An SDP approach for multiperiod mixed 0–1 linear programming models with stochastic dominance constraints for risk management

In this paper we consider multiperiod mixed 0–1 linear programming models under uncertainty. We propose a risk averse strategy using stochastic dominance constraints (SDC) induced by mixed-integer linear recourse as the risk measure. The SDC strategy extends the existing literature to the multistage...

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Vydáno v:Computers & operations research Ročník 58; s. 32 - 40
Hlavní autoři: Escudero, Laureano F., Monge, Juan Francisco, Romero Morales, Dolores
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Elsevier Ltd 01.06.2015
Pergamon Press Inc
Témata:
Accuracy
Comparative analysis
Cross-scenario constraints
Dominance
Generalized linear models
Linear programming
Mathematical models
Mathematical programming
Multiperiod stochastic mixed 0–1 linear programming
Risk
Risk assessment
Risk averse
Stochastic dominance constraints
Stochastic dynamic programming
Stochastic models
Stochasticity
Strategy
Studies
Supply chain management
Uncertainty
Multiperiod stochastic mixed 0–1 linear programming
Stochastic dynamic programming
Cross-scenario constraints
Stochastic dominance constraints
Risk averse
ISSN:0305-0548, 1873-765X, 0305-0548
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Shrnutí:In this paper we consider multiperiod mixed 0–1 linear programming models under uncertainty. We propose a risk averse strategy using stochastic dominance constraints (SDC) induced by mixed-integer linear recourse as the risk measure. The SDC strategy extends the existing literature to the multistage case and includes both the first-order and second-order constraints. We propose a stochastic dynamic programming (SDP) solution approach, where one has to overcome the negative impact of the cross-scenario constraints on the decomposability of the model. In our computational experience we compare our SDP approach against a commercial optimization package, in terms of solution accuracy and elapsed time. We use supply chain planning instances, where procurement, production, inventory, and distribution decisions need to be made under demand uncertainty. We confirm the hardness of the testbed, where the benchmark cannot find a feasible solution for half of the test instances while we always find one, and show the appealing tradeoff of SDP, in terms of solution accuracy and elapsed time, when solving medium-to-large instances.
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ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2014.12.007