A novel Markovian queueing-inventory model with imperfect production and inspection processes: A hospital case study

This paper studies an imperfect production process in an M/M/1 queueing system with an attached inventory screened by an imperfect inspector. The production system follows a Poisson process, and it may produce defective items that are supposed to be detected by an inspection process. The items form an M/M/1 queue in the inspection system. Moreover, the inspector is prone to type 1 and type 2 misclassifications. According to a Poisson process, customers arrive at the system and leave it after service with precisely one item. Provided that items are out-of-stock, the customers in the system must wait while the freshly arriving customers are lost. For the first time, this paper investigated the effect of the imperfect production process on the queuing-inventory system with an inspection process that may involve both type 1 and type 2 misclassifications. Under station-ary conditions, we prove that the number of customers in the system, the on-hand inventory, and the number of items in the inspection system are independent, which led to driving the joint stationary distribution in explicit product form. A single variable nonlinear programming model (SVNLPM) is developed to minimize the expected total cost concerning the production rate using long-run performance measures. A mathematical proof identifies the beneficial properties of the expected total cost. We also evaluate the impact of essential parameters such as defective probability, type 1 and type 2 misclassifications, customers arrival rate, etc., on the optimal production rate and the expected total cost through extensive numerical examples and sensitivity analysis. We also apply our model to a real case study of blood inventory management in a hospital in Tehran. Finally, remarkable mana-gerial and industrial implications are presented.