Monotonicity and supermodularity results for the Erlang loss system

For the Erlang loss system with s servers and offered load a, we show that: (i) the load carried by the last server is strictly increasing in a; (ii) the carried load of the whole system is strictly supermodular on f(s; a)js = 0; 1; : : : and a > 0g

Comparing Markov Chains: Aggregation and Precedence Relations Applied to Sets of States, with Applications to Assemble-to-Order Systems

International audienceSolving Markov chains is, in general, difficult if the state space of the chain is very large (or infinite) and lacking a simple repeating structure. One alternative to solving such chains is to construct models that are simple to analyze and provide bounds for a reward function of interest. We present a new bounding method for Markov chains inspired by Markov reward theory: Our method constructs bounds by redirecting selected sets of transitions, facilitating an intuitive interpretation of the modifications of the original system. We show that our method is compatible with strong aggregation of Markov chains; thus we can obtain bounds for an initial chain by analyzing a much smaller chain. We illustrate our method by using it to prove monotonicity results and bounds for assemble-to-order systems

Optimal Structural Results for Assemble-to-Order Generalized M-Systmes

Cataloged from PDF version of article.We consider an assemble-to-order generalized M-system with multiple components and multiple products, batch ordering of components, random lead times, and lost sales. We model the system as an in nite-horizon Markov decision process and seek an optimal control policy, which speci es when a batch of components should be produced and whether an arriving demand for each product should be satis ed. To facilitate our analysis, we introduce new functional characterizations for convexity and submodularity with respect to certain non-unitary directions. These help us characterize optimal inventory replenishment and allocation policies under a mild condition on component batch sizes via a new type of policy: lattice-dependent base-stock and lattice-dependent rationing

Applied Probability

[no abstract available

A Markovian approach to the mathematical control of NPD projects

+182hlm.;23c

Analysis of dual sourcing strategies under supply disruptions

We study a dual-sourcing problem of a firm in the face of supply disruptions from two suppliers: local and overseas. Under four different scenarios of disruption source and information availability, we characterize the optimal dynamic policy that simultaneously determines sourcing decisions to minimize the expected total discounted cost. Different from the previous dual-sourcing models without information availability in the literature, we develop a two-dimensional stochastic dynamic programming model to explicitly address this issue. Further, we analyze the impact of disruption source and information availability on cost performance. We find that (i) a supply disruption at the local source may cause a more remarkable deterioration of cost efficiency than a supply disruption at the overseas source; (ii) the information about the local source is more valuable than that about the overseas source; (iii) when a firm orders from both sources, the disruption information can achieve a significant cost saving. These findings contribute to the theory of strategic sourcing by demonstrating the value of information available at different sources. Moreover, they can also be used as a valuable guideline for managers to select an appropriate sourcing strategy in business practices. (C) 2015 Elsevier B.V. All rights reserved

Probability masses fitting in the analysis of manufacturing flow lines

A new alternative in the analysis of manufacturing systems with finite buffers is presented. We propose and study a new approach in order to build tractable phase-type distributions, which are required by state-of-the-art analytical models. Called "probability masses fitting" (PMF), the approach is quite simple: the probability masses on regular intervals are computed and aggregated on a single value in the corresponding interval, leading to a discrete distribution. PMF shows some interesting properties: it is bounding, monotonic and it conserves the shape of the distribution. After PMF, from the discrete phase-type distributions, state-of-the-art analytical models can be applied. Here, we choose the exactly model the evolution of the system by a Markov chain, and we focus on flow lines. The properties of the global modelling method can be discovered by extending the PMF properties, mainly leading to bounds on the throughput. Finally, the method is shown, by numerical experiments, to compute accurate estimations of the throughput and of various performance measures, reaching accuracy levels of a few tenths of percent.stochastic modelling, flow lines, probability masses fitting, discretization, bounds, performance measures, distributions.

