Stochastic-Equilibrium in Network Expansion Planning Under Uncertainty, Se-Nep

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.

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