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

Laureano F. Escudero, Juan Francisco Monge, Dolores Romero Morales

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

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.
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.
LanguageEnglish
JournalComputers & Operations Research
Volume58
Pages32-40
ISSN0305-0548
DOIs
StatePublished - Jun 2015

Keywords

    Cite this

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    title = "An SDP Approach for Multiperiod Mixed 0–1 Linear Programming Models with Stochastic Dominance Constraints for Risk Management",
    abstract = "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.",
    keywords = "Multiperiod stochastic mixed 0–1 linear programming, Risk averse, Stochastic dominance constraints, Stochastic dynamic programming, Cross-scenario constraints",
    author = "Escudero, {Laureano F.} and Monge, {Juan Francisco} and Morales, {Dolores Romero}",
    year = "2015",
    month = "6",
    doi = "10.1016/j.cor.2014.12.007",
    language = "English",
    volume = "58",
    pages = "32--40",
    journal = "Computers & Operations Research",
    issn = "0305-0548",
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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; Morales, Dolores Romero.

    In: Computers & Operations Research, Vol. 58, 06.2015, p. 32-40.

    Research output: Contribution to journalJournal articleResearchpeer-review

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    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 - Morales,Dolores Romero

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    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 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.

    KW - Multiperiod stochastic mixed 0–1 linear programming

    KW - Risk averse

    KW - Stochastic dominance constraints

    KW - Stochastic dynamic programming

    KW - Cross-scenario constraints

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