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

Publikation: Working paperForskningpeer review

Resumé

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.
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.
SprogEngelsk
Udgivelses stedwww
UdgiverMathematical Optimization Society
Antal sider24
StatusUdgivet - 2014
Udgivet eksterntJa
NavnOptimization Online
Nummer4524
Vol/bind08

Emneord

  • Multiperiod stochastic mixed 0–1 linear programming
  • Risk averse
  • Stochastic dominance constraints
  • Stochastic dynamic programming
  • Cross-scenario constraints

Citer dette

Escudero, L. F., Monge, J. F., & Morales, D. R. (2014). An SDP Approach for Multiperiod Mixed 0–1 Linear Programming Models with Stochastic Dominance Constraints for Risk Management. www: Mathematical Optimization Society. Optimization Online, Nr. 4524, Bind. 08
Escudero, Laureano F. ; Monge, Juan Francisco ; Morales, Dolores Romero. / An SDP Approach for Multiperiod Mixed 0–1 Linear Programming Models with Stochastic Dominance Constraints for Risk Management. www : Mathematical Optimization Society, 2014. (Optimization Online; Nr. 4524, ???volume??? 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; Morales, Dolores Romero.

www : Mathematical Optimization Society, 2014.

Publikation: Working paperForskningpeer review

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