A Capacity-Influenced Approach to Find Better Initial Solution in Transportation Problems

• Published in: International journal of advanced computer science & applications 2024-01, Vol.15 (9)
• Main Authors: Rahman, Md. Toufiqur, Jamali, A R M Jalal Uddin, Hena, Momta, Hassan, Mohammad Mehedi, Hassan, Md Rafiul
• Format: Article
• Language: English
• Subjects: Allocations; Computer science; Cost analysis; Costs; Inventory control; Linear programming; Methods; Nodes; Opportunity costs; Researchers; Transportation problem
• ISSN: 2158-107X; 2156-5570
• DOI: 10.14569/IJACSA.2024.0150928

Finding an Initial Basic Feasible Solution (IBFS) is the first and essential step in obtaining the optimal solution for any Transportation Problem. Numerous approaches are available in the literature to determine the IBFS; however, many of these methods are modifications of Vogel's Approximate Method (VAM) and/or the Least Cost Method (LCM). None of the existing methods directly consider the capacity of distributions among the nodes when selecting the allocation steps. While researchers have proposed various approaches and demonstrated improved solutions with numerical instances, they have not thoroughly investigated the underlying causes of these results. In this article, we explore the impact of capacity distributions among the nodes on the VAM and LCM in an experimental domain. The study introduces a novel and unique Capacity-Influenced Distribution Indicator (CI-DI) designed to control the flow of allocation. Ultimately, we propose a novel Capacity-Influenced approach that embeds both LCM and VAM to determine the IBFS for Transportation Problems (TPs). The novelty of the proposed approach lies in its direct consideration of capacity distribution among the nodes in the flow of allocations, this feature is lacking in LCM, VAM, and other established approaches. The proposed method develops a novel distribution indicator and a novel cost entry embedded capacity-based matrix to control the flow of allocations and thereby finds the IBFS for the Transportation Problem. We have conducted extensive numerical experiments to assess the effectiveness of the proposed approach. Experimental analysis demonstrates that the proposed method is more efficient in finding the IBFS than existing approaches. Moreover, as it uses a one-time generated Distribution Indicator (DI) for all steps of allocation, it is computationally cheaper than VAM, which generates a DI for each step of allocation.