A Mathematical Model for a Blood Supply Chain Network with the Robust Fuzzy Possibilistic Programming Approach: A Case Study at Namazi Hospital

Document Type : Original Article


1 Faculty of Engineering, Yazd University, Yazd, Iran

2 Yazd University

3 Industrial Engineering, Faculty of Engineering, Meybod University


The main challenge in blood supply chain is the shortage and wastage of blood products. Due to the perishable characteristics of this product, saving a large number of blood units on inventory causes the spoil of these limited and infrequent resources. On the other hand, a lack of blood may lead to the cancellation of health-related critical activities, and the result is a potential increase in mortality in hospitals. In this paper, an integer programming model was proposed to minimize the total cost, shortage, and wastage of blood products in Namazi hospital by considering the different types of blood groups. The parameters in the real-world are uncertain, and this problem will be examined in the paper. The robust fuzzy possibilistic programming approach is presented, and a numerical illustration of the Namazi hospital is used to show the application of the proposed optimization model. Sensitivity analysis is conducted to validate the model for problems such as certainty level, coefficient weight, and penalty value of the objective function in the robust fuzzy possibilistic programming. The numerical results imply the model is able to control uncertainty and the robustness price is imposed on the system; therefore, the value of the objective function in the robust fuzzy possibilistic is 80% lower than probabilistic.