Celeste Pizarro

On air traffic flow management with rerouting. Part II: Stochastic case

We present a framework for modeling multistage mixed 0–1 problems for the air traffic flow management problem with rerouting (ATFMRP) under uncertainty in the airport arrival and departure capacity, the air sector capacity and the flight demand. The model allows for flight cancelation, if necessary. It considers several types of objective functions to minimize, namely, total ground and air holding cost, penalization of the alternative routes to the scheduled one for each flight, delay cost for the flights to arrive to the airports and the air sector nodes, and penalization for advancing the arrival of the flights to the airport over the scheduled period. A scenario tree based scheme is used to represent the Deterministic Equivalent Model (DEM) of the stochastic mixed 0–1 program with full recourse. The nonanticipativity constraints that equate the so named common 0–1 and continuous variables from the same group of scenarios in each period are implicitly satisfied in the compact representation of DEM. Some computational experience is reported for medium-scale instances. The model is so tight that none of the instances of the testbed but two of them requires to execute the branch-and-cut phase of the MIP optimization engine of choice.

On air traffic flow management with rerouting. Part I: Deterministic case

In this paper a deterministic mixed 0–1 model for the air traffic flow management problem is presented. The model allows for flight cancelation and rerouting, if necessary. It considers several types of objective functions to minimize, namely, the number of flights exceeding a given time delay (that can be zero), separable and non-separable ground holding and air delay costs, penalization of alternative routes to the scheduled one for each flight, time unit delay cost to arrive to the nodes (i.e., air sectors and airports) and penalization for advancing arrival to the nodes over the schedule. The arrival and departure capacity at the airports is obviously considered, as well as the capacity of the different sectors in the airspace, being allowed to vary along the time horizon. So, the model is aimed to help for better decision-making regarding the ground holding and air delays imposed on flights in an air network, on a short term policy for a given time horizon. It is so strong that there is no additional cut appending, nor does it require the execution of the branch-and-bound phase to obtain the optimal solution for the problem in many cases of the testbeds with which we have experimented. In the other cases, the help of the cut identifying and heuristic schemes of the state-of-the art optimization engine of choice is required in order to obtain the solution of the problem, and the branch-and-bound phase is not required either. An extensive computational experience is reported for large-scale instances, some of which have been taken from the literature and some others were coming from industry.

Fix-and-Relax-Coordination for a multi-period location-allocation problem under uncertainty

A multi-period discrete facility location problem is introduced for a risk neutral strategy with uncertainty in the costs and some of the requirements along the planning horizon. A compact 0-1 formulation for the Deterministic Equivalent Model of the problem under two alternative strategies for the location decisions is presented. Furthermore, a new algorithmic matheuristic, Fix-and-Relax-Coordination, is introduced. This solution scheme is based on a specialization of the Branch-and-Fix Coordination methodology, which exploits the Nonanticipativity Constraints and uses the Twin Node Family concept. The results of an extensive computational experience allow to compare the alternative modeling strategies and assess the effectiveness of the proposed approach versus the plain use of a state-of-the-art MIP solver.

Uncertainty in Humanitarian Logistics for Disaster Management. A Review

Given their nature, disasters are generally characterized by a high level of uncertainty. In fact, both their occurrence and their consequences are not easily anticipated. Thus, NGOs and civil protection often have to take decisions and plan for their operations without having the possibility of relying on exact or complete information on the magnitude of the disaster. Over the years, a number of works and methodologies that address uncertainty in Disaster Management have been presented in the literature. In this chapter we review different forms of tackling uncertainty in Humanitarian Logistics for Disaster Management and propose a classification of the advances in this research field.

On SIP algorithms for minimizing the mean-risk function in the multi-period single-source problem under uncertainty

We present an algorithmic framework for solving the strategic problem of assigning retailers to facilities in a multi-period single-sourcing product environment under uncertainty in the demand from the retailers and the costs of production, inventory holding, backlogging and distribution of the product. The functional to minimize is included by the expected objective function and the excess probability functional. By considering a splitting variable mathematical representation of the Deterministic Equivalent Model, we introduce several so-called Fix-and-Relax procedures that exploit the excess probability functional structure in addition to the structure of the special ordered sets related to the non-anticipativity constraints for the assignment variables. Some computational experience is reported.

