A Non-Parametric Approach to Stochastic
Inventory Planning with
Lost Sales and Censored Demand
Woonghee
Tim Huh and Paat Rusmevichientong
Dept. of
Industrial Engineering and Operations Research
We study
stochastic inventory planning systems with lost sales. Contrary to the
classical inventory theory, we assume that no knowledge of demand is initially
available, and lost sales in each period is unobservable. We take a
non-parametric approach and propose adaptive inventory policies that depend
only on the historical sales data of the past.
To
assess the quality of our inventory policies, we use as a benchmark the optimal
expected cost that would have incurred if the true distribution were
known. Our adaptive algorithms are easy
to implement and converge to the optimal solution. Furthermore, the running
average of cost during the first T
period differs from the optimal cost by at most O(1/T1/2). Extensive
computation shows that our adaptive policies perform well.