Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-25T10:41:12.708Z Has data issue: false hasContentIssue false

The Dual of a Cost Minimizing Linear Transshipment Model: An Economic Interpretation of an Assembly-Plant Processing-Distribution Network for a Firm

Published online by Cambridge University Press:  28 April 2015

William. M. Holroyd*
Affiliation:
Farmer Cooperative Service of the U.S. Dept. of Agriculture

Extract

The general economic meanings and mathematical structure of the dual of a primal mathematical programming model have been discussed for many years. However, within the mathematical programming realm, many interesting formulization variations have developed partly in response to variations in particulars of problems.

A number of authors have discussed the economic meaning and mathematical structure of the primal of a linear cost minimizing transportation model. Some authors discussed the economic meaning and mathematical structure of the dual as well as the primal of the transportation model. Several authors discussed cost minimizing transshipment models. Recently, greater interest has been shown in specific economic meanings of the dual of the cost minimizing transshipment model.

Type
Research Article
Copyright
Copyright © Southern Agricultural Economics Association 1974

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Baumol, W.J.Economic Theory and Operations Analysis. 2nd ed. Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1965.Google Scholar
[2] Charnes, A., Cooper, W. W., and Henderson, A.. Introduction to Linear Programming. New York: John Wiley & Sons, Inc., 1953.Google Scholar
[3] Dantzig, George B.Linear Programming and Extensions. Princeton, N.J.: Princeton University Press, 1963.Google Scholar
[4] Gass, S.I.Linear Programming, Methods and Applications. 2nd ed. New York: McGraw-Hill, 1964.Google Scholar
[5] Hitchcock, F.L.Distribution of a Product from Several Sources to Numerous Localities.Journal of Mathematics and Physics, Vol. 21, 1941.Google Scholar
[6] Judge, G.G., Havlicek, J., and Rizel, R. L.. “An Interregional Model: Its Formulation and Application to the Livestock Industry.Agricultural Economics Research, Vol. 17, 1965.Google Scholar
[7] King, G.A., and Logan, S. H.. “Optimum Location, Number, Size of Processing Plants with Raw Product and Final Product Shipments.Journal of Farm Economics, Vol. 46, 1964.CrossRefGoogle Scholar
[8] Leath, Mack N., and Martin, James E.. “The Transshipment Problem with Inequality Restraints.Journal of Farm Economics, 48: 4, Nov. 1966.CrossRefGoogle Scholar
[9] Orden, A.The Transshipment Problem.Management Science, Vol. 2, 1956.CrossRefGoogle Scholar
[10] Samuelson, Paul A., Dorfman, Robert, and Solow, Robert. Linear Programming and Economic Analysis. New York: McGraw-Hill, 1958.Google Scholar
[11] Takayama, T., and Judge, G. C.. Spatial and Temporal Price and Allocation Models. Amsterdam: North Holland Publishing Co., 1971.Google Scholar