A two-stage stochastic transportation problem with fixed handling costs and a priori selection of the distribution channels

In this paper, a transportation problem comprising stochastic demands, fixed handling costs at the origins, and fixed costs associated with the links is addressed. It is assumed that uncertainty is adequately captured via a finite set of scenarios. The problem is formulated as a two-stage stochastic program. The goal is to minimize the total cost associated with the selected links plus the expected transportation and fixed handling costs. A prototype problem is initially presented which is then progressively extended to accommodate capacities at the origins and multiple commodities. The results of an extensive set of computational tests are reported and discussed

A cutting-plane approach for large-scale capacitated multi-period facility location using a specialized interior-point method

We propose a cutting-plane approach (namely, Benders decomposition) for a class of capacitated multi-period facility location problems. The novelty of this approach lies on the use of a specialized interior-point method for solving the Benders subproblems. The primal block-angular structure of the resulting linear optimization problems is exploited by the interior-point method, allowing the (either exact or inexact) efficient solution of large instances. The effect of different modeling conditions and problem specifications on the computational performance are also investigated both theoretically and empirically, providing a deeper understanding of the significant factors influencing the overall efficiency of the cutting-plane method. This approach allowed the solution of instances of up to 200 potential locations, one million customers and three periods, resulting in mixed integer linear optimization problems of up to 600 binary and 600 millions of continuous variables. Those problems were solved by the specialized approach in less than one hour, outperforming other stateof- the-art methods, which exhausted the (144 Gigabytes of) available memory in the largest instances.Preprin

Outsourcing policies for the Facility Location Problem with Bernoulli Demand

This paper focuses on the Facility Location Problem with Bernoulli Demand, a discrete facility location problem with uncertainty where the joint distribution of the customers' demands is expressed by means of a set of possible scenarios. A two-stage stochastic program with recourse is used to select the facility locations and the a priori assignments of customers to open plants, together with the a posteriori strategy to apply in those realizations where the a priori solution is not feasible. Four alternative outsourcing policies are studied for the recourse action, and a mathematical programming formulation is presented for each of them. Extensive computational experiments have been carried-out to analyze the performance of each of the formulations and to compare the quality of the solutions produced by each of them relative to the other outsourcing policies

Multitype Maximal Covering Location Problems: Hybridizing discrete and continuous problems

Acknowledgements This research has been partially supported by Spanish Ministerio de Ciencia e Innovación, AEI/FEDER grant number PID2020-114594GBC21, Junta de Andalucía projects P18-FR- 1422/2369 and projects FEDERUS-1256951, B-FQM-322-UGR20, CEI-3-FQM331 and Netmeet- Data (Fundación BBVA 2019). The first author was also partially supported by the IMAG-Maria de Maeztu grant CEX2020-001105-M /AEI /10.13039/501100011033. The second author was partially supported by Spanish Ministry of Education and Science grant number PEJ2018- 002962-A, the PhD Program in Mathematics at the Universidad de Granada and Becas de Movilidad entre Universidades Andaluzas e Iberoamericanas (AUIP). The third author was partially funded by grant UIDB/04561/2020 from National Funding from FCT|Fundaçao para a Ciencia e Tecnologia, Portugal.This paper introduces a general modeling framework for a multi-type maximal covering location problem in which the position of facilities in different metric spaces are simultaneously decided to maximize the demand generated by a set of points. From the need of intertwining location decisions in discrete and in continuous sets, a general hybridized problem is considered in which some types of facilities are to be located in finite sets and the others in continuous metric spaces. A natural non-linear model is proposed for which an integer linear programming reformulation is derived. A branch-and-cut algorithm is developed for better tackling the problem. The study proceeds considering the particular case in which the continuous facilities are to be located in the Euclidean plane. In this case, taking advantage from some geometrical properties it is possible to propose an alternative integer linear programming model. The results of an extensive battery of computational experiments performed to assess the methodological contribution of this work is reported on. The data consists of up to 920 demand nodes using real geographical and demographic data.Spanish Ministerio de Ciencia e Innovación, AEI/FEDER grant number PID2020-114594GBC21Junta de Andalucía projects P18-FR- 1422/2369FEDERUS-1256951B-FQM-322-UGR20CEI-3-FQM331Netmeet- Data (Fundación BBVA 2019)MAG-Maria de Maeztu grant CEX2020-001105-M /AEI /10.13039/501100011033Spanish Ministry of Education and Science grant number PEJ2018- 002962-Agrant UIDB/04561/2020 from National Funding from FCT|Fundaçao para a Ciencia e Tecnologia, Portuga

