Multi-objective inventory model incorporating shortage cost and delayed replenishment with diverse fuzzy number applications using C++ programming language

Abstract

Today’s supply chains face many problems, especially when it comes to managing inventory.  Delays in getting supplies, sudden changes in customer demand, and the high cost of running out of stock make  planning difficult. Most traditional models use fixed values, which don’t work well when things are uncertain.  Although fuzzy logic has been used to handle uncertainty, many studies only use simple fuzzy numbers, which  don’t fully capture the complexity of real-life situations. This study introduces an improved inventory model  that considers both shortage costs and delays in restocking. It uses four types of fuzzy numbers trapezoidal,  pentagonal, hexagonal, and decagonal to show different levels of uncertainty more accurately. The model is  programmed in C++ and uses a special method called graded mean integration to turn fuzzy numbers into  useful values. Results show that while trapezoidal numbers produce basic results, pentagonal and hexagonal  numbers are better especially hexagonal, which provides the lowest overall cost. The model also deals with  uncertainty in how long restocking takes. The article examines a fuzzy inventory model using trapezoidal,  pentagonal, and hexagonal fuzzy numbers. It finds trapezoidal fuzzy numbers ineffective for cost efficiency,  while pentagonal and hexagonal fuzzy numbers outperform crisp models, enhancing inventory management  decision-making.