A combinatorial equivalence between A class of multicommodity flow problems and the capacitated transportation problem

1976 ◽  
Vol 10 (1) ◽  
pp. 401-404 ◽  
Author(s):  
James R. Evans
Keyword(s):  
Transportation Problem ◽  
Multicommodity Flow ◽  
Flow Problems ◽  
Capacitated Transportation Problem

scholarly journals Enhancement of Capacitated Transportation Problem in Fuzzy Environment

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Hamiden Abd El-Wahed Khalifa ◽  
Pavan Kumar ◽  
Majed G. Alharbi
Keyword(s):  
Objective Function ◽  
Transportation Problem ◽  
Research Work ◽  
Policy Makers ◽  
Suggested Approach ◽  
Penalty Cost ◽  
Fuzzy Environment ◽  
Order Relations ◽  
Capacitated Transportation Problem ◽  
Interval Linear

This research work aims to study a capacitated transportation problem (CTP) with penalty cost, supplies, and demands represented by hexagonal fuzzy numbers. Based on ranking function, the supplies and demands are converted to the crisp form. Through the use of the α‐level, the problem is converted into interval linear programming. To optimize the interval objective function, we define the order relations represented by policy maker’s choice between intervals. The maximization (minimization) problem considering the interval objective function is transformed to multiobjective optimization problem based on order relations introduced by the preference of policy makers between interval profits (costs). A numerical example is given for illustration and to check the validity of the suggested approach.

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