Bounds and Heuristics for Optimal Bayesian Inventory Control with Unobserved Lost Sales
نویسنده
چکیده
In most retail environments, when inventory runs out, the unmet demand is lost and not observed. The sales data are effectively censored by the inventory level. Factoring this censored data effect into demand estimation and inventory control decision makes the problem difficult to solve. In this paper, we focus on developing bounds and heuristics for this problem. Specifically, we consider a finite-horizon inventory control problem for a nonperishable product with unobserved lost sales and a demand distribution having an unknown parameter. The parameter is estimated sequentially by the Bayesian updating method. We first derive a set of solution upper bounds that work for all prior and demand distributions. For a fairly general monotone likelihood-ratio distribution family, we derive relaxed but easily computable lower and upper bounds along an arbitrary sample path. We then propose two heuristics. The first heuristic is derived from the solution bound results. Computing this heuristic solution only requires the evaluation of the objective function in the observed lost-sales case. The second heuristic is based on the approximation of the first-order condition. We combine the first-order derivatives of the simpler observed lost-sales and perishable-inventory models to obtain the approximation. For the latter case, we obtain a recursive formula that simplifies the computation. Finally, we conduct an extensive numerical study to evaluate and compare the bounds and heuristics. The numerical results indicate that both heuristics perform very well. They outperform the myopic policies by a wide margin.
منابع مشابه
An Envelope Theorem for Bayesian Dynamic Program and Its Application to an Inventory Problem
A generalized envelope theorem is established for a Bayesian dynamic program problem. An application of the theorem is given in a Bayesian inventory management problem with unobserved lost sales. Specifically, we show that the optimal inventory level with unobserved lost sales is greater than the optimal inventory level with observed lost sales. We prove this result under the continuous demand ...
متن کاملInventory Control with Unobservable Lost Sales and Bayesian Updates
We study a finite-horizon lost-sales inventory model. The demand distribution is unknown and is dynamically updated based on the previous sales data in a Bayesian fashion. We derive a samplepath representation of the first order optimality condition, which characterizes the key tradeoff of the problem. The expression allows us to see why the computation of the optimal policy is difficult and wh...
متن کاملDynamic Inventory Management with Learning About the Demand Distribution and Substitution Probability
A result in the Bayesian inventory management literature is: If lost sales are not observed, the Bayesian optimal inventory level is larger than the myopic inventory level (one should “stock more” to learn about the demand distribution). This result has been proven in other studies under the assumption that inventory is perishable, so the myopic inventory level is equal to the Bayesian optimal ...
متن کاملPeriodic Review Inventory Control With Lost Sales and Fractional Lead Times
We introduce a single location periodic review inventory control problem with lost sales and fractional lead times. We model the optimal inventory control problem as a stochastic dynamic program and analyze properties of the objective function as well as the optimal policy. We present upper and lower bounds on the optimal policy. These bounds can readily be used in easily computable heuristics....
متن کاملOld and New Methods for Lost-Sales Inventory Systems
We present two results to aid the numerical solution of the notoriously di¢ cult discrete-time inventory model with stochastic demands, a constant leadtime, and lost sales. First, we show that the e¤ective state space is a relatively manageable compact set. Second, we show that the optimal cost is increasing in the leadtime, and we use this fact to construct a good lower bound on the optimal-co...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Operations Research
دوره 58 شماره
صفحات -
تاریخ انتشار 2010