Optimization Problems Subject to a Budget Constraint with Economies of Scale

Hillestad, Richard

doi:10.1287/opre.23.6.1091

Cited by 31 publications

(21 citation statements)

References 9 publications

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“…Also assume cx is not constant on F A. Problems of the form P have been studied by Bansal and Jacobsen [3,4] and Hillestad [8]. Under differentiability and separability of g in the decision variables x = ( x 1 ..... xn), references [3,4] develop a method for optimizing network flow capacity under economies-of-scale.…”

Section: G = { X~r " L G ( X ) >~O )mentioning

confidence: 99%

Linear programs with an additional reverse convex constraint

Hillestad

Jacobsen

1980

Appl Math Optim

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Abstract. A constraint g ( x )>1 0 is said to be a reverse convex constraint if the function g is continuous and strictly quasi-convex. The feasible regions for linear programs with an additional reverse convex constraint are generally non-convex and disconnected. It is shown that the convex hull of the feasible region is a convex polytope and, as a result, there is an optimal solution on an edge of the polytope defined by only the linear constraints. The only possible edges which can contain such an optimal solution are characterized in relation to the best feasible vertex of the polytope defined by only the linear constraints. This characterization then provides a finite algorithm for finding a globally optimal solution.

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Section: G = { X~r " L G ( X ) >~O )mentioning

confidence: 99%

Linear programs with an additional reverse convex constraint

Hillestad

Jacobsen

1980

Appl Math Optim

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“…The quality of labor force (measured by "occupation mix" index) and the quality of capital stock are independent variables of this study jointly with some other variables. We can also find a useful feedback about firm's production function and related optimization problems in some additional research works (Hillestad, 1975;Liou et al, 2006;Chen et al, 2003;Pujowidianto et al, 2009;Amoranto & Chun, 2011;and so on).…”

Section: Introductionmentioning

confidence: 99%

A new simple algorithm for solution of optimization problems

Abbasov

2018

Journal of International Studies

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Abstract. This paper is devoted to developing a new sample algorithm after the solution of optimization problems subject to a budget constraint in firms' production. In the calculation of the optimal composition of different items, there is one fundamental problem. In general, firm's behaviors are under a budget constraint and they always try to optimally allocate their resources among production factors. It is possible that there are some production factors like quality of labor force which influence firm's production after some period. In this case, when we want to solve optimization problems for these firms, we can encounter that the objective function (Revenue function, Production function or some other) of the optimization problem depends on the lags of the mentioned production factors. Therefore, the realization of the allocation of firm's resources among the production factors doesn't seem plausible (because some of them are on the lags). In this context, we have tried to prepare a simple algorithm for optimal allocation of firm's resources in the same period, using an optimal share which has been found for different lags of variables.

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“…The algorithms proposed since then can be classified roughly into four classes. The first class consists of algorithms based on the edge property of F \ G. As will be shown in Section 2, at least one optimal solution to LPAC lies on the intersection of the edges of F and the boundary of G. Exploiting this property, Hillestad [5] proposed a simplex-type pivoting algorithm for searching an optimal intersection point. Hillestad's algorithm has been modified and still developed by Hillestad-Jacobsen [7] and Thuong-Tuy [17].…”

Section: Introductionmentioning

confidence: 99%

Linear Programs With an Additional Separable Concave Constraint

Kuno

Shi

2004

J. of Appl. Math & Decision Sc.

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Abstract. In this paper, we develop two algorithms for globally optimizing a special class of linear programs with an additional concave constraint. We assume that the concave constraint is defined by a separable concave function. Exploiting this special structure, we apply Falk-Soland's branch-and-bound algorithm for concave minimization in both direct and indirect manners. In the direct application, we solve the problem alternating local search and branch-and-bound. In the indirect application, we carry out the bounding operation using a parametric right-hand-side simplex algorithm.

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Optimization Problems Subject to a Budget Constraint with Economies of Scale

Cited by 31 publications

References 9 publications

Linear programs with an additional reverse convex constraint

Linear programs with an additional reverse convex constraint

A new simple algorithm for solution of optimization problems

Linear Programs With an Additional Separable Concave Constraint

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