and supply chain management as well as selectively procurement. Companies in the oil and chemical industries have been leaders for almost 50 years in the development and use of linear and mixed integer programming models to support decision-making at all levels of planning (Shapiro 2004). 

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. 

Since the program (DEP) represents a mixed-integer linear program (MILP), it can be solved by commercially available state-of-the-art MILP solvers like CPLEX [3] or XPRESS-MP [4], These solvers are based on implementations of modem branch-and-bound search algorithms with cuts and heuristics. 

The hybrid algorithm is in general suitable for any two-stage stochastic mixed-integer linear program with integer requirements in the first-stage and in the... 

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],... 

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