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The average shadow price for MILPs with integral resource availability and its relationship to the marginal unit shadow price [An article from: European Journal of Operational Research] | ![The average shadow price for MILPs with integral resource availability and its relationship to the marginal unit shadow price [An article from: European Journal of Operational Research]](http://ecx.images-amazon.com/images/I/51G4P0G7AGL._SL160_.jpg)
 enlarge | Authors: S. Mukherjee, A.k. Chatterjee
Publisher: Elsevier
Category: Book
Buy New: $5.95
Format: Html
Media: Digital
Availability: Available for download now
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Product Description
This digital document is a journal article from European Journal of Operational Research, published by Elsevier in . The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.
Description:
The economic significance of the average shadow price for integer and mixed integer linear programming (MILP) problems has been established by researchers [Kim and Cho, Eur. J. Operat. Res. 37 (1988) 328; Crema Eur. J. Operat. Res. 85 (1995) 625]. In this paper we introduce a valid shadow price (ASPIRA) for integer programs where the right-hand side resource availability can only be varied in discrete steps. We also introduce the concept of marginal unit shadow price (MUSP). We show that for integer programs, a sufficient condition for the marginal unit shadow price to equal the average shadow price is that the Law of Diminishing Returns should hold. The polyhedral structures that will guarantee this equivalence have been explored. Identification of the problem classes for which the equivalence holds complements the existing procedure for determining shadow price for such integer programs. The concepts of ASPIRA and MUSP introduced in this paper can play a vital role in resource acquisition plans and in defining efficient market clearing prices in the presence of indivisibilities.
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