Abstract
Demand estimation is often confronted with incomplete information of censored demand because of lost sales. Many estimators have been proposed to deal with lost sales when estimating the parameters of demand distribution. This study introduces the cross-selling effect into estimations, where two items are cross-sold because of the positive externality in a newsvendor-type inventory system. We propose an approach to estimate the parameters of a jointly normally distributed demand for two cross-selling items based on an iterative framework considering lost sales. Computational results based on more than two million numerical examples show that our estimator achieves high precision. Compared with the point estimations without lost sales, all the relative errors of the estimations of demand expectation, standard deviation, and correlation coefficient are no larger than 2% on average if the sample size is no smaller than 800. In particular, for demand expectation, the error is smaller than 1% if the comprehensive censoring level is no larger than four standard deviations (implying a 2σ-level of safety stock for each item), even if the sample size decreases to 50. This implies that the demand estimator should be competent in modern inventory systems that are rich in data.
Highlights
In newsvendor-type inventory models, it is frequently assumed that the demand distribution for items is known or can be estimated based on sales data [1, 2]
This study introduces the crossselling effect into estimations, where two items are cross-sold because of the positive externality in a newsvendor-type inventory system
Many estimators estimate the parameters of demand distribution for a single item based on the observed demand and considering unobservable lost sales
Summary
In newsvendor-type inventory models, it is frequently assumed that the demand distribution for items is known or can be estimated based on sales data [1, 2]. Estimating the demand directly based on sales data implies that the sales quantity must be exactly equal to the realistic demand amount. This is not the case in practice [3]. The order quantity of an item is finite; the inventory is limited but demand is often uncertain. Studies show that more than 85% of customers choose to give up the products when the items are out of stock [4], and the sales amount is the censored information of demand. When sales data is considered, demand might be underestimated To remedy this flaw, demand estimation methods for censored sales data have been proposed [5, 6]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
