SSRN Author: Ruixia (Sandy) ShiRuixia (Sandy) Shi SSRN Content
https://privwww.ssrn.com/author=718960
https://privwww.ssrn.com/rss/en-usThu, 25 Jun 2020 01:18:16 GMTeditor@ssrn.com (Editor)Thu, 25 Jun 2020 01:18:16 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0REVISION: Partially Observed Inventory Systems: The Case of Rain ChecksIn many inventory control contexts, inventory levels are only partially (i.e., not fully) observed. This may be due to non-observation of demand, spoilage, misplacement, or theft of inventory. We study a periodic review inventory system where the unmet demand is backordered. When inventory level is nonnegative, the inventory manager does not know the exact inventory level. Otherwise, inventory shortages occur and the inventory manager issues rain checks to customers. The shortages are fully observable via the rain checks. The inventory manager determines the order quantity based on the partial information on the inventory level. The objective is to minimize the expected total discounted cost over an infinite horizon. The dynamic programming formulation of this problem has an infinite dimensional state space. We use the methodology of the unnormalized probability to establish the existence of an optimal feedback policy when the periodic cost has linear growth. Moreover, uniqueness and ...
https://privwww.ssrn.com/abstract=1087812
https://privwww.ssrn.com/1913012.htmlWed, 24 Jun 2020 14:10:59 GMTREVISION: Computation of Approximate Optimal Policies in a Partially Observed Inventory Model with Rain ChecksThis paper proposes a new methodology to solve partially observed inventory problems. Generally, these problems have infinitedimensional states that are conditional distribution of the inventory level. Our methodology involves linearizing the state transitions via unnormalized probabilities. It then uses an appropriate functional basis to represent the state. Considering the speed and stability of computations, we choose truncated Chebyshev polynomials as the basis. We use Fast Fourier Transforms along with an appropriate discretization of inventory levels to speed up the computations. These main ideas are to obtain an iterative algorithm to solve a partially observed inventory model with rain checks. In this model, the inventory manager (IM) does not know the inventory level when it is positive. Otherwise, the IM fully observes it. This model provides a context to illustrate our methodology, which applies to other such models. Although this model has been studied mathematically in ...
https://privwww.ssrn.com/abstract=1470519
https://privwww.ssrn.com/1886483.htmlThu, 16 Apr 2020 09:58:48 GMTREVISION: An Incomplete Information Inventory Model with Presence of Inventories or Backorders as Only ObservationsIn many real-life contexts, inventory levels are only incompletely observed due to nonobservation of demand, discrepancies in transmitting sales data, transaction errors, spoilage, misplacement, or theft of inventory. We study a periodic review inventory system where the demand is not observed and the unmet demand is backordered. As a result, the inventory manager cannot tell the exact quantities of inventories or backorders. However, by looking at the shelf, he knows whether the inventory is positive or non-positive. Only with this information, the inventory manager must determine the order quantity in each period that would minimize the expected total discounted cost over an infinite-horizon. The dynamic programming formulation of this problem has an infinitedimensional state space. We use the concept of unnormalized probability to establish the existence of an optimal feedback policy and the uniqueness of the solution of the dynamic programming equation when the periodic cost has ...
https://privwww.ssrn.com/abstract=1102846
https://privwww.ssrn.com/1845910.htmlMon, 02 Dec 2019 12:20:16 GMT