The Constrained Bottleneck Transportation Problem

Saeree Svetasreni,Peerayuth Charnsethi

doi:10.3844/jmssp.2007.24.27

Abstract

Two classes of the bottleneck transportation problem with an additional budget constraint are introduced. An exact approach was proposed to solve both problem classes with proofs of correctness and complexity. Moreover, the approach was extended to solve a class of multi-commodity transportation network with a special case of the multi-period constrained bottleneck assignment problem.

Highlights

The bottleneck transportation problem with an additional budget constraint referred as the constrained bottleneck transportation problem (CBTP) is an extension of the classical minimum cost flows problem[1] dealing with finding an appropriated allocation of commodity from a set of suppliers to a group of customers in order to minimize the maximal operation time under supply capacity, demand requirement and budget constraints, Mathematically, the problem can be formulated as two following models
Complexity of algorithm IV for this special case is within 0(n5s2) since the procedure bottleneck is to the iteration of steps 2 and 3 at most n2s times with solving the assignment problems s times in each iteration
The approach can be extended efficiently and effectively to solve a class of multi-commodity problem including the special case with the assignment constraints

Summary

INTRODUCTION

The bottleneck transportation problem with an additional budget constraint referred as the constrained bottleneck transportation problem (CBTP) is an extension of the classical minimum cost flows problem[1] dealing with finding an appropriated allocation of commodity from a set of suppliers to a group of customers in order to minimize the maximal operation time under supply capacity, demand requirement and budget constraints, Mathematically, the problem can be formulated as two following models

Model II Minimize T Subject to

Subject to n

Minimize Subject to

Minimize mn

Algorithm IV

CONCLUSION