Multi-period maximal covering location problem with capacitated facilities and modules for natural disaster relief services

The paper aims to study a multi-period maximal covering location problem with the configuration of different types of facilities, as an extension of the classical maximal covering location problem (MCLP). The proposed model can have applications such as locating disaster relief facilities, hospitals, and chain supermarkets. The facilities are supposed to be comprised of various units, called the modules. The modules have different sizes and can transfer between facilities during the planning horizon according to demand variation. Both the facilities and modules are capacitated as a real-life fact. To solve the problem, two upper bounds-(LR1) and (LR2)-and Lagrangian decomposition (LD) are developed. Two lower bounds are computed from feasible solutions obtained from (LR1), (LR2), and (LD) and a novel heuristic algorithm. The results demonstrate that the LD method combined with the lower bound obtained from the developed heuristic method (LD-HLB) shows better performance and is preferred to solve both small- and large-scale problems in terms of bound tightness and efficiency especially for solving large-scale problems. The upper bounds and lower bounds generated by the solution procedures can be used as the profit approximation by the managerial executives in their decision-making process

A Benders Based Rolling Horizon Algorithm for a Dynamic Facility Location Problem

This study presents a well-known capacitated dynamic facility location problem (DFLP) that satisfies the customer demand at a minimum cost by determining the time period for opening, closing, or retaining an existing facility in a given location. To solve this challenging NP-hard problem, this paper develops a unique hybrid solution algorithm that combines a rolling horizon algorithm with an accelerated Benders decomposition algorithm. Extensive computational experiments are performed on benchmark test instances to evaluate the hybrid algorithm’s efficiency and robustness in solving the DFLP problem. Computational results indicate that the hybrid Benders based rolling horizon algorithm consistently offers high quality feasible solutions in a much shorter computational time period than the stand-alone rolling horizon and accelerated Benders decomposition algorithms in the experimental range

Dynamic Facility Location with Modular Capacities : Models, Algorithms and Applications in Forestry

