A Robust Optimization Approach to Inventory Theory

We propose a general methodology based on robust optimization to address the problem of optimally controlling a supply chain subject to stochastic demand in discrete time. This problem has been studied in the past using dynamic programming, which suffers from dimensionality problems and assumes full...

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Vydáno v:Operations research Ročník 54; číslo 1; s. 150 - 168
Hlavní autoři: Bertsimas, Dimitris, Thiele, Aurelie
Médium: Journal Article
Jazyk:angličtina
Vydáno: Linthicum, MD INFORMS 01.01.2006
Institute for Operations Research and the Management Sciences
Témata:
Analysis
Applied sciences
Approximation
Carrying costs
Cost efficiency
Cost functions
Dynamic programming
Exact sciences and technology
Fixed costs
integer
Integer programming
inventory
Inventory control
Inventory control, production control. Distribution
Inventory management
linear
Linear programming
Logistics
Mathematical models
Mathematical programming
Operational research and scientific management
Operational research. Management science
Operations research
Optimal policy
Optimization
production
programming
Robust optimization
Robust statistics
stochastic
Studies
Supply chain management
Supply chains
uncertainty
United States
Uncertainty
Fixed cost
Optimal policy
Financial management
Linear programming
Mixed integer programming
integer
Optimization
Trade
Base stock
Inventory control
production: uncertainty
Robustness
Dynamic programming
Complex programming
programming: linear
stochastic; inventory
ISSN:0030-364X, 1526-5463
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Popis
Shrnutí:We propose a general methodology based on robust optimization to address the problem of optimally controlling a supply chain subject to stochastic demand in discrete time. This problem has been studied in the past using dynamic programming, which suffers from dimensionality problems and assumes full knowledge of the demand distribution. The proposed approach takes into account the uncertainty of the demand in the supply chain without assuming a specific distribution, while remaining highly tractable and providing insight into the corresponding optimal policy. It also allows adjustment of the level of robustness of the solution to trade off performance and protection against uncertainty. An attractive feature of the proposed approach is its numerical tractability, especially when compared to multidimensional dynamic programming problems in complex supply chains, as the robust problem is of the same difficulty as the nominal problem, that is, a linear programming problem when there are no fixed costs, and a mixed-integer programming problem when fixed costs are present. Furthermore, we show that the optimal policy obtained in the robust approach is identical to the optimal policy obtained in the nominal case for a modified and explicitly computable demand sequence. In this way, we show that the structure of the optimal robust policy is of the same base-stock character as the optimal stochastic policy for a wide range of inventory problems in single installations, series systems, and general supply chains. Preliminary computational results are very promising.
Bibliografie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0030-364X
1526-5463
DOI:10.1287/opre.1050.0238