Location models in the public sector

The past four decades have witnessed an explosive growth in the field of networkbased facility location modeling. This is not at all surprising since location policy is one of the most profitable areas of applied systems analysis in regional science and ample theoretical and applied challenges are offered. Location-allocation models seek the location of facilities and/or services (e.g., schools, hospitals, and warehouses) so as to optimize one or several objectives generally related to the efficiency of the system or to the allocation of resources. This paper concerns the location of facilities or services in discrete space or networks, that are related to the public sector, such as emergency services (ambulances, fire stations, and police units), school systems and postal facilities. The paper is structured as follows: first, we will focus on public facility location models that use some type of coverage criterion, with special emphasis in emergency services. The second section will examine models based on the P-Median problem and some of the issues faced by planners when implementing this formulation in real world locational decisions. Finally, the last section will examine new trends in public sector facility location modeling.Location analysis, public facilities, covering models

Robust Design of Distribution Networks Considering Worst Case Interdictions

Multi-echelon facility location models are commonly employed to design transportation systems. While they provide cost-efficient designs, they are prone to severe financial loss in the event of the disruption of any of its facilities. Additionally, the recent crisis in the world motivates OR practitioners to develop models that better integrate disruptive event in the design phase of a distribution network. In this research, we propose a two-echelon capacitated facility location model under the risk of a targeted attack, which identifies the optimal location of intermediate facilities by minimizing the weighted sum of pre and post interdiction flow cost and the fixed cost of opening intermediate facilities. The developed model results in a tri-level Mixed Integer Programming (MIP) formulation, reformulated in a two-level MIP. Hence, we prescribe solution methods based on Bender Decomposition as well as two variants that enhance the speed performance of the algorithm. The results reveal the importance of selecting backup facilities and highlight that premium paid to design a robust distribution network is negligible given the benefit of reducing the post-interdiction cost when a disruptive event occurs

Pricing Schemes in Electric Energy Markets

abstract: Two thirds of the U.S. power systems are operated under market structures. A good market design should maximize social welfare and give market participants proper incentives to follow market solutions. Pricing schemes play very important roles in market design. Locational marginal pricing scheme is the core pricing scheme in energy markets. Locational marginal prices are good pricing signals for dispatch marginal costs. However, the locational marginal prices alone are not incentive compatible since energy markets are non-convex markets. Locational marginal prices capture dispatch costs but fail to capture commitment costs such as startup cost, no-load cost, and shutdown cost. As a result, uplift payments are paid to generators in markets in order to provide incentives for generators to follow market solutions. The uplift payments distort pricing signals. In this thesis, pricing schemes in electric energy markets are studied. In the first part, convex hull pricing scheme is studied and the pricing model is extended with network constraints. The subgradient algorithm is applied to solve the pricing model. In the second part, a stochastic dispatchable pricing model is proposed to better address the non-convexity and uncertainty issues in day-ahead energy markets. In the third part, an energy storage arbitrage model with the current locational marginal price scheme is studied. Numerical test cases are studied to show the arguments in this thesis. The overall market and pricing scheme design is a very complex problem. This thesis gives a thorough overview of pricing schemes in day-ahead energy markets and addressed several key issues in the markets. New pricing schemes are proposed to improve market efficiency.Dissertation/ThesisMasters Thesis Electrical Engineering 201

Introducing capacitaties in the location of unreliable facilities

The goal of this paper is to introduce facility capacities into the Reliability Fixed-Charge Location Problem in a sensible way. To this end, we develop and compare different models, which represent a tradeoff between the extreme models currently available in the literature, where a priori assignments are either fixed, or can be fully modified after failures occur. In a series of computational experiments we analyze the obtained solutions and study the price of introducing capacity constraints according to the alternative models both, in terms of computational burden and of solution cost.Peer ReviewedPostprint (author's final draft

On High-Performance Benders-Decomposition-Based Exact Methods with Application to Mixed-Integer and Stochastic Problems