Les décisions de localisation sont souvent soumises à des aspects dynamiques comme des changements dans la demande des clients. Pour y répondre, la solution consiste à considérer une flexibilité accrue concernant l’emplacement et la capacité des installations. Même lorsque la demande est prévisible, trouver le planning optimal pour le déploiement et l'ajustement dynamique des capacités reste un défi. Dans cette thèse, nous nous concentrons sur des problèmes de localisation avec périodes multiples, et permettant l'ajustement dynamique des capacités, en particulier ceux avec des structures de coûts complexes. Nous étudions ces problèmes sous différents points de vue de recherche opérationnelle, en présentant et en comparant plusieurs modèles de programmation linéaire en nombres entiers (PLNE), l'évaluation de leur utilisation dans la pratique et en développant des algorithmes de résolution efficaces. Cette thèse est divisée en quatre parties. Tout d’abord, nous présentons le contexte industriel à l’origine de nos travaux: une compagnie forestière qui a besoin de localiser des campements pour accueillir les travailleurs forestiers. Nous présentons un modèle PLNE permettant la construction de nouveaux campements, l’extension, le déplacement et la fermeture temporaire partielle des campements existants. Ce modèle utilise des contraintes de capacité particulières, ainsi qu’une structure de coût à économie d’échelle sur plusieurs niveaux. L'utilité du modèle est évaluée par deux études de cas. La deuxième partie introduit le problème dynamique de localisation avec des capacités modulaires généralisées. Le modèle généralise plusieurs problèmes dynamiques de localisation et fournit de meilleures bornes de la relaxation linéaire que leurs formulations spécialisées. Le modèle peut résoudre des problèmes de localisation où les coûts pour les changements de capacité sont définis pour toutes les paires de niveaux de capacité, comme c'est le cas dans le problème industriel mentionnée ci-dessus. Il est appliqué à trois cas particuliers: l'expansion et la réduction des capacités, la fermeture temporaire des installations, et la combinaison des deux. Nous démontrons des relations de dominance entre notre formulation et les modèles existants pour les cas particuliers. Des expériences de calcul sur un grand nombre d’instances générées aléatoirement jusqu’à 100 installations et 1000 clients, montrent que notre modèle peut obtenir des solutions optimales plus rapidement que les formulations spécialisées existantes. Compte tenu de la complexité des modèles précédents pour les grandes instances, la troisième partie de la thèse propose des heuristiques lagrangiennes. Basées sur les méthodes du sous-gradient et des faisceaux, elles trouvent des solutions de bonne qualité même pour les instances de grande taille comportant jusqu’à 250 installations et 1000 clients. Nous améliorons ensuite la qualité de la solution obtenue en résolvent un modèle PLNE restreint qui tire parti des informations recueillies lors de la résolution du dual lagrangien. Les résultats des calculs montrent que les heuristiques donnent rapidement des solutions de bonne qualité, même pour les instances où les solveurs génériques ne trouvent pas de solutions réalisables. Finalement, nous adaptons les heuristiques précédentes pour résoudre le problème industriel. Deux relaxations différentes sont proposées et comparées. Des extensions des concepts précédents sont présentées afin d'assurer une résolution fiable en un temps raisonnable.Location decisions are frequently subject to dynamic aspects such as changes in customer demand. Often, flexibility regarding the geographic location of facilities, as well as their capacities, is the only solution to such issues. Even when demand can be forecast, finding the optimal schedule for the deployment and dynamic adjustment of capacities remains a challenge. In this thesis, we focus on multi-period facility location problems that allow for dynamic capacity adjustment, in particular those with complex cost structures. We investigate such problems from different Operations Research perspectives, presenting and comparing several mixed-integer programming (MIP) models, assessing their use in practice and developing efficient solution algorithms. The thesis is divided into four parts. We first motivate our research by an industrial application, in which a logging company needs to locate camps to host the workers involved in forestry operations. We present a MIP model that allows for the construction of additional camps, the expansion and relocation of existing ones, as well as partial closing and reopening of facilities. The model uses particular capacity constraints that involve integer rounding on the left hand side. Economies of scale are considered on several levels of the cost structure. The usefulness of the model is assessed by two case studies. The second part introduces the Dynamic Facility Location Problem with Generalized Modular Capacities (DFLPG). The model generalizes existing formulations for several dynamic facility location problems and provides stronger linear programming relaxations than the specialized formulations. The model can address facility location problems where the costs for capacity changes are defined for all pairs of capacity levels, as it is the case in the previously introduced industrial problem. It is applied to three special cases: capacity expansion and reduction, temporary facility closing and reopening, and the combination of both. We prove dominance relationships between our formulation and existing models for the special cases. Computational experiments on a large set of randomly generated instances with up to 100 facility locations and 1000 customers show that our model can obtain optimal solutions in shorter computing times than the existing specialized formulations. Given the complexity of such models for large instances, the third part of the thesis proposes efficient Lagrangian heuristics. Based on subgradient and bundle methods, good quality solutions are found even for large-scale instances with up to 250 facility locations and 1000 customers. To improve the final solution quality, a restricted model is solved based on the information collected through the solution of the Lagrangian dual. Computational results show that the Lagrangian based heuristics provide highly reliable results, producing good quality solutions in short computing times even for instances where generic solvers do not find feasible solutions. Finally, we adapt the Lagrangian heuristics to solve the industrial application. Two different relaxations are proposed and compared. Extensions of the previous concepts are presented to ensure a reliable solution of the problem, providing high quality solutions in reasonable computing times

A Heuristic for the Two-Echelon Multi-Period Multi-Product Location–Inventory Problem with Partial Facility Closing and Reopening

In this paper, the two-echelon multi-period multi-product location–inventory problem with partial facility closing and reopening is studied. For each product and period, plants serve warehouses, which serve consolidation hubs, which service customers with independent, normally distributed demands. The schedule of construction, temporary partial closing, and reopening of modular capacities of facilities, the continuous-review inventory control policies at warehouses, the allocation of customer demands to hubs, and the allocation of hubs to warehouses are determined. The service levels for stockout at warehouses during lead time and the violation of warehouse and hub capacities are explicitly considered. The proposed mixed-integer non-linear program minimizes the weighted summation of the number of different facilities and logistical costs, so that the number of different facilities can be controlled. Since the proposed model is np-hard, the multi-start construction and tabu search improvement heuristic (MS-CTSIH) with two improvement strategies and the modified MS-CTSIH incorporating both strategies are proposed. The experiment shows that the two improvement strategies appear non-dominated, and the modified MS-CTSIH yields the best results. The comparison of the modified MS-CTSIH and a commercial solver on a small instance shows the efficiency and effectiveness of the modified MS-CTSIH. The sensitivity analyses of problem parameters are performed on a large instance

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

Relocatable modular capacities in risk aware strategic supply network planning under demand uncertainty

