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We consider a stochastic inventory system that has been operated under a policy different from the one that will be implemented in the future. Such a situation may arise as a result of changes in model assumptions leading to the implementation of a different policy. Before the new policy is implemented, there may be some units on hand which may exceed the optimal order-up-to level. Hence, one needs to evaluate a one-time inventory disposal decision immediately before the new policy replaces the policy in use. For this purpose, we develop three models under different assumptions that describe the demand during the disposal period and present analytical results characterizing their optimal solutions. [ABSTRACT FROM AUTHOR]

In many inventory control contexts, inventory levels are only partially (i.e., not fully) observed. This may be due to nonobservation of demand, spoilage, misplacement, or theft of inventory. We study a discrete-time periodic-review inventory system where the unmet demand is backordered. When the 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 observed 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 continuity of the solution to dynamic programming equations are proved when the discount factor is sufficiently small. [ABSTRACT FROM AUTHOR]

In many inventory control contexts, inventory levels are only partially (i.e., not fully) observed. This may be due to nonobservation of demand, spoilage, misplacement, or theft of inventory. We study a partially observed inventory system where the demand is not observed, inventory level is noticed when it reaches zero, the unmet demand is lost, and replenishment orders must be decided so as to minimize the total discounted costs over an infinite horizon. This problem has an infinite-dimensional state space, and for it we establish the existence of a feedback policy when single-period costs are bounded or when the discount factor is sufficiently small. We also provide an approximately optimal feedback policy that uses a finite state representation. [ABSTRACT FROM AUTHOR]

Information delays exist when the most recent inventory information available to the Inventory Manager (IM) is dated. In other words, the IM observes only the inventory level that belongs to an earlier period. Such situations are not uncommon, and they arise when it takes a while to process the demand data and pass the results to the IM. We introduce dynamic information delays as a Markov process into the standard multiperiod stochastic inventory problem with backorders. We develop the concept of a reference inventory position. We show that this position along with the magnitude of the latest observed delay and the age of this observation are sufficient statistics for finding the optimal order quantities. Furthermore, we establish that the optimal ordering policy is of state-dependent base-stock type with respect to the reference inventory position (or state-dependent ( s, S) type if there is a fixed ordering cost). The optimal base stock and ( s, S) levels depend on the magnitude of the latest observed delay and the age of this observation. Finally, we study the sensitivity of the optimal base stock and the optimal cost with respect to the sufficient statistics. [ABSTRACT FROM AUTHOR]

Information delays exist when the most recent inventory information available to the inventory manager (IM) is dated; namely, the IM observes only the inventory level of an earlier period. We introduce information delays into the standard multiperiod stochastic inventory problem with backorders. We consider two types of information delays: (i) a constant delay and (ii) a random delay. We define an appropriate reference inventory position, which is a sufficient statistics for finding the optimal order quantity. We show that the optimal ordering policy is of base-stock type with respect to the reference inventory position and is of (s, S) type if there is also a fixed cost of ordering. [ABSTRACT FROM AUTHOR]

We consider a periodic-review stochastic inventory problem in which demands for a single product in each of a finite number of periods are independent and identically distributed random variables. We analyze the case where shortages (stockouts) are penalized via fixed and proportional costs simultaneously. For this problem, due to the finiteness of the planning horizon and non-linearity of the shortage costs, computing the optimal inventory policy requires a substantial effort as noted in the previous literature. Hence, our paper is aimed at reducing this computational burden. As a resolution, we propose to compute "the best stationary policy." To this end, we restrict our attention to the class of stationary base-stock policies, and show that the multi-period, stochastic, dynamic problem at hand can be reduced to a deterministic, static equivalent. Using this important result, we introduce a model for computing an optimal stationary base-stock policy for the finite horizon problem under consideration. Fundamental analytic conclusions, some numerical examples, and related research findings are also discussed. [ABSTRACT FROM AUTHOR]

This study analyzes a stochastic continuous review inventory system (Q,r) using a simulation-based optimization model. The lead time depends on lot size, unit production time, setup time, and a shop floor factor that represents moving, waiting, and lot size inspection times. A simulation-based model is proposed for optimizing order quantity (Q) and reorder point (r) that minimize the total inventory costs (holding, backlogging, and ordering costs) in a two-echelon supply chain, which consists of two identical retailers, a distributor, and a supplier. The simulation model is created with Arena software and validated using an analytical model. The model is interfaced with the OptQuest optimization tool, which is embedded in the Arena software, to search for the least cost lot sizes and reorder points. The proposed model is designed for general demand distributions that are too complex to be solved analytically. Hence, for the first time, the present study considers the stochastic inventory continuous review policy (Q,r) in a two-echelon supply chain system with lot size-dependent lead time L(Q). An experimental study is conducted, and results are provided to assess the developed model. Results show that the optimized Q and r for different distributions of daily demand are not the same even if the associated total inventory costs are close to each other. [ABSTRACT FROM AUTHOR]