  This study presents a comprehensive approach to optimizing inventory
management under stochastic demand by leveraging Monte Carlo Simulation (MCS)
with grid search and Bayesian optimization. By using a business case of
historical demand data and through the comparison of periodic review (p, Q) and
continuous review (r, Q) inventory policies, it demonstrates that the (r, Q)
policy significantly increases expected profit by dynamically managing
inventory levels based on daily demand and lead time considerations. The
integration of random and conditional sampling techniques highlights critical
periods of high demand, providing deeper insights into demand patterns. While
conditional sampling reduces execution time, it yields slightly lower profits
compared to random sampling. Though Bayesian optimization marginally
outperforms grid search in identifying optimal reorder quantities and points,
however, given the stochastic nature of the algorithm, this can change with
multiple runs. This study accentuates the effectiveness of advanced simulation
and optimization techniques in addressing complex inventory challenges,
ultimately supporting more informed and profitable inventory management
decisions. The simulation model and optimization framework are open-source and
written in Python, promoting transparency and enabling other researchers and
practitioners to replicate and build upon this work. This contributes to the
advancement of knowledge and the development of more effective inventory
management solutions.
