Inventory Management Under Stochastic Demand: A Simulation-Optimization Approach

TL;DR

This paper introduces a simulation-optimization framework using Monte Carlo Simulation, grid search, and Bayesian optimization to improve inventory management under stochastic demand, comparing different policies and sampling techniques.

Contribution

It presents an open-source Python-based simulation and optimization framework that enhances inventory decision-making under demand uncertainty, with insights into sampling methods and policy performance.

Findings

(r, Q) policy increases expected profit significantly.

Conditional sampling reduces execution time but slightly lowers profits.

Bayesian optimization marginally outperforms grid search in finding optimal parameters.

Abstract

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.