An Integrated GMIR And Lagrangian Optimization ApproachFor Triangular Fuzzy Inventory Management In Frozen FoodSupply Chain

Abstract

Efficient inventory management in the frozen food supply chain is challenging because of
uncertain demand, refrigeration requirements, transportation variability, and backup
cooling costs. This study proposes a triangular fuzzy inventory optimization model
integrated with the Graded Mean Integration Representation (GMIR) approach to support
cost-effective replenishment decisions under uncertain operating conditions. A real-life
frozen food application involving products such as frozen shrimp, fish fillets, frozen
vegetables, and ready-to-cook items is considered. The uncertain parameters are
represented by triangular fuzzy numbers, while deterministic parameters related to
refrigeration operations and storage are maintained in crisp form. The fuzzy parameters are
defuzzified using the GMIR method, and the resulting inventory model is optimized through
a nonlinear cost minimization procedure to determine the optimal order quantity and the
corresponding minimum total inventory cost. A numerical example demonstrates the
applicability of the proposed framework in balancing replenishment, refrigeration,
transportation, spoilage, and backup refrigeration expenses. Furthermore, a sensitivity
analysis using a dataset of 200 frozen food products is conducted to evaluate the robustness
of the model under varying demand and operational conditions. The results indicate that the
proposed GMIR-based triangular fuzzy model provides stable inventory planning in frozen
food supply chain systems. The proposed framework offers a practical decisions-support tool
for sustainable, energy-efficient, and economically optimized frozen food inventory
management.