Range-Consistent Answers of Aggregate Queries under Aggregate Constraints
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The real Production Possibility Set (PPS) is completely generated by observations in the real approach, but generating the integer PPS may not be possible by only using observations in the integer approach. In other words, this phenomenon says that all points in the real generated PPS are dominated by a point of the linear combination of observations, whereas there might be some points in the integer generated PPS which are not dominated with the points of the linear combination of observations. This paper shows how the integer production possibility set is made and the mixed-integer linear programming is defined. The paper also addresses some shortcomings in the recent mixed-integer linear programming while the integer axioms are considered.
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The optimal timing of air-to-ground tasks for Unmanned Aerial Vehicles is undertaken.In this paper,a mixed integer linear program(MILP) is posed to resolve the optimal task assignment and timing problem.The simulation indicates a successful implementation of a MILP task allocation solution for a team of Unmanned Aerial Vehicles.
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A Novel Alternative Algorithm for Solving Integer Linear Programming Problems Having Three Variables
Abstract In this study, a novel alternative method based on parameterization for solving Integer Linear Programming (ILP) problems having three variables is developed. This method, which is better than the cutting plane and branch boundary method, can be applied to pure integer linear programming problems with m linear inequality constraints, a linear objective function with three variables. Both easy to understand and to apply, the method provides an effective tool for solving three variable integer linear programming problems. The method proposed here is not only easy to understand and apply, it is also highly reliable, and there are no computational difficulties faced by other methods used to solve the three-variable pure integer linear programming problem. Numerical examples are provided to demonstrate the ease, effectiveness and reliability of the proposed algorithm.
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The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric integer programs are studied from a group theoretical viewpoint. We investigate the structure of integer solutions of integer programs and show that any integer program on n variables having an alternating group A_n as a group of symmetries can be solved in linear time in the number of variables.
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Time, raw materials and labour are some of the nite resources in the world. Due to this, Linear Programming* (LP) is adopted by key decision-markers as an innovative tool to wisely consume these resources. This paper test the strength of linear programming models and presents an optimal solution to a diet problem on a multi-shop system formulated as linear, integer linear and mixed-integer linear programming models. All three models gave different least optimal values, that is, in linear programming, the optimal cost was GHS15.26 with decision variables being continuous (R+) and discrete (Z+). The cost increased to GHS17.50 when the models were formulated as mixed-integer linear programming with decision variables also being continuous (R+) and discrete (Z+) and lastly GHS17.70 for integer linear programming with discrete (Z+) decision variables. The difference in optimal cost for the same problem under different search spaces sufficiently establish that, in programming, the search space undoubtedly affect the optimal value. Applications to most problems like the diet and scheduling problems periodically require both discrete and continuous decision variables. This makes integer and mixed-integer linear programming models also an effective way of solving most problems. Therefore, Linear Programming* is applicable to numerous problems due to its ability to provide different required solutions.
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For many practical multiple objective network programming (MONP) problems, only integer solutions are meaningful and acceptable. Representative efficient solutions are usually generated by solving augmented weighted Tchebycheff network programs (AWTNPs), sub-problems derived from MONP problems. However, efficient solutions generated this way are usually not integer valued. In this study, two algorithms are developed to construct integer efficient solutions starting from fractional efficient solutions. One algorithm finds a single integer efficient solution in the neighborhood of the fractional efficient solution. The other enumerates all integer efficient solutions in the same neighborhood. Theory supporting the proposed algorithms is developed. Two detailed examples are presented to demonstrate the algorithms. Computational results are reported. The best integer efficient solution is very close, if not equal, to the integer optimal solution. The CPU time taken to find integer efficient solutions is negligible, when compared with that taken to solve AWTNPs. © 2010 Wiley Periodicals, Inc. NETWORKS, Vol. 57(4), 362-375 2011
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The mixed-integer linear programming data envelopment analysis models were proposed due to this reason that the conventional DEA models may suggest some non-integer values for the inputs and/or outputs of decision making units (DMUs) which those data can only be specified with integer values such as the number of employees and books. There are a few researches on integer-valued DEA and this paper focuses on the three previous ones. The paper characterizes some shortcomings on those researches with some mathematic logics.
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