B0189
Title: Likelihood based estimation in three parameter beta distribution with application in critical inventory decision
Authors: Soham Ghosh - Indian Institute of Technology Indore (India) [presenting]
Sujay Mukhoti - Indian Institute of Management Indore (India)
Pritee Sharma - Indian Institute of Technology Indore (India)
Abhirup Banerjee - University of Oxford (United Kingdom)
Abstract: In classical newsvendor problems, losses are assumed to be linear in quantity. For critical yet perishable commodities, this linearity assumption is not appropriate. A generalized model is proposed by substituting the piecewise linear cost function with the piecewise polynomial cost function. A large proportion of works on the newsvendor model assume the vendor has complete knowledge about the true demand. Such situations are rarely encountered in the real world, and she has to estimate the demand from the historically available data. The demand is assumed to follow a completely unknown probability distribution. For the parametric estimation, multi-parameter families like log-normal and scaled beta distributions are considered. They provide a more realistic fit to complex demands but are computationally complicated. Simple demands are also considered such as single parameter uniform and exponential, which are computationally less complex although being unrealistic. The existence and consistency of the estimated optimal order quantity are established. Non-parametric estimator of optimal order quantity is determined by solving an estimating equation and strong consistency of the estimator is established when multiple solutions of the equation are available. A comparative study is performed between two approaches in terms of accuracy, precision, and computational complexity based on both simulated and real-life datasets.
