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We study a class of chance constrained programs (CCPs) where the underlying distribution is modeled by a Gaussian mixture model. As the original work, Hu et al. (IISE Trans 54(12):1117–1130, 2022. https://doi.org/10.1080/24725854.2021.2001608) developed a spatial branch-and-bound (B &B) algorithm to solve the problems. In this paper, we propose an enhanced procedure to speed up the computation of B &B algorithm. We design an enhanced pruning strategy that explores high-potential domains and an augmented branching strategy that prevents redundant computations. We integrate the new strategies into original framework to develop an enhanced B &B algorithm, and illustrate how the enhanced algorithm improves on the original approach. Furthermore, we extend the enhanced B &B framework to handle the CCPs with multiple chance constraints, which is not considered in the previous work. We evaluate the performance of our new algorithm through extensive numerical experiments and apply it to solve a real-world portfolio selection problem. [ABSTRACT FROM AUTHOR]

The Multi-commodity Capacitated Multi-facility Weber Problem is concerned with locating I capacitated facilities in the plane in order to satisfy the demands of J customers for K commodities such that the total transportation cost is minimized. This is a multi-commodity extension of the well-known Capacitated Multi-facility Weber Problem and difficult to solve. In this work, we propose two branch-and-bound algorithms for exactly solving this nonconvex optimization problem. One of them considers partitioning of the allocation space while the other one considers partitioning of the location space. We have implemented two lower bounding schemes for both algorithms and tested several branching strategies. The results of an extensive computational study are also included. [ABSTRACT FROM AUTHOR]

This paper presents an integrated mathematical programming formulation of the manufacturing cell formation problem introduced by Nagi et al. The formulation incorporates critical production planning issues that include long-term projected production requirements, resource capacity constraints, functionally identical machines and alternative process plans in the cell formation problem, with a common objective of minimizing the resulting inter-cell material handling effort. This problem is NP-hard. The previous work presented a heuristic solution based on decomposing the integrated problem into capacitated route selection and cell formation sub-problems that are solved iteratively until convergence. Like all fast heuristics, the method may suffer from poor solution quality, and non-heuristic methods cannot address problems of typical industrial dimensions because they would require exorbitant amounts of computing time. To overcome both these deficiencies, this paper (i) presents a 0–1 Mixed Integer Linear Programming (MILP) formulation alternative to the integrated cell formation problem, (ii) based on this formulation, develops a branch-and-bound procedure that provides improved solutions compared to those obtained by the heuristic of Nagi et al. (1990), and (iii) makes possible derivation of lower bounds to assess the quality gap when optimal solutions are unavailable or require excessive computing time. This work is important because it allows for better solutions to realistic industrial-sized problem instances. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of grouping machines in order to design cellular manufacturing cells, with an objective to minimize inter-cell flow. This problem is related to one of the major aims of group technology (GT): to decompose the manufacturing system into manufacturing cells that are as independent as possible. This problem is NP-hard. Thus, nonheuristic methods cannot address problems of typical industrial dimensions because they would require exorbitant amounts of computing time, while fast heuristic methods may suffer from poor solution quality. We present a branch-and-bound statespace search algorithm that attempts to overcome both these deficiencies. One of the major strengths of this algorithm is its efficient branching and search strategy. In addition, the algorithm employs the fast Inter-Cell Traffic Minimization Method to provide good upper bounds, and computes lower bounds based on a relaxation of merging. [ABSTRACT FROM AUTHOR]