RÉSUMÉ : La programmation stochastique en nombres entiers (SIP) combine la difficulté de l’incertitude et de la non-convexité et constitue une catégorie de problèmes extrêmement difficiles à résoudre. La résolution efficace des problèmes SIP est d’une grande importance en raison de leur vaste applicabilité. Par conséquent, l’intérêt principal de cette dissertation porte sur les méthodes de résolution pour les SIP. Nous considérons les SIP en deux étapes et présentons plusieurs algorithmes de décomposition améliorés pour les résoudre. Notre objectif principal est de développer de nouveaux schémas de décomposition et plusieurs techniques pour améliorer les méthodes de décomposition classiques, pouvant conduire à résoudre optimalement divers problèmes SIP. Dans le premier essai de cette thèse, nous présentons une revue de littérature actualisée sur l’algorithme de décomposition de Benders. Nous fournissons une taxonomie des améliorations algorithmiques et des stratégies d’accélération de cet algorithme pour synthétiser la littérature et pour identifier les lacunes, les tendances et les directions de recherche potentielles. En outre, nous discutons de l’utilisation de la décomposition de Benders pour développer une (méta- )heuristique efficace, décrire les limites de l’algorithme classique et présenter des extensions permettant son application à un plus large éventail de problèmes. Ensuite, nous développons diverses techniques pour surmonter plusieurs des principaux inconvénients de l’algorithme de décomposition de Benders. Nous proposons l’utilisation de plans de coupe, de décomposition partielle, d’heuristiques, de coupes plus fortes, de réductions et de stratégies de démarrage à chaud pour pallier les difficultés numériques dues aux instabilités, aux inefficacités primales, aux faibles coupes d’optimalité ou de réalisabilité, et à la faible relaxation linéaire. Nous testons les stratégies proposées sur des instances de référence de problèmes de conception de réseau stochastique. Des expériences numériques illustrent l’efficacité des techniques proposées. Dans le troisième essai de cette thèse, nous proposons une nouvelle approche de décomposition appelée méthode de décomposition primale-duale. Le développement de cette méthode est fondé sur une reformulation spécifique des sous-problèmes de Benders, où des copies locales des variables maîtresses sont introduites, puis relâchées dans la fonction objective. Nous montrons que la méthode proposée atténue significativement les inefficacités primales et duales de la méthode de décomposition de Benders et qu’elle est étroitement liée à la méthode de décomposition duale lagrangienne. Les résultats de calcul sur divers problèmes SIP montrent la supériorité de cette méthode par rapport aux méthodes classiques de décomposition. Enfin, nous étudions la parallélisation de la méthode de décomposition de Benders pour étendre ses performances numériques à des instances plus larges des problèmes SIP. Les variantes parallèles disponibles de cette méthode appliquent une synchronisation rigide entre les processeurs maître et esclave. De ce fait, elles souffrent d’un important déséquilibre de charge lorsqu’elles sont appliquées aux problèmes SIP. Cela est dû à un problème maître difficile qui provoque un important déséquilibre entre processeur et charge de travail. Nous proposons une méthode Benders parallèle asynchrone dans un cadre de type branche-et-coupe. L’assouplissement des exigences de synchronisation entraine des problèmes de convergence et d’efficacité divers auxquels nous répondons en introduisant plusieurs techniques d’accélération et de recherche. Les résultats indiquent que notre algorithme atteint des taux d’accélération plus élevés que les méthodes synchronisées conventionnelles et qu’il est plus rapide de plusieurs ordres de grandeur que CPLEX 12.7.----------ABSTRACT : Stochastic integer programming (SIP) combines the difficulty of uncertainty and non-convexity, and constitutes a class of extremely challenging problems to solve. Efficiently solving SIP problems is of high importance due to their vast applicability. Therefore, the primary focus of this dissertation is on solution methods for SIPs. We consider two-stage SIPs and present several enhanced decomposition algorithms for solving them. Our main goal is to develop new decomposition schemes and several acceleration techniques to enhance the classical decomposition methods, which can lead to efficiently solving various SIP problems to optimality. In the first essay of this dissertation, we present a state-of-the-art survey of the Benders decomposition algorithm. We provide a taxonomy of the algorithmic enhancements and the acceleration strategies of this algorithm to synthesize the literature, and to identify shortcomings, trends and potential research directions. In addition, we discuss the use of Benders decomposition to develop efficient (meta-)heuristics, describe the limitations of the classical algorithm, and present extensions enabling its application to a broader range of problems. Next, we develop various techniques to overcome some of the main shortfalls of the Benders decomposition algorithm. We propose the use of cutting planes, partial decomposition, heuristics, stronger cuts, and warm-start strategies to alleviate the numerical challenges arising from instabilities, primal inefficiencies, weak optimality/feasibility cuts, and weak linear relaxation. We test the proposed strategies with benchmark instances from stochastic network design problems. Numerical experiments illustrate the computational efficiency of the proposed techniques. In the third essay of this dissertation, we propose a new and high-performance decomposition approach, called Benders dual decomposition method. The development of this method is based on a specific reformulation of the Benders subproblems, where local copies of the master variables are introduced and then priced out into the objective function. We show that the proposed method significantly alleviates the primal and dual shortfalls of the Benders decomposition method and it is closely related to the Lagrangian dual decomposition method. Computational results on various SIP problems show the superiority of this method compared to the classical decomposition methods as well as CPLEX 12.7. Finally, we study parallelization of the Benders decomposition method. The available parallel variants of this method implement a rigid synchronization among the master and slave processors. Thus, it suffers from significant load imbalance when applied to the SIP problems. This is mainly due to having a hard mixed-integer master problem that can take hours to be optimized. We thus propose an asynchronous parallel Benders method in a branchand- cut framework. However, relaxing the synchronization requirements entails convergence and various efficiency problems which we address them by introducing several acceleration techniques and search strategies. In particular, we propose the use of artificial subproblems, cut generation, cut aggregation, cut management, and cut propagation. The results indicate that our algorithm reaches higher speedup rates compared to the conventional synchronized methods and it is several orders of magnitude faster than CPLEX 12.7

