A Robust Optimization Approach to Dynamic Pricing and Inventory Control with no Backorders

Adida, Elodie; Perakis, Georgia

doi:10.1007/s10107-005-0681-5

Cited by 117 publications

(70 citation statements)

References 23 publications

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“…This work is in line with some recent literature on robust optimization [1,5] and control [2] of inventory systems. Here as well as in [2] we focus on saturated linear state feedback controls since such controls arise naturally in any system with bounded controls.…”

Section: Introductionsupporting

confidence: 76%

Robust control of uncertain multi-inventory systems via linear matrix inequality

Bauso

Giarré

Pesenti

2010

International Journal of Control

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We consider a continuous time linear multi-inventory system with unknown demands bounded within ellipsoids and controls bounded within ellipsoids or polytopes. We address the problem of ε-stabilizing the inventory since this implies some reduction of the inventory costs. The main results are certain conditions under which ε-stabilizability is possible through a saturated linear state feedback control. All the results are based on a Linear Matrix Inequalities (LMIs) approach and on some recent techniques for the modeling and analysis of polytopic systems with saturations.

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Section: Introductionsupporting

confidence: 76%

Robust control of uncertain multi-inventory systems via linear matrix inequality

Bauso

Giarré

Pesenti

2010

International Journal of Control

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“…AARC offers a computationally tractable alternative to multi-stage problems with uncertain data. Successful applications of this approach to multistage inventory management problems is reported in [1,4,6]. These works stimulated investigation of LDR in stochastic programming [22].…”

Section: Introductionmentioning

confidence: 98%

Step decision rules for multistage stochastic programming: A heuristic approach

Thénie

Vial

2008

Automatica

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Stochastic programming with step decision rules, SPSDR, is an attempt to overcome the curse of computational complexity of multistage stochastic programming problems. SPSDR combines several techniques. The first idea is to work with independent experts. Each expert is confronted with a sample of scenarios drawn at random from the original stochastic process. The second idea is to have each expert work with step decision rules. The optimal decision rules of the individual experts are then averaged to form the final decision rule. The final solution is tested on a very large sample of scenarios. SPSDR is then tested against two alternative methods: regular stochastic programming on a problem with 3 stages and 2 recourses; robust optimization with affinely adjustable recourses on a 12-stage model. The performance of the new method turns out to be competitive on those examples, while it permits a tighter control on computational complexity than standard stochastic programming.

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“…Bertsimas and Perakis (2006) present an optimization approach to dynamically set prices in order to maximize revenue in both competitive and non-competitive settings, and suggest that a decision-maker does better by incorporating realized demand information as time evolves into the policy. Adida and Perakis (2006) study a robust optimization approach to dynamic pricing in a multiple product setting under demand uncertainty, highlight the difficulties of computing the optimal pricing policy over a given time horizon, and suggest methods of keeping the formulation tractable. Robust optimization is a framework to handle uncertainty where the decision-maker optimizes the worst-case objective, with the worst case measured over a set centered at the nominal value of the uncertain parameters.…”

Section: Introductionmentioning

confidence: 99%

Robust timing of markdowns

Dziecichowicz

Caro²,

Thiele

2015

Ann Oper Res

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We propose an approach to the timing of markdowns over a finite time horizon in a continuous setting that does not require the precise knowledge of the underlying probabilities, instead relying on range forecasts for the arrival rates of the demand processes, and that captures the degree of the manager's risk aversion through intuitive budget of uncertainty functions. These budget functions bound the cumulative deviation of the arrival rates from their nominal values over the lengths of time for which a product is offered at a given price. A key issue is that using lengths of time as decision variables introduces non-convexities when budget functions are concave. In the single-product case, we describe a tractable and intuitive framework to incorporate uncertainty on customers' arrival rates, formulate the resulting robust optimization model, describe an efficient procedure to compute the optimal sale times, and provide theoretical insights. We then describe how to use the solution of the static robust optimization model to implement a dynamic markdown policy. We also extend the robust optimization approach to multiple products and suggest the idea of constraint aggregation to preserve performance for this type of problem structure.

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A Robust Optimization Approach to Dynamic Pricing and Inventory Control with no Backorders

Cited by 117 publications

References 23 publications

Robust control of uncertain multi-inventory systems via linear matrix inequality

Robust control of uncertain multi-inventory systems via linear matrix inequality

Step decision rules for multistage stochastic programming: A heuristic approach

Robust timing of markdowns

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