Structuring Bilateral Energy Contract Portfolios in Competitive Markets

A multistage complete recourse model for structuring energy contract portfolios in competitive markets is presented for price-taker operators. The main uncertain parameters are spot price, exogenous water inflow to the hydro system and fuel-oil and gas cost. A mean-risk objective function is considered as a composite function of the expected trading profit and the weighted probability of reaching a given profit target. The expected profit is given by the bilateral contract profit and the spot market trading profit along the time horizon over the scenarios. The uncertainty is represented by a set of scenarios. The problem is formulated as a mixed 0–1 deterministic equivalent model. Only 0–1 variables have nonzero coefficients in the first-stage constraint system, such that the continuous variables only show up in the formulation of the later stages. A problem-solving approach based on a splitting variable mathematical representation of the scenario clusters is considered. The approach uses the twin node family concept within the algorithmic framework presented in the chapter. The Kyoto protocol-based regulations for the pollutant emission are considered.

On efficient matheuristic algorithms for multi-period stochastic facility location-assignment problems

In this work we present two matheuristic procedures to build good feasible solutions (frequently, the optimal one) by considering the solutions of relaxed problems of large-sized instances of the multi-period stochastic pure 0–1 location-assignment problem. The first procedure is an iterative one for Lagrange multipliers updating based on a scenario cluster Lagrangean decomposition for obtaining strong (lower, in case of minimization) bounds of the solution value. The second procedure is a sequential one that works with the relaxation of the integrality of subsets of variables for different levels of the problem, so that a chain of (lower, in case of minimization) bounds is generated from the LP relaxation up to the integer solution value. Additionally, and for both procedures, a lazy heuristic scheme, based on scenario clustering and on the solutions of the relaxed problems, is considered for obtaining a (hopefully good) feasible solution as an upper bound of the solution value of the full problem. Then, the same framework provides for the two procedures lower and upper bounds on the solution value. The performance is compared over a set of instances of the stochastic facility location-assignment problem. It is well known that the general static deterministic location problem is NP-hard and, so, it is the multi-period stochastic version. A broad computational experience is reported for 14 instances, up to 15 facilities, 75 customers, 6 periods, over 260 scenarios and over 420 nodes in the scenario tree, to assess the validity of proposals made in this work versus the full use of a state-of the-art IP optimizer.

A Metaheuristic for Solving Large-Scale Two-Stage Stochastic Mixed 0-1 Programs with the Time Stochastic Dominance Risk Averse Strategy

Abstract Supply Chain Design problems often result into multiperiod stochastic mixed integer problems that are hard to solve. In this paper we propose a metaheuristic algorithm as a specialization for two- stage problems of the so-named Fix-and-Relax Algorithm presented previously for solving large- scale multiperiod stochastic mixed 0–1 optimization problems under a time stochastic dominance risk averse strategy, so-named TSD. Some computational experience is presented.

On risk management of a two-stage stochastic mixed 0–1 model for the closed-loop supply chain design problem

Abstract In this work, the design and operation planning of a multi-period, multi-product closed-loop supply chain is addressed. Recovered end-of-life products from customers are evaluated in disassembly centers and accordingly are sent back to factories for remanufacturing, or leave the network either by being sold to third parties or by being sent to disposal. Typical uncertain parameters are product demand, production cost, and returned product volume and evaluation, among others. So, stochastic optimization approaches should be used for problem solving, where different topology decisions on the timing, location and capacity of some entities (factories, and distribution and sorting centers) are to be considered along a time horizon. A two-stage multi-period stochastic mixed 0–1 bilinear optimization model is introduced, where the combined definition of the available entities at the periods and the products’ flow among the entities, maximizes the net present value of the expected total profit along the time horizon. A version of the mixture of chance-constrained and second order stochastic dominance risk averse measures is considered for risk management at intermediate periods of the time horizon. Given the high dimensions of the model it is unrealistic to look for the optimality of the solution in an affordable computing effort for current hardware and optimization software resources. So, a decomposition approach is considered, namely a Fix-and-Relax decomposition algorithm. For assessing the computational validation of the modeling and algorithmic proposals, pilot cases are taken from a real-life glass supply chain network whose main features are retained.