An approximate solution to fixed charge fuzzy transshipment problems

This paper aims to find an approximate solution to the fixed charge fuzzy transshipment problem using asymmetric pentagonal fuzzy numbers. Transshipment problems involve the movement of goods from supply nodes to demand nodes through intermediate nodes, minimizing transshipment costs while satisfying supply and demand constraints. The methodology presented formulates the problem as an integer-programming model, incorporating fuzzy parameters to account for uncertainties in costs. Fixed charges play a critical role in this context, as they are often incurred whenever a shipment is made, regardless of the quantity transported. This requirement adds a layer of complexity to decision-making, necessitating careful consideration of fixed charges/costs to achieve cost-effective solutions. In this study, we develop a technique to approximate the solution to fixed charge fuzzy transshipment problem by establishing both lower and upper bounds for the optimal value taking into account asymmetric pentagonal fuzzy numbers. Our work includes a comprehensive analysis of the problem structure and the development of a systematic solution method. Illustrative examples are provided to demonstrate the effectiveness of the proposed method in finding approximate solution. The findings have significant applications in logistics and supply chain management, particularly in industries where uncertainty plays a crucial role.