Optimality of Base-Stock and (s, S) Policies for Inventory Problems with Information Delays

Bensoussan, Alain; Çakanyıldırım, M.; Sethi, Suresh P.

doi:10.1007/s10957-006-9106-8

Cited by 22 publications

(27 citation statements)

References 8 publications

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“…This relation can be recursively proved as in Lemma 3 of Bensoussan, Ç akanyıldırım, and Sethi (2006). To succinctly write the single-period costs, we let D i denote the sum of i many i.i.d.…”

Section: Dynamic Programming Formulationmentioning

confidence: 99%

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Optimal Ordering Policies for Inventory Problems With Dynamic Information Delays

Bensoussan

Çakanyıldırım

Sethi

2007

Production and Operations Management

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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.

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Section: Dynamic Programming Formulationmentioning

confidence: 99%

“…We had achieved the same amount of reduction with independent delays. Also, the case of a random delay requires two dimensional state space (Bensoussan, Ç akanyıldırım, Sethi 2006). When the delays are modelled by a general Markov chain, the dimension of the state space can be reduced only to three.…”

Section: Noncrossing Delaysmentioning

confidence: 99%

Optimal Ordering Policies for Inventory Problems With Dynamic Information Delays

Bensoussan

Çakanyıldırım

Sethi

2007

Production and Operations Management

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“…In their model, however, the latest market demand information is exploited when the order quantity is determined. Bensoussan et al (2006) and Bensoussan et al (2007) investigate the optimum ordering policy when inventory information is lagged. They conclude that an Order-Up-To (OUT) type policy is an optimum ordering policy for this problem when only inventory costs are present.…”

Section: Introductionmentioning

confidence: 99%

On the replenishment policy when the market demand information is lagged

Hosoda

Disney

2012

International Journal of Production Economics

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We consider a situation where the most up-to-date information on the market demand and the inventory levels is not available to a replenishment decision maker in a single echelon of a supply chain. The objective of the decision maker is to minimise the sum of the inventory and the production costs. An intuitively attractive strategy under this setting might be to reduce the information time lag as much as possible by utilising information technologies such as RFID. We call this strategy the Time lag Elimination Strategy (TES). However, this course of action requires investment in information systems and will incur a running cost. We propose an alternative strategy that has similar economic consequences as the TES strategy, but it does not require new information systems. We call this strategy the Controlling Dynamics Strategy (CDS). The benefit coming from CDS is quantified and is compared to that from TES. We also quantify the benefits gained from the combined use of these two strategies. A new ordering policy is introduced that is easy to implement without any forecasting systems and can reduce the production cost significantly.

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“…In Section 4, we provide an inventory model which admits a sufficient statistic. Sections 2, 3 and 4 are respectively based on [5], [3] and [4].…”

Section: Introductionmentioning

confidence: 99%

On the Optimal Control of Partially Observed Inventory Systems

2008

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This paper introduces recent developments in the analysis of inventory systems with partial observations. The states of these systems are typically conditional distributions, which evolve in infinite dimensional spaces over time. Our analysis involves introducing unnormalized probabilities to transform nonlinear state transition equations to linear ones. With the linear equations, the existence of the optimal feedback policies are proved for two models where demand and inventory are partially observed. In a third model where the current inventory is not observed but a past inventory level is fully observed, a sufficient statistic is provided to serve as a state. The last model serves as an example where a partially observed model has a finite dimensional state. In that model, we also establish the optimality of the basestock and (s, S) policies, hence generalizing the corresponding classical models with full information. RésuméOn présente un certain nombre de modèles de systèmes de stocks avec information partielle. Ils sont formalisés comme des problèmes de contrôle où l'etat est une probabilité conditionnelle, dans un espace de dimension infinie. On introduit des probabilités non normalisées, permettant de transformer deséquations non linéaires enéquations linéaires. On peut alors montrer l'existence de feedbacks optimaux pour deux modèles où la demande et le stock sont partiellement observables. Dans un troisième modèle, le stock n'est pas observé, mais un stock antérieur est observé. Une statistique exhaustive est obtenue, et l'état est de dimension finie. Onétablit l'optimalité des politiques "stock de base" et (s, S), généralisant les modèles classiques avec information complète. * Recherche Opérationnelle/ Operations Research, présentée par Alain Bensoussan † Professeur Emerite, Université Paris Dauphine ‡ {alain.bensoussan, metin, sethi}@utdallas.edu Version Française AbrégéeBien que la gestion des stocks aitété l'objet d'une littérature considérable, la situation où l'information est partielle n'a pratiquement pasété abordée jusqu'à présent. On montre, sur un certain nombre de modèles, comment l'idée très féconde des probabilités conditionnelles non normalisées, introduites dans le filtrage non linéaire par Zakaï peutêtre adaptée et permet d'établir l'existence de politiques optimales. Les problèmesà traiter sont du type suivantoù p(x|ξ) est la probabilité de transition d'une chaîne de Markov, z t est le processus observé, q t le contrôle adaptéà Z t−1 . π t (x) est une probabilité conditionnelle et représente l'état du système. L'équation de Bellman associée est donnée parLa linéarisation est obtenue par les equations (8), (10), (11) ci dessous. Un principe de contraction peut s'appliquerà (8) et permet de résoudre aussi (2), et d'obtenir un feedback optimal. Un problème beaucoup plus complexe est décrit par leséquations (25), (32), (33). Là aussi, la linéarisation simplifie considérablement, même si le principe de contraction ne s'applique plus. On prouve l'existence d'une solution maximale qu...

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Optimality of Base-Stock and (s, S) Policies for Inventory Problems with Information Delays

Cited by 22 publications

References 8 publications

Optimal Ordering Policies for Inventory Problems With Dynamic Information Delays

Optimal Ordering Policies for Inventory Problems With Dynamic Information Delays

On the replenishment policy when the market demand information is lagged

On the Optimal Control of Partially Observed Inventory Systems

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