Exact Solution for the Upper Minimal Total Cost Bound of Multi-Supplier Single-Buyer Interval Transportation Problem

Abstract

Transporting a commodity from sources to destinations with minimal transportation cost is the main goal in all industries. In the literature, researchers have given considerable attention to find the total minimum transportation cost in fixed supply and fixed demand quantities. However, in the real-world supply, demand values will vary in a certain range due to the variation of the global economy. The number of combinations of supplies and demands rapidly increase in their respective ranges as the number of suppliers and buyers increases. To make better decisions on investments, it is useful to know the lower and the upper bounds of the minimal total costs in the interval transportation problem (ITP). However, no exact solution has been identified to obtain the upper bound of minimal transportation cost. In this research, a new algorithm has been developed to determine all the choices of supplies and demands in multi-supplier singlebuyer transportation problems. Based on the new method, the minimum transportation cost can be found for each combination that satisfies the fundamental theory of transportation problem (total supplies value ≥ demand value). Furthermore, the maximum cost as the upper minimal total cost bound can also be obtained. The new methodology is illustrated using real data. It is also shown that the proposed method is able to obtain the exact solution for the upper minimal total cost bound of multi-supplier single-buyer ITP. Keywords: Demand and Supply; Transportation problem; Transportation cost; Total cost bound