We propose a new model formulation for a three-echelon supply network design problem incorporating the concept of relocatable modular capacities. A robust supply network configuration must be determined based on uncertain demand. Furthermore, by incorporating the conditional value at risk (CVaR), the risk induced by uncertain demand is explicitly considered. The derived supply network configuration should maximize the weighted sum of the expected net present value and the CVaR. The resulting nonlinear model formulation is approximated by a piecewise linearization. Our numerical investigation shows that the derived supply network configuration is robust and stable in the presence of uncertain demand

Best matching processes in distributed systems

The growing complexity and dynamic behavior of modern manufacturing and service industries along with competitive and globalized markets have gradually transformed traditional centralized systems into distributed networks of e- (electronic) Systems. Emerging examples include e-Factories, virtual enterprises, smart farms, automated warehouses, and intelligent transportation systems. These (and similar) distributed systems, regardless of context and application, have a property in common: They all involve certain types of interactions (collaborative, competitive, or both) among their distributed individuals—from clusters of passive sensors and machines to complex networks of computers, intelligent robots, humans, and enterprises. Having this common property, such systems may encounter common challenges in terms of suboptimal interactions and thus poor performance, caused by potential mismatch between individuals. For example, mismatched subassembly parts, vehicles—routes, suppliers—retailers, employees—departments, and products—automated guided vehicles—storage locations may lead to low-quality products, congested roads, unstable supply networks, conflicts, and low service level, respectively. This research refers to this problem as best matching, and investigates it as a major design principle of CCT, the Collaborative Control Theory. The original contribution of this research is to elaborate on the fundamentals of best matching in distributed and collaborative systems, by providing general frameworks for (1) Systematic analysis, inclusive taxonomy, analogical and structural comparison between different matching processes; (2) Specification and formulation of problems, and development of algorithms and protocols for best matching; (3) Validation of the models, algorithms, and protocols through extensive numerical experiments and case studies. The first goal is addressed by investigating matching problems in distributed production, manufacturing, supply, and service systems based on a recently developed reference model, the PRISM Taxonomy of Best Matching. Following the second goal, the identified problems are then formulated as mixed-integer programs. Due to the computational complexity of matching problems, various optimization algorithms are developed for solving different problem instances, including modified genetic algorithms, tabu search, and neighbourhood search heuristics. The dynamic and collaborative/competitive behaviors of matching processes in distributed settings are also formulated and examined through various collaboration, best matching, and task administration protocols. In line with the third goal, four case studies are conducted on various manufacturing, supply, and service systems to highlight the impact of best matching on their operational performance, including service level, utilization, stability, and cost-effectiveness, and validate the computational merits of the developed solution methodologies

A Lagrangian Heuristic for a Variant of Capacitated Facility Location with Single Source Constarints

Cataloged from PDF version of article.Facility location problems (FLP) are extensively studied in the literature in the context of supply chain management. Wide variety of real life situations are analyzed and modeled using techniques developed for FLP. In this thesis we take a comparably new model, Capacitated Facility Location with Single Source constraints (CFLPSS) from the literature and add an additional feature of Minimum Supply (MM) requirements (CFLPSSMM). Then we devise a Lagrangian Heuristic, which is highly efficient for CFLPSS models and for this new variant of CFLPSS. This heuristic, which is modified from the heuristics devised for CFLPSS, is then tested both on data from the literature and on new data set. Results indicate that it can be a resourceful alternative; especially the lower bounds provided by the heuristic are quite effective both for CFLPSS and CFLPSSMM.Ayrım, Yusuf ZiyaM.S

Multi-level facility location problems

We study of a class of discrete facility location problems, called multi-level facility location problems, that has received major attention in the last decade. These problems arise in several applications such as in production-distribution systems, telecommunication networks, freight transportation, and health care, among others. Moreover, they generalize well-known facility location problems which have been shown to lie at the heart of operations research due to their applicability and mathematical structure. We first present a comprehensive review of multi-level facility location problems where we formally define and categorize them based on the types of decisions involved. We also point out some gaps in the literature and present overviews of related applications, models and algorithms. We then concentrate our efforts on the development of solution methods for a general multi-level uncapacitated facility location problem. In particular, based on an alternative combinatorial representation of the problem whose objective function satisfies the submodularity property, we propose a mixed integer linear programming formulation. Using that same representation, we present approximation algorithms with constant performance guarantees for the problem and analyze some special cases where these worst-case bounds are sharper. Finally, we develop an exact algorithm based on Benders decomposition for a slightly more general problem where the activation of links between level of facilities is also considered part of the decision process. Extensive computational experiments are presented to assess the performance of the various models and algorithms studied. We show that the multi-level extension of some fundamental problems in operations research maintain certain structure that allows us to develop more efficient algorithms in practice