Industrial water management by multiobjective optimization: from individual to collective solution through eco-industrial parks.

Industrial water networks are designed in the first part by a multiobjective optimization strategy, where fresh water, regenerated water flow rates as well as the number of network connections (integer variables) are minimized. The problem is formulated as a Mixed-Integer Linear Programming problem (MILP) and solved by the ε-constraint method. The linearization of the problem is based on the necessary conditions of optimality defined by Savelski and Bagajewicz (2000). The approach is validated on a published example involving only one contaminant. In the second part the MILP strategy is implemented for designing an Eco-Industrial Park (EIP) involving three companies. Three scenarios are considered: EIP without regeneration unit, EIP where each company owns its regeneration unit and EIP where the three companies share regeneration unit(s). Three possible regeneration units can be chosen, and the MILP is solved under two kinds of conditions: limited or unlimited number of connections, same or different gains for each company. All these cases are compared according to the global equivalent cost expressed in fresh water and taking also into account the network complexity through the number of connections. The best EIP solution for the three companies can be determined

Finite Alphabet Control of Logistic Networks with Discrete Uncertainty

We consider logistic networks in which the control and disturbance inputs take values in finite sets. We derive a necessary and sufficient condition for the existence of robustly control invariant (hyperbox) sets. We show that a stronger version of this condition is sufficient to guarantee robust global attractivity, and we construct a counterexample demonstrating that it is not necessary. Being constructive, our proofs of sufficiency allow us to extract the corresponding robust control laws and to establish the invariance of certain sets. Finally, we highlight parallels between our results and existing results in the literature, and we conclude our study with two simple illustrative examples

The N-K Problem in Power Grids: New Models, Formulations and Numerical Experiments (extended version)

Given a power grid modeled by a network together with equations describing the power flows, power generation and consumption, and the laws of physics, the so-called N-k problem asks whether there exists a set of k or fewer arcs whose removal will cause the system to fail. The case where k is small is of practical interest. We present theoretical and computational results involving a mixed-integer model and a continuous nonlinear model related to this question.Comment: 40 pages 3 figure

Bartering integer commodities with exogenous prices

The analysis of markets with indivisible goods and fixed exogenous prices has played an important role in economic models, especially in relation to wage rigidity and unemployment. This research report provides a mathematical and computational details associated to the mathematical programming based approaches proposed by Nasini et al. (accepted 2014) to study pure exchange economies where discrete amounts of commodities are exchanged at fixed prices. Barter processes, consisting in sequences of elementary reallocations of couple of commodities among couples of agents, are formalized as local searches converging to equilibrium allocations. A direct application of the analyzed processes in the context of computational economics is provided, along with a Java implementation of the approaches described in this research report.Comment: 30 pages, 5 sections, 10 figures, 3 table

On the flexibility of an eco-industrial park (EIP) for managing industrial water

In a recent paper, a generic model, based on a multiobjective optimization procedure, for water supply system for a single company and for an eco-industrial park was proposed and illustrated by a park involving three companies A, B and C. The best configuration was identified by simultaneously minimizing the fresh water flow rate, the regenerated water flow rate and the number of connections in the eco-industrial park. The question is now to know what the maximal increase/decrease in pollutant flow rates is, so that the eco-industrial park remains feasible, economically profitable and environmentally friendly. A preliminary study shows that the park can accept an increase of pollutant flow rates of 29% in company A, 12% in company B and only 1% in company C; beyond these limits the industrial symbiosis becomes not feasible. The proposed configuration is not flexible with a very limited number of connections. Indeed, the solution implemented for conferring some flexibility to this network is to increase the number of connections within the park. However, connections have a cost, so the increase of their number needs to remain moderate. The number of connections is augmented until the symbiosis becomes unfeasible, or until the gain for each company to participate to the park becomes lower than a given threshold. Several cases are studied by increasing the pollutant flow rates under two different scenarios: 1) in only one company, 2) in two or three companies simultaneously