Optimal Facility Location with Concave Costs

Soland, Richard M.

doi:10.1287/opre.22.2.373

Cited by 144 publications

(43 citation statements)

References 20 publications

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“…Several models and algorithms have been developed that can be used to formulate and solve facility location problems subject to changing economies of scale in a deterministic setting: Soland [33] develops an algorithm for a facility location problem with facility costs that are concave in the amount produced and transportation costs that are concave in the amount shipped. Domschke and Voß [11] formulate a multi-product facility location model with concave production costs.…”

Section: Introductionmentioning

confidence: 99%

Stochastic facility location with general long-run costs and convex short-run costs

Schütz

Stougie

Tomasgård

2008

Computers & Operations Research

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This paper addresses the problem of minimizing the expected cost of locating a number of single product facilities and allocating uncertain customer demand to these facilities. The total costs consist of two components: firstly linear transportation cost of satisfying customer demand and secondly the costs of investing in a facility as well as maintaining and operating it. These facility costs are general and non-linear in shape and could express both changing economies of scale and diseconomies of scale. We formulate the problem as a two-stage stochastic programming model where both demand and short-run costs may be uncertain at the investment time. We use a solution method based on Lagrangean relaxation, and show computational results for a slaughterhouse location case from the Norwegian meat industry.

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Section: Introductionmentioning

confidence: 99%

Stochastic facility location with general long-run costs and convex short-run costs

Schütz

Stougie

Tomasgård

2008

Computers & Operations Research

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“…Because this is still a nonconvex function, some sort of iterative procedure is required, and it appears that a judicious application of the branch and bound method could give a very satisfactory answer. We apply the branch and bound type algorithm proposed in Rech and Barton [14] and Soland [19], to decompose the original problem into a series of linear programming problems, which use piecewise linear convex envelopes underestimating the nonconvex objective function. We now propose a complete algorithm to solve the multiple process problem.…”

Section: Lemmamentioning

confidence: 99%

Stochastic allocation of inspection capacity to competitive processes

Jang

Shanthikumar

2002

Naval Research Logistics

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Abstract:Optimal allocation and control of limited inspection capacity for multiple production processes are considered. The production processes, which operate independently but share inspection capacity, are subject to random failures and are partially observed through inspection. This study proposes an approach of stochastic allocation, using a Markov decision process, to minimize expected total discounted cost over an infinite time horizon. Both an optimal model and a disaggregate approximation model are introduced. The study provides some structural results and establishes that the control policy is of a threshold type. Numerical experiments demonstrate a significantly decreased amount of computational time required for the disaggregate approach when compared to the optimal solution, while generating very good control policies.

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“…Close this node and generate two additional open nodes corresponding to Equations (13) and (14). Solve the two resultant transportation problems using operator theory from the solution of the old open node.…”

Section: The Deterministic Demand Modelmentioning

confidence: 99%

Optimal Facility Location Under Random Demand With General Cost Structure

Balachandran

Jain

1976

Naval Research Logistics

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This paper investigates the problem of determining the optimal location of plants, and their respective production and distribution levels, in order to meet demand at a finite number of centers. The possible locations of plants are restricted to a finite set of sites, and the demands are allowed to be random. The cost structure of operating a plant is dependent on its location and is assumed to be a piecewise linear function of the production level, though not necessarily concave or convex. The paper is organized in three parts. In the first part, a branch and bound procedure for the general piecewise linear cost problem is presented, assuming that the demand is known. In the second part, a solution procedure is presented for the case when the demand is random, assuming a linear cost of production. Finally, in the third part, a solution procedure is presented for the general problem utilizing the results of the earlier parts. Certain extensions, such as capacity expansion or reduction at existing plants, and geopolitical configuration constraints can be easily incorporated within this framework.

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Optimal Facility Location with Concave Costs

Cited by 144 publications

References 20 publications

Stochastic facility location with general long-run costs and convex short-run costs

Stochastic facility location with general long-run costs and convex short-run costs

Stochastic allocation of inspection capacity to competitive processes

Optimal Facility Location Under Random Demand With General Cost Structure

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