Modified Dynamically-updated Weighted Opportunity Cost Based Algorithm for Unbalanced Transportation Problem

Abstract

Recently, Weighted Opportunity Cost (WOC) based algorithms are developed for solving balanced Transportation Problems (TPs). The exceptionality of the WOC based approaches is to introduce supply and demand as weight factor to cost entries for the control of flow of allocations. But in the unbalanced TP, there exist a pitfall whenever balancing the TP with zero dummy transportation cost as done in existing classical approaches, so that the total cost is unaffected due to dummy transportations. A modified dynamically-updated weighted opportunity cost-based algorithm embedded on Least Cost Method (LCM) is proposed which is suitable for both balanced and unbalanced TPs. Numerical instances have been carried out to demonstrate the effectiveness and efficiency of the proposed method. It is observed that, the proposed modified dynamically-updated weighted opportunity cost-based algorithm sometimes outperforms for the LCM as well as the existing weighted opportunity cost-based algorithm in unbalanced TPs.

Keywords

• cost matrix; dummy route; least cost method; transportation; unbalanced problem; weighted opportunity cost