Retailer-Supplier Flexible Commitments Contracts: A Robust Optimization Approach

Ben‐Tal, Aharon; Golany, Boaz; Nemirovski, Arkadi; Vial, Jean–Philippe

doi:10.1287/msom.1050.0081

Cited by 296 publications

(216 citation statements)

References 30 publications

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“…We assume W andŴ are nonempty. Note thatŴ ⊆ W ; thus, we may assumeŜ ⊆ S. If the factor means are completely unknown, we havê W = W , which becomes the adjustable robust counterpart model of Ben-Tal et al (2005).…”

Section: Factor-based Demand Modelmentioning

confidence: 99%

“…The authors propose a linear decision rule called affinely adjustable robust counterpart. Ben-Tal et al (2005) demonstrate that an affinely adjustable robust counterpart can be remarkably effective in minimizing the worst-case objective of a multiperiod inventory control problem. Bertsimas et al (2010) show that the affinely adjustable robust counterpart can be optimal in some situations.…”

Section: Introductionmentioning

confidence: 95%

“…In our model we adopt the approach of Gilboa and Schmeidler (1989) of minimizing the worst-case expected total cost. In contrast, Ben-Tal et al (2005) minimize the worst-case total cost, which is a special case of our model in which the factor means support set is the same as the factors support set.…”

Section: Introductionmentioning

confidence: 99%

“…We characterize the factors support set to ensure feasibility in the storage assignment problem under a linear decision rule. Such characterization is not required in the inventory control problem of Ben-Tal et al (2005), where feasibility is guaranteed for any bounded support set, which is not the case for the storage assignment problem.…”

Section: Introductionmentioning

confidence: 99%

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Robust Storage Assignment in Unit-Load Warehouses

2012

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A ssigning products to and retrieving them from proper storage locations are crucial decisions in minimizing the operating cost of a unit-load warehouse. The problem becomes intractable when the warehouse faces variable supply and uncertain demand in a multiperiod setting. We assume a factor-based demand model in which demand for each product in each period is affinely dependent on some uncertain factors. The distributions of these factors are only partially characterized. We introduce a robust optimization model that minimizes the worst-case expected total travel in the warehouse with distributional ambiguity of demand. Under a linear decision rule, we obtain a storage and retrieval policy by solving a moderate-size linear optimization problem. Surprisingly, despite imprecise specification of demand distributions, our computational studies suggest that the linear policy achieves close to the expected value given perfect information and significantly outperforms existing heuristics in the literature.

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Section: Factor-based Demand Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust Storage Assignment in Unit-Load Warehouses

2012

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“…The first problem considered here was originally proposed by Ben-Tal et al [2005]. We discuss a simplified version due to Bertsimas et al [2010], which we denote by R COC .…”

Section: Inventory Management With Cumulative Order Constraintsmentioning

confidence: 99%

A constraint sampling approach for multi-stage robust optimization

2012

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We propose a tractable approximation scheme for convex (not necessarily linear) multi-stage robust optimization problems. We approximate the adaptive decisions by finite linear combinations of prescribed basis functions and demonstrate how one can optimize over these decision rules at low computational cost through constraint randomization. We obtain a-priori probabilistic guarantees on the feasibility properties of the optimal decision rule by extending existing constraint sampling techniques from the single-to the multi-stage case. We demonstrate that for a suitable choice of basis functions, the approximation converges as the size of the basis and the number of sampled constraints tend to infinity. The approach yields an algorithm parameterized in the basis size, the probability of constraint violation and the confidence that this probability will not be exceeded. These three parameters serve to tune the trade-off between optimality and feasibility of the decision rules and the computational cost of the algorithm. We assess the convergence and scalability properties of our approach in the context of two inventory management problems.

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Dynamic Models for Robust Optimization

Düzgün

Thiele

2011

Wiley Encyclopedia of Operations Research and Management Science

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This article discusses recent developments in robust optimization, with a focus on dynamic models. Traditional techniques such as stochastic programming and dynamic programming face dimensionality issues as the size of the problem increases; furthermore, probability distributions are often difficult to accurately estimate. After robust optimization emerged as a tractable modeling framework in static optimization, researchers investigated its applicability to dynamic decision making under uncertainty. We provide an overview and discussion of their findings.

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Retailer-Supplier Flexible Commitments Contracts: A Robust Optimization Approach

Cited by 296 publications

References 30 publications

Robust Storage Assignment in Unit-Load Warehouses

Robust Storage Assignment in Unit-Load Warehouses

A constraint sampling approach for multi-stage robust optimization

Dynamic Models for Robust Optimization

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