scholarly journals Sampling-Based Approximation Schemes for Capacitated Stochastic Inventory Control Models

2015 ◽  
Author(s):  
Wang Chi Cheung ◽  
David Simchi-Levi
Keyword(s):  
Inventory Control ◽  
Approximation Schemes ◽  
Stochastic Inventory ◽  
Stochastic Inventory Control ◽  
Control Models

Approximation Algorithms for Stochastic Inventory Control Models

2005 ◽  
pp. 306-320 ◽  
Author(s):  
Retsef Levi ◽  
Martin Pál ◽  
Robin Roundy ◽  
David B. Shmoys
Keyword(s):  
Approximation Algorithms ◽  
Inventory Control ◽  
Stochastic Inventory ◽  
Stochastic Inventory Control ◽  
Control Models

Approximation Algorithms for Stochastic Inventory Control Models

2007 ◽  
Vol 32 (2) ◽  
pp. 284-302 ◽  
Author(s):  
Retsef Levi ◽  
Martin Pál ◽  
Robin O. Roundy ◽  
David B. Shmoys
Keyword(s):  
Approximation Algorithms ◽  
Inventory Control ◽  
Stochastic Inventory ◽  
Stochastic Inventory Control ◽  
Control Models

scholarly journals Sampling-Based Approximation Schemes for Capacitated Stochastic Inventory Control Models

2019 ◽  
Vol 44 (2) ◽  
pp. 668-692 ◽  
Author(s):  
Wang Chi Cheung ◽  
David Simchi-Levi
Keyword(s):  
Inventory Control ◽  
Sample Average Approximation ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Data Driven ◽  
Approximation Schemes ◽  
Stochastic Inventory ◽  
Stochastic Inventory Control ◽  
Sample Average ◽  
Full Knowledge

We study the classical multiperiod capacitated stochastic inventory control problems in a data-driven setting. Instead of assuming full knowledge of the demand distributions, we assume that the demand distributions can only be accessed through drawing random samples. Such data-driven models are ubiquitous in practice, where the cumulative distribution functions of the underlying random demand are either unavailable or too complex to work with. We consider the sample average approximation (SAA) method for the problem and establish an upper bound on the number of samples needed for the SAA method to achieve a near-optimal expected cost, under any level of required accuracy and prespecified confidence probability. The sample bound is polynomial in the number of time periods as well as the confidence and accuracy parameters. Moreover, the bound is independent of the underlying demand distributions. However, the SAA requires solving the SAA problem, which is #P-hard. Thus, motivated by the SAA analysis, we propose a polynomial time approximation scheme that also uses polynomially many samples. Finally, we establish a lower bound on the number of samples required to solve this data-driven newsvendor problem to near-optimality.

Provably Near-Optimal Approximation Schemes for Implicit Stochastic and Sample-Based Dynamic Programs

2020 ◽  
Author(s):  
Nir Halman
Keyword(s):  
Inventory Control ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Approximation Schemes ◽  
Stochastic Inventory ◽  
Cumulative Distribution Functions ◽  
Stochastic Inventory Control ◽  
Random Samples ◽  
Random Events ◽  
Dynamic Programs

In this paper, we address two models of nondeterministic discrete time finite-horizon dynamic programs (DPs): implicit stochastic DPs (the information about the random events is given by value oracles to their cumulative distribution functions) and sample-based DPs (the information about the random events is deduced by drawing random samples). Such data-driven models frequently appear in practice, where the cumulative distribution functions of the underlying random variables are either unavailable or too complicated to work with. In both models, the single-period cost functions are accessed via value oracle calls and assumed to possess either monotone or convex structure. We develop the first near-optimal relative approximation schemes for each of the two models. Applications in stochastic inventory control (that is, several variants of the so-called newsvendor problem) are discussed in detail. Our results are achieved by a combination of Bellman equation calculations, density estimation results, and extensions of the technique of K-approximation sets and functions introduced by Halman et al. (2009) [Halman N, Klabjan D, Mostagir M, Orlin J, Simchi-Levi D (2009) A fully polynomial time approximation scheme for single-item stochastic inventory control with discrete demand. Math. Oper. Res. 34(3):674–685.].

R-approximation Method for Stochastic Inventory Control Models

2016 ◽  
Vol 5 (84) ◽  
pp. 91-97
Author(s):  
A. A. Nazarov ◽  
◽  
V. I. Broner ◽  
Keyword(s):  
Inventory Control ◽  
Approximation Method ◽  
Stochastic Inventory ◽  
Stochastic Inventory Control ◽  
Control Models

scholarly journals A 2-Approximation Algorithm for Stochastic Inventory Control Models with Lost Sales

2008 ◽  
Vol 33 (2) ◽  
pp. 351-374 ◽  
Author(s):  
Retsef Levi ◽  
Ganesh Janakiraman ◽  
Mahesh Nagarajan
Keyword(s):  
Approximation Algorithm ◽  
Inventory Control ◽  
Lost Sales ◽  
Stochastic Inventory ◽  
Stochastic Inventory Control ◽  
Control Models

Approximation Algorithms for Capacitated Stochastic Inventory Control Models

2008 ◽  
Vol 56 (5) ◽  
pp. 1184-1199 ◽  
Author(s):  
Retsef Levi ◽  
Robin O. Roundy ◽  
David B. Shmoys ◽  
Van Anh Truong
Keyword(s):  
Approximation Algorithms ◽  
Inventory Control ◽  
Stochastic Inventory ◽  
Stochastic Inventory Control ◽  
Control Models

Provably Near-Optimal Sampling-Based Policies for Stochastic Inventory Control Models

2007 ◽  
Vol 32 (4) ◽  
pp. 821-839 ◽  
Author(s):  
Retsef Levi ◽  
Robin O. Roundy ◽  
David B. Shmoys
Keyword(s):  
Inventory Control ◽  
Optimal Sampling ◽  
Stochastic Inventory ◽  
Stochastic Inventory Control ◽  
Control Models
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