**DATES:** 1-5 April 2019 (5 sessions)

**TIME:** 10:00 - 12:00 (a total of 10 hours)

**LOCATION:** BCAM Seminar room

A new scheme is presented for dealing with uncertainty in scenario trees for dynamic mixed 0-1 optimization problems with strategic and tactical/operational stochastic parameters. Let us generically name this type of problems as hub and non-hub Network Expansion Planning (NEP) in a given system, e.g., supply chain, production, rapid transit network, energy generation and transmission network, etc. The strategic scenario tree is usually a multistage one with replicas of the strategic nodes rooted structures in the form of either a special scenario graph or a two-stage scenario tree, depending on the type of tactical/operational activity in the system. Those tactical/operational scenario structures impact in the constraints of the model and, thus, in the decomposition methodology for solving usually large-scale instances. A scheme is presented for scenario reduction based on hunging the tactical/operational stochastic nodes on strategic nodes. A strong modeling framework for NEP is also presented, being based on the step-variable concept as a counterpart to the impulse one. Two types of risk-averse measures are considered. The first one is a time-inconsistent mixture of the chance-constrained and second-order stochastic dominance functionals of the value of a given set of functions up to the strategic nodes in selected stages along the time horizon, The second type is a strategic node-based time-consistent SSD functional for the set of tactical/operational scenarios in the strategic nodes at selected stages. The stochastic Equilibrium in NEP is presented by considering a mixed 0-1 bilinear bilevel primal-model for the multi-period NEP, where different agents are competing on an open market. The huge problem’s dimensions (due to the network size of realistic instances as well as the cardinality of the strategic tree and tactical/operational subtrees) renders unrealistic to seek for an optimal solution. It motivates the development of several versions of a matheuristic algorithm based on the Nested Stochastic Decomposition methodology for problem-solving, where a solution optimality gap is guaranteed in the Lagrangean-based versions and a good estimation of that gap is given in a heuristic Benders-based version. Its advantages and drawbacks are also presented as well as the framework for some schemes to, partially at least, avoid those drawbacks. A broad computational experience is studied based on realistic problems so diverse as Non-Close-Loop Supply Network Management, Close-Loop SCM, Rapid Transit Network design Management, Tall Assignment NEP and Forest harvestry NEP.

**PROGRAMME: **
**1.** Introduction to Network Expansion Planning and Multistage Stochastic mixed 0-1 Optimization.

**2.** Stochastic multistage Strategic scenario trees, multiperiod Tactical scenario graphs and Operational two-stage trees. Scenario reduction.

**3.** Hub and non-hub Network Expansion Planning strong modeling and its Stochastic Equilibrium via multistage stochastic bi-level optimization.

**4. **Risk averse functionals. Motivation of time-inconsistent and time-consistent versions of Average Value-at-Risk and Stochastic Dominance measures.

**5. **Nested Stochastic Decomposition methodology for problem-solving and computational experience study for some realistic problems.

**REFERENCES: **
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[2] A. Alonso-Ayuso, L.F. Escudero, M. Guignard, A. Weintraub. On dealing with strategic and tactical decision levels in forestry planning under uncertainty. Submitted, 2018

[3] S. Baptista, A.P. Barbosa-Povoa, L.F. Escudero, M.I. Gomes and C. Pizarro. On risk management for a two-stage stochastic mixed 0-1 model for designing and operation planning of a closed-loop supply chain. European Journal of Operational Research, 274:91-107, 2019.

[4] J.R. Birge and F.V. Louveaux. Introduction to Stochastic Programming. Springer, 2nd edition, 2011.

[5] L. Cadarso, L.F. Escudero and A. Marín. On strategic multistage operational two-stage stochastic 0-1 optimization for the Rapid Transit Network Design problem. European Journal of Operational Research, 271:577-593, 2018.

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[7] L.F. Escudero, M.A. Gar ́ın, C. Pizarro and A. Unzueta. On efficient matheuristic algorithms for Multi-period Stochastic Facility Location-assignment Problems. Computational Optimization and Applications, 70:865-888, 2018.

[8] L.F. Escudero, A. Gar ́ın and A. Unzueta. Cluster Lagrangean decomposition for risk averse in multistage stochastic optimization. Computers & Operations Research, 85:154-171, 2017.

[9] L.F. Escudero and J.F. Monge. On capacity expansion planning under strategic and operational uncertainties based on stochastic dominance risk averse management. Computational Management Science, 15:479-500, 2018.

[10] L.F. Escudero, J.F. Monge and A.M. Rodr ́ıguez-Ch ́ıa. On stochastic equilibrium for network expansion planning. A multi-period bilevel approach under uncertainty. Submitted, 2019.

[11] L.F. Escudero, J.F. Monge and D. Romero-Morales. On the time-consistent stochastic dominance risk averse measure for tactical supply chain planning under uncertainty. Computers & Operations Research, 100:270-286, 2018.

[12] M. Fischetti, I. Ljubic, M. Monaci and M. Sinnl. On the use of intersection cuts for bilevel optimization. Mathematical Programming, Ser. B, 172:77-103, 2018.

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[18] J. Zou, S. Ahmed and X.A. Sun. Multistage stochastic unit commitment using Stochastic Dual Dynamic intger Programming. Mathematical Programming, doi.org/10.1007/s10107-018-1249-5, 2018.

***Registration is free, but mandatory before March 29th: **So as to inscribe go to

https://bit.ly/2UNDfQw and fill the registration form. Student grants are available. Please, let us know if you need support for travel and accommodation expenses when you fill the form.