In this note, we show how interval arithmetic can be used to give a solution to the linear programming problem which is guaranteed to be on the safe side of the true solution, where roundoff error is taken into account.
In this note, we show how interval arithmetic can be used to give a solution to the linear programming problem which is guaranteed to be on the safe side of the true solution, where roundoff error is taken into account.
We consider the optimal control problem for a stochastic sequence (not necessarily Markov) in which besides the main criterion there are a number of other functionals of the sample paths;their expectations must satisf...
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We consider the optimal control problem for a stochastic sequence (not necessarily Markov) in which besides the main criterion there are a number of other functionals of the sample paths;their expectations must satisfy a certain system of inequalities. The life time of the process is assumed to be finite and all basic spaces are Borel spaces. The paper studies some properties of the space of strategy measures (for example, we prove that the selectors correspond to extreme points of this space). The optimal control problem is reformulated in terms of the theory of abstract linearprogramming which allows us to obtain necessary and sufficient conditions of optimality. Moreover, the paper proves the existence of an optimal strategy and its form is established (a finite mixture of selectors);at the end some exactly solved examples are cited.
The author formulates mixed Boolean linear programming problems to find the shortest route and the shortest cycle that pass through the given number of nodes in a complete graph. Their special cases provide formulatio...
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The author formulates mixed Boolean linear programming problems to find the shortest route and the shortest cycle that pass through the given number of nodes in a complete graph. Their special cases provide formulations of problems for finding the shortest Hamiltonian path and the shortest Hamiltonian cycle. The problems include no more than 2n(2) variables and no more than (n+1)(2) constraints, where n is the number of nodes of the complete graph.
In this paper, the uncertainty of the demand in newsvendor problems is characterized by interval probabilities. The characteristics of interval probabilities, the method for estimating interval probabilities from subj...
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ISBN:
(纸本)9781424426294
In this paper, the uncertainty of the demand in newsvendor problems is characterized by interval probabilities. The characteristics of interval probabilities, the method for estimating interval probabilities from subject and decision criteria with interval probabilities are addressed. The newsvendor models under interval probabilities are proposed for obtaining the optimal order quantity.
This paper proposes a solution for solving a specific problem that requires a team of identical robots to collect in a specific order different types of resources scattered throughout an environment. A Petri net with ...
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ISBN:
(纸本)9781479948451
This paper proposes a solution for solving a specific problem that requires a team of identical robots to collect in a specific order different types of resources scattered throughout an environment. A Petri net with outputs models the environment, the team possible movements and the regions with resources. An iterative solution plans the team such that each robot collects and assembles resources in the required order. Each iteration step is based on a linear programming problem that is guaranteed to return a feasible firing vector for the Petri net system. A pseudo-code description of the procedure is given and a simulation example is included.
The “relaxation” procedure introduced by Held and Karp for approximately solving a large linear programming problem related to the traveling-salesman problem is refined and studied experimentally on several classes ...
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This paper studies some properties of hypergraphs in connection with a class of integer linear programming problems. The main result (theorem 3) states that the strong chromatic number of a balanced hypergraph is equa...
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In this paper we consider the question: how does the flow algorithm and the simplex algorithm work? The usual answer has two parts: first a description of the "improvement process", and second a proof that i...
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In many real-life situations, we come across problems with imprecise input values. Imprecisions are dealt with by various ways. One of them is interval based approach in which we model imprecise quantities by interval...
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ISBN:
(纸本)9781479944675
In many real-life situations, we come across problems with imprecise input values. Imprecisions are dealt with by various ways. One of them is interval based approach in which we model imprecise quantities by intervals, and suppose that the quantities may vary independently and simultaneously within their intervals. In most optimization problems, they are formulated using imprecise parameters. Such parameters can be considered as fuzzy intervals, and the optimization tasks with interval cost function are obtained. When realistic problems are formulated, a set of intervals may appear as coefficients in the objective function or the constraints of a linear programming problem. In this paper, we introduce a new method for solving linear optimization problems with interval parameters in the objective function and the inequality constraints, and we show the efficiency of the proposed method by presenting a numerical example.
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