Inventory Planning in a G/G/1/∞ Queuing System with Multiple Suppliers using Simulation and Response Surface Methodology

In this study, a G/G/1/∞ queuing system is considered in which to servicing each costumer, an on-hand inventory is required. Continuous review (r, Q) policy is considered and procurement is done through multiple suppliers and lead time is stochastic with certain probability density functions. During stock out, arriving demands are rejected and their requests are lost also a waiting cost is considered for customers within the system. Our goal in this study is determining economic order quantity (Q) and reorder point (r) whit minimizing summation of various costs includes holding costs, ordering costs, shortage and waiting costs. Due to complexity of exact approaches such as Markov process, we considered a simulation-optimization approach that combines simulation with design of experiments. To evaluate the efficiency of proposed approach, in a special case (two suppliers with exponential lead times) several numerical examples are solved by both exact and simulation-optimization approaches. Comparing the results shows that while our proposed method is much simpler in terms of computational complexity than the Markovian model, offers very close answers to the optimal answer.