Abstract
This paper presents a model capable of accommodating plant location problems where 1) the long-run source or plant cost function exhibits a positive intercept (fixed charge), 2) the long-run plant cost function is discontinuous, and 3) there are economies of scale associated with increasing plant size. The model developed and presented here reverses the cost minimizing sequence of the Chern and Polopolus formulation, a model designed to include a discontinuous long-run plant cost function. For many types of plant location problems, the developed model (source location cost-sequencing model) will yield a lower cost solution than the Chern and Polopolus formulation.
Highlights
Distribution costs between each pair of potential source locations and destinations are proportional to the quantity distributed and the distance between the pair of points
Unit distribution cost from the ith potential source location to the jth destination is represented by tij, while Xij denotes quantity of commodity or service transported from the ith source location to the jth destination
Tij, from the three potential source locations to the three demand locations is given by the following matrix: Potential source Location 1
Summary
This paper presents a model capable of accommodating plant location problems where 1) the long-run source or plant cost function exhibits a positive intercept (fixed charge), 2) the long-run plant cost function is discontinuous, and 3) there are economies of scale associated with increasing plant size. The model developed and presented here reverses the cost minimizing sequence of the Chern and Polopolus formulation, a model designed to include a discontinuous long-run plant cost frmction. For many types of plant location problems, the developed model (source location cost-sequencing model) will yield a lower cost solution than the Chern and Polopolus formulation. The discontinuous plant cost function argument centers on the in divisibility of durable equipment available to construct alternative source sizes.^ Because technology for constructing alternative plant sizes is restricted, a limited number of short-run plant cost functions may exist.
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