CAPACITATED TRANSPORTATION PROBLEM WITH CONVEX POLYGONAL COSTS,
Abstract
This memorandum considers an extension of the classical transportation problem. In problems of this type, a minimal cost schedule is derived for shipping a commodity from a set of origins to a set of destinations. However, in the classical model, the only constraints permitted are total capacities at origins and destinations, and the cost is strictly a linear function of the amount shipped on any route. The extension presented here enables us to put an upper bound on each individual route. Furthermore, it permits us to impose increased or penalty costs for excessive amounts shipped on any individual route. The greater realism possible with this model should be of value of anyone concerned with transportation problems. Constructive proofs leading to a machine-oriented algorithm are given for the extension considered. The basic technique employed is a labelling process similar to that used by Ford and Fulkerson for the general network problem, and by Balinski and Gomory for the standard transportation problem. The objective of the present work is to trade off some of the generality of the general network problem for increased computational efficiency. It is conjectured, on the basis of limited hand calculations and certain theoretical features, that the present algorithm will also be useful for the standard transportation problem. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1966
- Accession Number
- AD0631311
Entities
People
- G. W. Graves
- R. M. Thrall
Organizations
- RAND Corporation