The classical transportation problem (having source and destination as
indices) deals with the objective of minimizing a single criterion, i.e. cost
of transporting a commodity. Additional indices such as commodities and modes
of transport led to the Multi Index transportation problem. An additional
fixed cost, independent of the units transported, led to the Multi Index
Fixed Charge transportation problem. Criteria other than cost (such as time,
profit etc.) led to the Multi Index Bi-criteria transportation problem. The
application of fuzzy and stochastic concept in the above transportation
problems would enable researchers to not only introduce real life
uncertainties but also obtain solutions of these transportation problems. The
review article presents an organized study of the Multi Index transportation
problem and its fuzzy and stochastic extensions till today, and aims to help
researchers working with complex transportation problems.
Approximation algorithms for multi-index transportation problems with decomposable costs
