Papers
This section presents a collection of AHP/ANP papers. Whether you are a student, academic and/or professional in the field of decision making, you can help us expand this collection by sharing your papers on decision making with the Analytic Hierarchy Process (AHP) and the Analytic Network Process (ANP).
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Paper results for keyword: Linear programmingThe Analytic Hierarchy Process and human resource allocation: Half the story
Thomas Saaty, Kirti Peniwati, Jennifer ShangJournal: Mathematical and Computer ModellingThe Analytic Hierarchy Process (AHP) provides a way to rank the alternatives of a problem by deriving priorities. A question that occurs in practice is: what is the best combination of alternatives that has the largest sum of priorities and satisfies given constraints? This leads one to consider ...
Read MoreThe analytic hierarchy process and linear programming in human resource allocation
Thomas Saaty, Kirti PeniwatiJournal: Proceedings of the Fourth International Symposium on the Analytic Hierarchy Process (ISAHP’96)The Analytic Hierarchy Process (AHP) provides a way to rank the alternatives of a problem by deriving priorities. A question that occurs in practice is: what is the best combination of alternatives that has the largest sum of priorities and satisfies given constraints? This leads one to consider ...
Read MoreOn nonlinear optimization in integers
Thomas SaatyJournal: Naval Research Logistics QuarterlyThe purpose of this paper is to give some elementary theorems on optimization in integers of nonlinear expressions subject to simple equality constraints. Other than the complicated algorithms of integer linear-programming, there is a dirth of examples and a
tradition to follow which might help ...
Read MoreLetter to the Editor—A Conjecture Concerning the Smallest Bound on the Iterations in Linear Programming
Thomas SaatyJournal: Operations ResearchIn solving linear programming problems accurate estimates of the number of iterations needed to reach the optimum are important to have. It has been mentioned in the literature that computing experience indicates this number of iterations to be of the order of twice the number of constraints. We ...
Read MoreCoefficient perturbation of a constrained extremum
Thomas SaatyJournal: Operations ResearchA schedule of allocating labor (in a shipping operation) whose available amount is a function of time, to different tasks, in order to minimize the total cost, is given. The problem is cast in linear-programming form in which all the coefficients are parameterized. An illustration is given follow...
Read MoreThe computational algorithm for the parametric objective function
Saul Guss, Thomas SaatyJournal: Naval research logistics quarterlyIf a linear programming problem involves two objective functions, it is desirable to learn all solutions depending on the relative weight attached to the two functions. This paper presents details of an algorithm which finds these solutions systematically.
Read MoreParametric objective function (part 2)—generalization
Saul Guss, Thomas SaatyJournal: Journal of the Operations Research Society of AmericaIn Part 1 (Saaty, T. L., S. I. Gass. 1954. Parametric objective function (Part 1). J. Opns. Res. Soc. Am.2 316.), the cost function in the general linear programming problem was parametrized with one parameter and the problem of generating solutions completely studied. In Part 2, a generalization...
Read MoreParametric objective function (part 1)
Saul Guss, Thomas SaatyJournal: Journal of the Operations Research Society of AmericaIn the linear programming problem where there is a linear function to be optimized (called the objective function), it is desirable to study the behaviour of solutions when the (cost) coefficients in the objective function are parametrized. The problem is then to find the set of xj (j = 1, 2, …, ...
Read More
The Analytic Hierarchy Process and human resource allocation: Half the story
Thomas Saaty, Kirti Peniwati, Jennifer ShangJournal: Mathematical and Computer ModellingThe Analytic Hierarchy Process (AHP) provides a way to rank the alternatives of a problem by deriving priorities. A question that occurs in practice is: what is the best combination of alternatives that has the largest sum of priorities and satisfies given constraints? This leads one to consider ...
Read MoreThe analytic hierarchy process and linear programming in human resource allocation
Thomas Saaty, Kirti PeniwatiJournal: Proceedings of the Fourth International Symposium on the Analytic Hierarchy Process (ISAHP’96)The Analytic Hierarchy Process (AHP) provides a way to rank the alternatives of a problem by deriving priorities. A question that occurs in practice is: what is the best combination of alternatives that has the largest sum of priorities and satisfies given constraints? This leads one to consider ...
Read MoreOn nonlinear optimization in integers
Thomas SaatyJournal: Naval Research Logistics QuarterlyThe purpose of this paper is to give some elementary theorems on optimization in integers of nonlinear expressions subject to simple equality constraints. Other than the complicated algorithms of integer linear-programming, there is a dirth of examples and a tradition to follow which might help ...
Read MoreLetter to the Editor—A Conjecture Concerning the Smallest Bound on the Iterations in Linear Programming
Thomas SaatyJournal: Operations ResearchIn solving linear programming problems accurate estimates of the number of iterations needed to reach the optimum are important to have. It has been mentioned in the literature that computing experience indicates this number of iterations to be of the order of twice the number of constraints. We ...
Read MoreCoefficient perturbation of a constrained extremum
Thomas SaatyJournal: Operations ResearchA schedule of allocating labor (in a shipping operation) whose available amount is a function of time, to different tasks, in order to minimize the total cost, is given. The problem is cast in linear-programming form in which all the coefficients are parameterized. An illustration is given follow...
Read MoreThe computational algorithm for the parametric objective function
Saul Guss, Thomas SaatyJournal: Naval research logistics quarterlyIf a linear programming problem involves two objective functions, it is desirable to learn all solutions depending on the relative weight attached to the two functions. This paper presents details of an algorithm which finds these solutions systematically.
Read MoreParametric objective function (part 2)—generalization
Saul Guss, Thomas SaatyJournal: Journal of the Operations Research Society of AmericaIn Part 1 (Saaty, T. L., S. I. Gass. 1954. Parametric objective function (Part 1). J. Opns. Res. Soc. Am.2 316.), the cost function in the general linear programming problem was parametrized with one parameter and the problem of generating solutions completely studied. In Part 2, a generalization...
Read MoreParametric objective function (part 1)
Saul Guss, Thomas SaatyJournal: Journal of the Operations Research Society of AmericaIn the linear programming problem where there is a linear function to be optimized (called the objective function), it is desirable to study the behaviour of solutions when the (cost) coefficients in the objective function are parametrized. The problem is then to find the set of xj (j = 1, 2, …, ...
Read More