Heuristic solucions to the facility location problem with general Bernoulli demands

In this paper, a heuristic procedure is proposed for the facility location problem with general Bernoulli demands. This is a discrete facility location problem with stochastic demands that can be formulated as a two-stage stochastic program with recourse. In particular, facility locations and customer assignments must be decided here and now, i.e., before knowing the customers who will actually require to be served. In a second stage, service decisions are made according to the actual requests. The heuristic proposed consists of a greedy randomized adaptive search procedure followed by a path relinking. The heterogeneous Bernoulli demands make prohibitive the computational effort for evaluating feasible solutions. Thus the expected cost of a feasible solution is simulated when necessary. The results of extensive computational tests performed for evaluating the quality of the heuristic are reported, showing that high-quality feasible solutions can be obtained for the problem in fairly small computational times.Peer ReviewedPostprint (author's final draft

Solutions to the facility location problem with general Bernoulli demands

In this work we address the facility location problem with general Bernoulli demands. Extended formulations are proposed for two different outsourcing policies, which allow using sample average approximation for estimating optimal values. In addition, solutions are obtained heuristically and their values compared with the obtained estimates. Numerical results of a series of computational experiments are presented and analyzed.In this work we address the facility location problem with general Bernoulli demands. Extended formulations are proposed for two different outsourcing policies, which allow using sample average approximation for estimating optimal values. In addition, solutions are obtained heuristically and their values compared with the obtained estimates. Numerical results of a series of computational experiments are presented and analyzed.Postprint (published version

Modeling congestion and service time in hub location problems

The final publication is available at Elsevier via http://dx.doi.org/10.1016/j.apm.2017.10.033 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In this paper, we present a modeling framework for hub location problems with a service time limit considering congestion at hubs. Service time is modeled taking the traveling time on the hub network as well as the handling time and the delay caused by congestion at hubs into account. We develop mixed-integer linear programming formulations for the single and multiple allocation versions of this problem. We further extend the multiple allocation model with a possibility of direct shipments. We test our models on the well-known AP data set and analyze the effects of congestion and service time on costs and hub network design. We introduce a measure for the value of modeling congestion and show that not considering the effects of congestion may result in increased costs as well as in building infeasible hub networks

A Stochastic Bi-objective Location Model for Reverse Logistics

Se presenta un modelo estocástico bietapa con dos criteros (coste, efecto obnoxio) para el diseño de una red de recogida de residuos

Location problems with multiple criteria

This chapter analyzes multicriteria continuous, network, and discrete location problems. In the continuous framework, we provide a complete description of the set of weak Pareto, Pareto, and strict Pareto locations for a general Q-criteria location problem based on the characterization of three criteria problems. In the network case, the set of Pareto locations is characterized for general networks as well as for tree networks using the concavity and convexity properties of the distance function on the edges. In the discrete setting, the entire set of Pareto locations is characterized using rational generating functions of integer points in polytopes. Moreover, we describe algorithms to obtain the solutions sets (the different Pareto locations) using the above characterizations. We also include a detailed complexity analysis. A number of references has been cited throughout the chapter to avoid the inclusion of unnecessary technical details and also to be useful for a deeper analysis