A0339
Title: Likelihood based estimation of optimal order quantity
Authors: Sujay Mukhoti - Indian Institute of Management Indore (India) [presenting]
Soham Ghosh - Indian Institute of Technology Indore (India)
Abstract: Three distinct approaches are proposed and evaluated: Maximum likelihood estimation (MLE), Markov chain Monte Carlo (MCMC), and non-parametric estimation for determining the optimal order quantity in inventory systems under demand uncertainty. As a benchmark, maximum likelihood estimation is employed to fit conventional demand distributions (e.g., log-normal, generalized beta), and the optimal order quantity is computed based on estimated parameters. This method offers analytical tractability and ease of implementation, particularly when demand closely follows known parametric forms. Alternatively, MCMC-based estimators are constructed to account for parameter and model uncertainty by exploring posterior distributions over both space and structure. To provide a more assumption-agnostic alternative, a non-parametric method is also implemented based solely on historical demand data. This approach directly minimizes the empirical cost function over order quantities without imposing any parametric form, thereby enhancing flexibility and robustness in real-world contexts where demand may be skewed. A detailed simulation study compares these three approaches across varying demand scenarios.
