### Abstract

Original language | English |
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Place of Publication | www |

Publisher | Mathematical Optimization Society |

Number of pages | 24 |

Publication status | Published - 2014 |

Externally published | Yes |

Series | Optimization Online |
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Number | 4524 |

Volume | 08 |

### Cite this

*An SDP Approach for Multiperiod Mixed 0–1 Linear Programming Models with Stochastic Dominance Constraints for Risk Management*. www: Mathematical Optimization Society. Optimization Online, No. 4524, Vol.. 08

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**An SDP Approach for Multiperiod Mixed 0–1 Linear Programming Models with Stochastic Dominance Constraints for Risk Management.** / Escudero, Laureano F.; Monge, Juan Francisco; Romero Morales, Dolores .

Research output: Working paper › Research › peer-review

TY - UNPB

T1 - An SDP Approach for Multiperiod Mixed 0–1 Linear Programming Models with Stochastic Dominance Constraints for Risk Management

AU - Escudero, Laureano F.

AU - Monge, Juan Francisco

AU - Romero Morales, Dolores

PY - 2014

Y1 - 2014

N2 - 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 first-order and second-order constraints. We propose a stochastic dynamic programming (SDP) solution approach, where one has to overcome the negative impact the cross-scenario constraints, due to SDC, have on the decomposability of the model. In our computational experience we compare our SDP 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.

AB - 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 first-order and second-order constraints. We propose a stochastic dynamic programming (SDP) solution approach, where one has to overcome the negative impact the cross-scenario constraints, due to SDC, have on the decomposability of the model. In our computational experience we compare our SDP 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.

KW - Multiperiod stochastic mixed 0–1 linear programming

KW - Risk averse

KW - Stochastic dominance constraints

KW - Stochastic dynamic programming

KW - Cross-scenario constraints

M3 - Working paper

BT - An SDP Approach for Multiperiod Mixed 0–1 Linear Programming Models with Stochastic Dominance Constraints for Risk Management

PB - Mathematical Optimization Society

CY - www

ER -