The Experts below are selected from a list of 21 Experts worldwide ranked by ideXlab platform
Søren Johansen - One of the best experts on this subject based on the ideXlab platform.
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Pure and modified base-stock policies for the lost sales inventory system with Negligible Set-up costs and constant lead times
International Journal of Production Economics, 2001Co-Authors: Søren JohansenAbstract:Abstract The studied inventory system with continuous review has an easily computed optimal (S−1,S) policy when unsatisfied demands are backlogged. We assume that unsatisfied demands are lost and then it is also easy to compute the best (S−1,S) policy. But, as demonstrated by Roger Hill at the ISIR Symposium in 1996, this pure base-stock policy can never be optimal if S⩾2. Our focus is on periodic review. We use Erlang's loss formula to derive approximate expressions for the stockout probability and the average cost. These expressions are used to approximate the average cost and to compute a good base-stock. We formulate and implement a Markov decision model to find the optimal replenishment policy. The model is solved by a policy-iteration algorithm. Because the optimal policy is often rather complicated, we introduce modified base-stock policies. They are specified by a pair (S,t) where S is the base-stock and t is a lower bound for the number of review periods between review epochs in which placing a replenishment order is permitted. A simple one has S equal to the base-stock computed from Erlang's formula and fixes t as the largest integer which is less than or equal to the ratio of the number of review periods per delivery period and S. Our numerical examples show that the simple modified base-stock policy provides most of the cost reduction which can be obtained by replacing the best pure base-stock policy by the optimal policy.
Dmitry Krass - One of the best experts on this subject based on the ideXlab platform.
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inventory models with minimal service level constraints
European Journal of Operational Research, 2001Co-Authors: Frank Y Chen, Dmitry KrassAbstract:Abstract This paper investigates inventory models in which the stockout cost is replaced by a minimal service level constraint (SLC) that requires a certain level of service to be met in every period. The minimal service level approach has the virtue of simplifying the computation of an optimal ordering policy, because the optimal reorder level is solely determined by the minimal SLC and demand distributions. It is found that above a certain “critical” service level, the optimal (s,S) policy “collapses” to a simple base-stock or order-up-to level policy, which is independent on the cost parameters. This shows the minimal SLC models to be qualitatively different from their shortage cost counterparts. We also demonstrate that the “imputed shortage cost” transforming a minimal SLC model to a shortage cost model does not generally exist. The minimal SLC approach is extended to models with Negligible Set-up costs. The optimality of myopic base-stock policies is established under mild conditions.
Frank Y Chen - One of the best experts on this subject based on the ideXlab platform.
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inventory models with minimal service level constraints
European Journal of Operational Research, 2001Co-Authors: Frank Y Chen, Dmitry KrassAbstract:Abstract This paper investigates inventory models in which the stockout cost is replaced by a minimal service level constraint (SLC) that requires a certain level of service to be met in every period. The minimal service level approach has the virtue of simplifying the computation of an optimal ordering policy, because the optimal reorder level is solely determined by the minimal SLC and demand distributions. It is found that above a certain “critical” service level, the optimal (s,S) policy “collapses” to a simple base-stock or order-up-to level policy, which is independent on the cost parameters. This shows the minimal SLC models to be qualitatively different from their shortage cost counterparts. We also demonstrate that the “imputed shortage cost” transforming a minimal SLC model to a shortage cost model does not generally exist. The minimal SLC approach is extended to models with Negligible Set-up costs. The optimality of myopic base-stock policies is established under mild conditions.
Francesco Maggi - One of the best experts on this subject based on the ideXlab platform.
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regularity of free boundaries in anisotropic capillarity problems and the validity of young s law
Archive for Rational Mechanics and Analysis, 2015Co-Authors: Guido De Philippis, Francesco MaggiAbstract:Local volume-constrained minimizers in anisotropic capillarity problems develop free boundaries on the walls of their containers. We prove the regularity of the free boundary outside a closed Negligible Set, showing in particular the validity of Young’s law at almost every point of the free boundary. Our regularity results are not specific to capillarity problems, and actually apply to Sets of finite perimeter (and thus to codimension one integer rectifiable currents) arising as minimizers in other variational problems with free boundaries.
M. A. Shubin - One of the best experts on this subject based on the ideXlab platform.
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discreteness of spectrum and positivity criteria for schrodinger operators
Annals of Mathematics, 2005Co-Authors: Vladimir Mazya, M. A. ShubinAbstract:We provide a class of necessary and sufficient conditions for the discreteness of spectrum of Schrodinger operators with scalar potentials which are semibounded below. The classical discreteness of spectrum criterion by A. M. Molchanov (1953) uses a notion of Negligible Set in a cube as a Set whose Wiener capacity is less than a small constant times the capacity of the cube. We prove that this constant can be taken arbitrarily between 0 and 1. This solves a problem formulated by I. M. Gelfand in 1953. Moreover, we extend the notion of negligibility by allowing the constant to depend on the size of the cube. We give a complete description of all negligibility conditions of this kind. The a priori equivalence of our conditions involving different negligibility classes is a nontrivial property of the capacity. We also establish similar strict positivity criteria for the Schrodinger operators with nonnegative potentials.
