Scenario Cluster Lagrangian Decomposition in two stage stochastic mixed 0-1 optimization

In this paper we introduce four scenario Cluster based Lagrangian Decomposition (CLD) procedures for obtaining strong lower bounds to the (optimal) solution value of two-stage stochastic mixed 0-1 problems. At each iteration of the Lagrangian based procedures, the traditional aim consists of obtaining the solution value of the corresponding Lagrangian dual via solving scenario submodels once the nonanticipativity constraints have been dualized. Instead of considering a splitting variable representation over the set of scenarios, we propose to decompose the model into a set of scenario clusters. We compare the computational performance of the four Lagrange multiplier updating procedures, namely the Subgradient Method, the Volume Algorithm, the Progressive Hedging Algorithm and the Dynamic Constrained Cutting Plane scheme for different numbers of scenario clusters and different dimensions of the original problem. Our computational experience shows that the CLD bound and its computational effort depend on the number of scenario clusters to consider. In any case, our results show that the CLD procedures outperform the traditional LD scheme for single scenarios both in the quality of the bounds and computational effort. All the procedures have been implemented in a C++ experimental code. A broad computational experience is reported on a test of randomly generated instances by using the MIP solvers COIN-OR and CPLEX for the auxiliary mixed 0-1 cluster submodels, this last solver within the open source engine COIN-OR. We also give computational evidence of the model tightening effect that the preprocessing techniques, cut generation and appending and parallel computing tools have in stochastic integer optimization. Finally, we have observed that the plain use of both solvers does not provide the optimal solution of the instances included in the testbed with which we have experimented but for two toy instances in affordable elapsed time. On the other hand the proposed procedures provide strong lower bounds (or the same solution value) in a considerably shorter elapsed time for the quasi-optimal solution obtained by other means for the original stochastic problem.

Reference Points Based on Dynamic Optimisation: A Versatil Algorithm for Mixed Fishery Management with Bio-economic Agestructured Models

Single-species management objectives may not be consistent within mixed fisheries. They may lead species to unsafe situations, promote discarding of over-quota and/or misreporting of catches. We provide an algorithm for characterising bio-economic reference points for a mixed fishery as the steady-state solution of a dynamic optimal management problem. The optimisation problem takes into account: i) that species are fishing simultaneously in unselective fishing operations and ii)intertemporal discounting and fleet costs to relate reference points to discounted economic profits along optimal trajectories. We illustrate how the algorithm can be implemented by applying it to the European Northern Stock of Hake (Merluccius merluccius), where fleets also capture Northern megrim (Lepidorhombus whiffiagonis) and Northern anglerfish (Lophius piscatorius and Lophius budegassa). We find that optimal mixed management leads to a target reference point that is quite similar to the 2/3 of the Fmsy single-species (hake) target. Mixed management is superior to singlespecies management because it leads the fishery to higher discounted profits with higher long-term SSB for all species. We calculate that the losses due to the use of the Fmsy single-species (hake) target in this mixed fishery account for 11.4% of total discounted profits.

Some experiments on solving multistage stochastic mixed 0-1 programs with time stochastic dominance constraints

In this work we extend to the multistage case two recent risk averse measures for two-stage stochastic programs based on first- and second-order stochastic dominance constraints induced by mixed-integer linear recourse. Additionally, we consider Time Stochastic Dominance (TSD) along a given horizon. Given the dimensions of medium-sized problems augmented by the new variables and constraints required by those risk measures, it is unrealistic to solve the problem up to optimality by plain use of MIP solvers in a reasonable computing time, at least. Instead of it, decomposition algorithms of some type should be used. We present an extension of our Branch-and-Fix Coordination algorithm, so named BFC-TSD, where a special treatment is given to cross scenario group constraints that link variables from different scenario groups. A broad computational experience is presented by comparing the risk neutral approach and the tested risk averse strategies. The performance of the new version of the BFC algorithm versus the plain use of a state-of-the-artMIP solver is also reported.

The Stability of the Roommate Problem Revisited

The lack of stability in some matching problems suggests that alternative solution concepts to the core might be applied to find predictable matchings. We propose the absorbing sets as a solution for the class of roommate problems with strict preferences. This solution, which always exists, either gives the matchings in the core or predicts some other matchings when the core is empty. Furthermore, it satisfies an interesting property of outer stability. We also characterize the absorbing sets, determine their number and, in case of multiplicity, we find that they all share a similar structure.

Optimal Minimum Wage in a Competitive Economy: an Alternative Modelling Approach

This paper analyzes whether a minimum wage can be an optimal redistribution policy when distorting taxes and lump-sum transfers are also available in a competitive economy. We build a static general equilibrium model with a Ramsey planner making decisions on taxes, transfers, and minimum wage levels. Workers are assumed to differ only in their productivity. We find that optimal redistribution may imply the use of a minimum wage. The key factor driving our results is the reaction of the demand for low skilled labor to the minimum wage law. Hence, an optimal minimum wage appears to be most likely when low skilled households are scarce, the complementarity between the two types of workers is large or the difference in productivity is small. The main contribution of the paper is a modelling approach that allows us to adopt analysis and solution techniques widely used in recent public finance research. Moreover, this modelling strategy is flexible enough to allow for potential extensions to include dynamics into the model.