Optimal analysis of a multi-server queue with preprocessing time and replenishment inventory

Abstract

ABSTRACT Recently, e-commerce has had the advantage of lower rental expenses. Convenient online payment has rapidly grown and provides a great business opportunity for enterprises. Inventory management plays a critical role in the competitiveness of most electronic business enterprises. Before the products hit the store shelves or are available online to customers, the quantity and quality of the products should be confirmed and inspected. Thus, in addition to the replenishment lead time, the preprocessing time has essential effects on inventory management. To reduce the inventory cost and determine a proper replenishment policy, we propose a multi-server inventory queue with a preprocessing time, which is seldom mentioned by the existing studies. The steady-state probabilities, system stability conditions, and expressions of several critical system characteristics are derived. Subsequently, the operating cost function is developed to determine the optimal reorder point and an appropriate number of servers with the minimum cost. The established numerical results and sensitivity analysis help managers identify critical variables and enhance operational efficiency.