This paper studies a flow hub location problem (FHLP) stemming from recent trends in network design for e-commerce businesses. Specifically, e-commerce companies are flexible and agile in reoptimizing their logistics networks, including supplier (origin) and customer zone (destination) decisions. Furthermore, a large number of commodities (flows) and a relatively small sales volume for each product incentivize e-commerce retailers to lease warehouse spaces as hubs, yielding a large number of hub location candidates. As such, the proposed FHLP determines the origin and destination of each flow simultaneously with the hub location and flow routing decisions in contrast to the classical hub location problems, where the origins and destinations of all flows are predetermined. To solve this large-scale optimization problem, we propose an optimization algorithm that combines Lagrangian relaxation and Benders decomposition. Novel acceleration techniques, such as a clustering-empowered multicommodity Benders reformulation, learning-empowered elimination tests, and variable reduction techniques, are further developed to improve the performance and convergence of the algorithm. The efficiency of the proposed algorithm is evaluated via extensive computational experiments. The numerical results show that when compared with five other benchmark methods, the proposed algorithm can achieve optimal solutions faster for small-sized test instances and reduce optimality gaps for large-sized ones. For example, the proposed method achieves optimal solutions for a set of 10 test instances, with node sizes ranging from 225 to 450, within 20 minutes on average. In comparison, the automatic Benders decomposition method implemented in the commercial CPLEX solver achieves an average optimality gap of 2% within one hour. History: Accepted by Russell Bent, Area Editor for Network Optimization: Algorithms & Applications. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0367 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0367 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

This study proposes a production hub location (PHL) problem that integrates the classical multiplant lot-sizing and hub location problems. The PHL problem is to determine the location of production facilities, lot-sizing, inventory, hub location, and the distribution of multiple commodities from plants to customers, with an objective to minimize the total production, setup, inventory, hub operating, and transportation costs. The PHL problem applies to manufacturing companies that either have built a hub-and-spoke distribution network or are accessible to such a network through collaborations with other third-party logistics companies. Because the PHL problem is [Formula: see text]-hard, we propose an exact method that integrates dynamic programming and Benders decomposition (DPBD) for solving the problem. The DPBD method is enhanced by exploring several problem properties, such as a multicut reformulation, the generation of Pareto-optimal cuts, a two-stage hub elimination and restoration procedure, and the inclusion of a novel heuristic procedure. We compare the PHL model with several related models theoretically and computationally with newly created benchmark instances. The computational results indicate that the proposed model can reduce the total costs and facilitate better network designs and system decisions, highlighting the value of an integrated approach. We also provide managerial insights into the benefits of integration and show the efficiency of the DPBD method through an extensive number of computational tests. History: Accepted by Andrea Lodi, Area Editor for Design and Analysis of Algorithms—Discrete. Supplemental Material: The online supplement is available at https://doi.org/10.1287/ijoc.2023.0339 .

For capacitated multi-item lot sizing problems, we propose a predictive search method that integrates machine learning/advanced analytics, mathematical programming, and heuristic search into a single framework. Advanced analytics can predict the probability that an event will happen and has been applied to pressing industry issues, such as credit scoring, risk management, and default management. Although little research has applied such technique for lot sizing problems, we observe that advanced analytics can uncover optimal patterns of setup variables given properties associated with the problems, such as problem attributes, and solution values yielded by linear programming relaxation, column generation, and Lagrangian relaxation. We, therefore, build advanced analytics models that yield information about how likely a solution pattern is the same as the optimum, which is insightful information used to partition the solution space into incumbent, superincumbent, and nonincumbent regions where an analytics-driven heuristic search procedure is applied to build restricted subproblems. These subproblems are solved by a combined mathematical programming technique to improve solution quality iteratively. We prove that the predictive search method can converge to the global optimal solution point. The discussion is followed by computational tests, where comparisons with other methods indicate that our approach can obtain better results for the benchmark problems than other state-of-the-art methods. Summary of Contribution: In this study, we propose a predictive search method that integrates machine learning/advanced analytics, mathematical programming, and heuristic search into a single framework for capacitated multi-item lot sizing problems. The advanced analytics models are used to yield information about how likely a solution pattern is the same as the optimum, which is insightful information used to divide the solution space into incumbent, superincumbent, and nonincumbent regions where an analytics-driven heuristic search procedure is applied to build restricted subproblems. These subproblems are solved by a combined mathematical programming technique to improve solution quality iteratively. We prove that the predictive search method can converge to the global optimal solution point. Through computational tests based on benchmark problems, we observe that the proposed approach can obtain better results than other state-of-the-art methods.

The coupled lot-sizing and cutting-stock problem has been a challenging and significant problem for industry, and has therefore received sustained research attention. The quality of the solution is a major determinant of cost performance in related production and inventory management systems, and therefore there is intense pressure to develop effective practical solutions. In the literature, a number of heuristics have been proposed for solving the problem. However, the heuristics are limited in obtaining high solution qualities. This paper proposes a new progressive selection algorithm that hybridizes heuristic search and extended reformulation into a single framework. The method has the advantage of generating a strong bound using the extended reformulation, which can provide good guidelines on partitioning and sampling in the heuristic search procedure to ensure an efficient solution process. We also analyze per-item and per-period Dantzig–Wolfe decompositions of the problem and present theoretical comparisons. The master problem of the per period Dantzig–Wolfe decomposition is often degenerate, which results in a tailing-off effect for column generation. We apply a hybridization of Lagrangian relaxation and stabilization techniques to improve the convergence. The discussion is followed by extensive computational tests, where we also perform detailed statistical analyses on various parameters. Comparisons with other methods indicate that our approach is computationally tractable and is able to obtain improved results. The online supplement is available at https://doi.org/10.1287/ijoc.2017.0746 .

Despite the significant attention they have drawn, big-bucket lot-sizing problems remain notoriously difficult to solve. Previous literature contained results (computational and theoretical) indicating that what makes these problems difficult are the embedded single-machine, single-level, multiperiod submodels. We therefore consider the simplest such submodel, a multi-item, two-period capacitated relaxation. We propose a methodology that can approximate the convex hulls of all such possible relaxations by generating violated valid inequalities. To generate such inequalities, we separate two-period projections of fractional linear programming solutions from the convex hulls of the two-period closure we study. The convex hull representation of the twoperiod closure is generated dynamically using column generation. Contrary to regular column generation, our method is an outer approximation and can therefore be used efficiently in a regular branch-and-bound procedure. We present computational results that illustrate how these two-period models could be effective in solving complicated problems.

In this paper, we consider the capacitated multi-item lot sizing problem with setup times. The problem is to schedule J different items over a horizon of T periods with the objective to minimize the sum of setup cost and inventory holding cost. To achieve feasible high-quality solutions, we propose a new solution approach which hybrids Nested Partitions and Mathematical Programming (HNP-MP). Nested Partitions is a partitioning and sampling based heuristic method with a global perspective on the problem. In the proposed new method the Mathematical Programming method is implemented to calculate the promising index and to provide a good guidance on partitioning in the Nested Partitions framework. A time-oriented decomposition heuristic method, Relax-and-Fix, is also implemented to obtain good promising regions and speed up the computational process. Computational results based on benchmark test problems show that the approach is computationally tractable and is able to obtain good results. The approach outperforms other state-of-the-art approaches found in the literature.