Gestion des stocks et de la production intégrant des retours de produits

De nombreux retours de produits dus au recyclage et à la réutilisation des déchets se développent dans le but de préserver les ressources naturelles limitées de notre planète. Ces nouveaux flux interagissant avec les flux de production traditionnels, il est important de les piloter de façon à satisfaire au mieux les demandes des clients et minimiser l'encours dans la chaîne logistique. Nos travaux s'inscrivent dans cette démarche. Nous nous plaçons dans un contexte où la capacité de production est limitée et nous considérons un problème opérationnel de gestion des stocks et de la production intégrant des flux de retours. Nous modélisons trois problèmes de production et de stockage à temps continu, avec des capacités de production limitées, des délais aléatoires et des coûts linéaires. Le premier prenant en compte la probabilité qu'un produit puisse être réutilisé comme produit fini ou seulement comme produit semi-fini (par partie), le deuxième présentant un problème où la réutilisation d'un retour comme produit fini nécessite une étape de remise à neuf et le troisième modélisant un système où les clients préviennent à l'avance du renvoi potentiel de leurs produits. Outre la caractérisation des politiques optimales de gestion, une part importante de nos contributions réside dans l'évaluation des performances de différentes politiques heuristiques et l'étude de l'impact de la capacité de production sur celles-ci. Enfin, nous nous servons dans tout ce document d'outils permettant la caractérisation des politiques optimales. La dernière partie de ce document vise à développer ces outils et à permettre l'étude de l'effet des paramètres d'un système formulé en processus de décision Markovien sur la politique optimale de celui-ci.Flows of returns due to recycling and reusing waste are developing in order to preserve the limited natural resources of our planet. These new flows interact with the traditional production flows. Therefore, in order to provide customers with the best service level and minimize the stock in the supply chain, the control of the return flows appears to be of highest importance. We address this problem by modeling a situation with a limited porduction capacity and we consider an operational production/inventory problem that incorporates flows of returns. We model three continuous-time production/inventory problems with limited produc- tion capacities, random lead times, and linear costs. In the first problem we take into account the probability that a product can be reused as a finished product or only as semi-finished product (by parts), in the second problem we include a step of remanufac- turing before reusing the returned product, and in the third problem we consider a system with product returns that are announced in advance by the customers. Apart from the caracterization of the optimal policies for these cases, the performance assessments of some heuristic policies and the study of the poduction capacity effect on these heuristic policies stand as main contributions. Throughout this work we have used existing tools to characterize optimal policies for different Markov decision processes. The last chapter aims to improve these tools and enable us to study the influence of several system parameters on its optimal policy.SAVOIE-SCD - Bib.électronique (730659901) / SudocGRENOBLE1/INP-Bib.électronique (384210012) / SudocGRENOBLE2/3-Bib.électronique (384219901) / SudocSudocFranceF

Condition-Based Production for Stochastically Deteriorating Systems: Optimal Policies and Learning

Production systems deteriorate stochastically due to usage and may eventually break down, resulting in high maintenance costs at scheduled maintenance moments. This deterioration behavior is affected by the system's production rate. While producing at a higher rate generates more revenue, the system may also deteriorate faster. Production should thus be controlled dynamically to trade-off deterioration and revenue accumulation in between maintenance moments. We study systems for which the relation between production and deterioration is known and the same for each system as well as systems for which this relation differs from system to system and needs to be learned on-the-fly. The decision problem is to find the optimal production policy given planned maintenance moments (operational) and the optimal interval length between such maintenance moments (tactical). For systems with a known production-deterioration relation, we cast the operational decision problem as a continuous-time Markov decision process and prove that the optimal policy has intuitive monotonic properties. We also present sufficient conditions for the optimality of bang-bang policies and we partially characterize the structure of the optimal interval length, thereby enabling efficient joint optimization of the operational and tactical decision problem. For systems that exhibit variability in their production-deterioration relations, we propose a Bayesian procedure to learn the unknown deterioration rate under any production policy. Our extensive numerical study indicates significant profit increases of our approaches compared to the state-of-the-art

Service Level Constrained Inventory Systems

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151878/1/poms13060_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151878/2/poms13060.pd