On the capacitated step-fixed charge and facility location problem : a row perturbation heuristic

The Classical Transportation Problem (TP) Tableau which utilizes continuous variable cost has been used to model and solve distribution problems. However, many real distribution problem decisions which require various combination of fixed and variable cost and having several mixed variables of the binary integers and continuous types make this approach limited. This challenge requires new integrated models that are also NP hard for which exact algorithms such as Branch and bound, cutting plane algorithm may be inefficient to use as the problem size increases in practical business cases. We present in this paper, an integrated model of Facility Location (FL) and Step Fixed charge Transportation Problem (SFCTP). This problem is solved using a solution heuristic that utilizes relaxation and linearization approach to recast it to the classical TP as a starting solution. For the improved solution, a low cost and efficient perturbation heuristic that works in a row-wise manner is developed. We also propose a lower bound based on literature as a guide in achieving a solution. Lastly, a numerical example is presented to illustrate the procedures of the solution.http://www.naturalspublishing.com/show.asp?JorID=1&pgid=02019-03-01hj2018Industrial and Systems Engineerin

Hub Network Design and Discrete Location: Economies of Scale, Reliability and Service Level Considerations

In this thesis, we study three related decision problems in location theory. The first part of the dissertation presents solution algorithms for the cycle hub location problem (CHLP), which seeks to locate p-hub facilities that are connected by means of a cycle, and to assign non-hub nodes to hubs so as to minimize the total cost of routing flows through the network. This problem is useful in modeling applications in transportation and telecommunications systems, where large setup costs on the links and reliability requirements make cycle topologies a prominent network architecture. We present a branch and-cut algorithm that uses a flow-based formulation and two families of mixed-dicut inequalities as a lower bounding procedure at nodes of the enumeration tree. We also introduce a greedy randomized adaptive search algorithm that is used to obtain initial upper bounds for the exact algorithm and to obtain feasible solutions for large-scale instances of the CHLP. Numerical results on a set of benchmark instances with up to 100 nodes confirm the efficiency of the proposed solution algorithms. In the second part of this dissertation, we study the modular hub location problem, which explicitly models the flow-dependent transportation costs using modular arc costs. It neither assumes a full interconnection between hub nodes nor a particular topological structure, instead it considers link activation decisions as part of the design. We propose a branch-and-bound algorithm that uses a Lagrangean relaxation to obtain lower and upper bounds at the nodes of the enumeration tree. Numerical results are reported for benchmark instances with up to 75 nodes. In the last part of this dissertation we study the dynamic facility location problem with service level constraints (DFLPSL). The DFLPSL seeks to locate a set of facilities with sufficient capacities over a planning horizon to serve customers at minimum cost while a service level requirement is met. This problem captures two important sources of stochasticity in facility location by considering known probability distribution functions associated with processing and routing times. We present a nonlinear mixed integer programming formulation and provide feasible solutions using two heuristic approaches. We present the results of computational experiments to analyze the impact and potential benefits of explicitly considering service level constraints when designing distribution systems

Models and solution approaches for intermodal and less-than-truckload network design with load consolidations

Logistics and supply chain problems arising in the context of intermodal transportation and less-than-truckload (LTL) network design typically require commodities to be consolidated and shipped via the most economical route to their destinations. Traditionally, these problems have been modelled using network design or hub-and- spoke approaches. In a network design problem, one is given the network and flow requirements between the origin and destination pairs (commodities), and the objective is to route the flows over the network so as to minimize the sum of the fixed charge incurred in using arcs and routing costs. However, there are possible benefits, due to economies-of-scale in transportation, that are not addressed in standard network design models. On the other hand, hub location problems are motivated by potential economies-of-scale in transportation costs when loads are consolidated and shipped together over a completely connected hub network. However, in a hub location problem, the assignment of a node to a hub is independent of the commodities originating at, or destined to, this node. Such an indiscriminate assignment may not be suitable for all commodities originating at a particular node because of their different destinations. Problems arising in the area of LTL transportation, intermodal transportation and package routing generally have characteristics such as economies- of-scale in transportation costs in addition to the requirement of commodity-based routing. Obviously, the existing network design and hub location-based models are not directly suitable for these applications. In this dissertation, we investigate the development of models and solution algorithms for problems in the areas of LTL and intermodal transportation as well as in the freight forwarders industry. We develop models and solution methods to address strategic, tactical and operational level decision issues and show computational results. This research provides new insights into these application areas and new solution methods therein. The solution algorithms developed here also contribute to the general area of discrete optimization, particularly for problems with similar characteristics

Multi-level Facility Location Problems

We conduct a comprehensive review on multi-level facility location problems which extend several classical facility location problems and can be regarded as a subclass within the well-established field of hierarchical facility location. We first present the main characteristics of these problems and discuss some similarities and differences with related areas. Based on the types of decisions involved in the optimization process, we identify three different categories of multi-level facility location problems. We present overviews of formulations, algorithms and applications, and we trace the historical development of the field