Designing a new mathematical model based on ABC analysis for inventory control problem: A real case study

In modern business today, organizations that hold large numbers of inventory items, do not find it economical to make policies for the management of individual inventory items. Managers, thus, need to classify these items according to their importance and fit each item to a certain asset class. The method of grouping and inventory control available in traditional ABC has several disadvantages. These shortcomings have led to the development of an optimization model in the present study to improve the grouping and inventory control decisions in ABC. Moreover, it simultaneously optimizes the existing business relationships among revenue, investment in inventory and customer satisfaction (through service levels) as well as a company’s budget for inventory costs. In this paper, a mathematical model is presented to classify inventory items, taking into account significant profit and cost reduction indices. The model has an objective function to maximize the net profit of items in stock. Limitations such as budget even inventory shortages are taken into account too. The mathematical model is solved by the Benders decomposition and the Lagrange relaxation algorithms. Then, the results of the two solutions are compared. The TOPSIS technique and statistical tests are used to evaluate and compare the proposed solutions with one another and to choose the best one. Subsequently, several sensitivity analyses are performed on the model, which helps inventory control managers determine the effect of inventory management costs on optimal decision making and item grouping. Finally, according to the results of evaluating the efficiency of the proposed model and the solution method, a real-world case study is conducted on the ceramic tile industry. Based on the proposed approach, several managerial perspectives are gained on optimal inventory grouping and item control strategies.