Sequentially Renew Weighted Opportunity Cost Based Algorithm in Transportation Problems

Abstract

Transportation models are of multidisciplinary fields of interest. In classical transportation approaches, the flow of allocation is controlled by the cost entries and/or manipulation of cost entries – so called Distribution Indicator (DI) or Total Opportunity Cost (TOC). But these DI or TOC tables are formulated by the manipulation of cost entries only. None of them considers demand and/or supply entry to formulate the DI/ TOC table. In this research we have developed Weighted Opportunity Cost (WOC) matrix, which is off course a new idea, for the control of the flow of allocations. It is noted that this WOC matrix is formulated by the manipulation of supply and demand entries along with cost entries as well. In this WOC matrix, the supply and demand entries act as weighted factors. Now it is known that, in Least Cost Matrix method, the flow of allocations are controlled by the least cost entries only and we do not need to change allocation direction in sub-sequence steps. On the other hand in Vogel’s Approximation Method, the flow of allocation is controlled by the DI table and this table is updated after each allocation step. Motivated by this idea, we have reformed the WOC matrix as Sequentially Updated Weighted Opportunity Cost (SUWOC) matrix. The significance difference of these two matrices is that, WOC matrix is invariant through all over the allocation procedures whereas SUWOC matrix is updated in each step of allocation procedures. Note that here update (/invariant) means changed (/unchanged) the weighted opportunity cost of the cells. Finally by incorporating this SUWOC matrix in LCM, we have developed a new approach to find out Initial Feasible Basic Solution of Transportation Problems. Some experiments have been carried out to justify the validity and the effectiveness of the proposed SUWOC-LCM approach. Experimental results have shown that the SUWOC-LCM approach outperforms. Moreover sometime this approach is able to find out optimal solution too.