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Types of Mixed Integer Linear Programming Problems
2021In this chapter a number of standard ILP problems will be formulated. As in Chap. 4, we shall look at some straightforward problems that are easy to formulate and then consider harder ILP problems. For many of the problem types a case study is provided, and for some of these, a model relating to the case is supplied in MCOL.
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Marginal values in mixed integer linear programming
Mathematical Programming, 1989Marginal values of a given optimization problem are the directional partial derivatives of the value with respect to perturbations in the data. If \(v(c,A,b)=\min \{cx|\) Ax\(\geq b\), \(x\geq 0\}\) and if \(u=(c',A',b')\) is a vector, then the marginal value in direction u is defined by \[ \frac{\partial v}{\partial u}=\lim_{\epsilon \to 0+}\frac{v(c+\
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Valid Inequalities for Mixed-Integer Linear and Mixed-Integer Conic Programs
2016Mixed-integer programming provides a natural framework for modeling optimization problems which require discrete decisions. Valid inequalities, used as cutting-planes and cuttingsurfaces in integer programming solvers, are an essential part of today’s integer programming technology.
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Optimization algorithm study : mixed integer linear programming
2023In the present, many petrochemical and petroleum products (engine fuel, solvent, plastic and synthetic rubber. etc.) are important. They are transported by ship, pipe line or train every day. So, minimizing transportation cost and time or maximizing profit is an important key of every company. In this optimization process, the optimal supply chain must
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Test Scheduling Using Mixed-Integer Linear Programming
2002In this chapter1, we present optimal solutions to several test scheduling problems for core-based systems. Given a set of tasks (test sets for the cores), a set of test resources (e.g., test buses, BIST hardware) and a test access architecture, we determine start times for the tasks such that the total test application time is minimized.
Krishnendu Chakrabarty +2 more
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Multiobjective Integer and Mixed-Integer Linear Programming
2016The introduction of discrete variables into multiobjective programming problems leads to all-integer or mixed-integer problems that are more difficult to tackle, even if they have linear objective functions and constraints. The feasible set is no longer convex, and the additional difficulties go beyond those of changing from single objective linear ...
Carlos Henggeler Antunes +2 more
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Linear, Integer, and Mixed Integer Programming
2021William P. Fox, Robert E. Burks
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Integer and Mixed Integer Linear Fractional Programming
1997Some of the problems mentioned in Chapter 1 required that either part of the variables, or all of them take integer values. This chapter will study such problems. In particular, we will address the bivalent programming in which part of the variables or all of them can take only values 0 or 1 (Section 9.1).
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