Optimal division of inventory in a supply chain through estimation of quantiles of non-stationary demand distributions
Hadar Amrani - Ph.D. student
Abstract:
How can the stock in a two echelon inventory system be optimally divided between a logistic depot and several geographically-dispersed bases? We address this question and show that the solution is given in terms of quantiles of the demand distribution functions. If the distribution functions are unknown and the only data we have are samples of demand from previous time periods, then a further question is how to utilize the samples in order to estimate as close as possible the required quantiles. To address this second question, we suggest a new estimator for quantiles of stationary and non-stationary demand distributions and evaluate its quality in the context of the inventory division problem.
The objective of the inventory division problem is to minimize the total cost of inventory shipment, taking into account direct shipments between the depot and the bases, and lateral transshipments between bases. We prove the convexity of the objective function and suggest a procedure for identifying the optimal inventory shares. Small-dimensional cases, as well as a limit case in which the number of bases tends to infinity, are solved analytically for arbitrary distributions of demand. For a general case, an approximation is suggested. We show that, in many practical cases, large proportions of the inventory should be kept at the bases rather than at the depot.
The inventory division problem, as well as some other supply chain problems involve the use of quantiles of demand probability distributions. In real life situations, however, the demand distribution is usually unknown, and has to be estimated from past data. In these cases, quantile prediction is a complicated task, given that: 1. the number of available samples is usually small; 2. the demand distribution is not necessarily stationary. In some cases, the distribution type can be meaningfully presumed, whereas the parameters of the distribution remain unknown. This work suggests a new method for estimating a quantile at a future time period. The method attaches weights to the available samples according to their chronological order, and then, similarly to the sample quantile method, it sets the estimator at the sample that reaches the desired quantile value. The method looks for the weights that minimize the expected absolute error of the estimator. The applicability of the method is illustrated by solving the inventory division problem discussed above, when only limited information about demand distributions in the bases is available.
This work was performed under the supervision of Prof. Eugene Khmelnitsky
ההרצאה תתקיים ביום שלישי, 17.01.17 בשעה 14:00 , בחדר 206, בניין וולפסון, הפקולטה להנדסה, אוניברסיטת תל-אביב.
