Software:
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| Inventory Control with Unobservable Lost Sales and Bayesian Updates |
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| Abstract: |
This paper studies a finite-horizon inventory
model in which demand forecasts are dynamically updated based on sales data and
lost sales are unobservable. Departing from the literature on inventory problems
with censored demand data, which primarily focuses on perishable products, we
assume the product is nonperishable within the planning horizon. This implies
that inventory leftovers can be carried over to fulfill demand in future
periods, which complicates the analysis significantly. We show that the optimal
inventory level in each period is state-dependent but computationally
intractable to obtain. We derive a sample-path expression of the first
derivative function of the optimality equation to characterize the tradeoff in
the inventory decision making. From this expression, we can see that, unlike in
the perishable-product case, the myopic solution is no longer a lower bound on
the optimal inventory level. We then develop tractable bounds on the optimal
inventory level and use them to devise heuristic policies. Finally, to assess
the effectiveness of these heuristic policies, we develop upper bounds on their
value loss relative to the optimal cost. Numerical examples are presented to
illustrate the results. | |
| Keyword: |
Stochastic; inventory; unknown demand
distribution; unobservable lost sales; Bayesian updating; dynamic programming | | |
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