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Averbakh, I., & Pereira, J. (2018). Lateness Minimization in Pairwise Connectivity Restoration Problems. INFORMS J. Comput., 30(3), 522–538.
Abstract: A network is given whose edges need to be constructed (or restored after a disaster). The lengths of edges represent the required construction/restoration times given available resources, and one unit of length of the network can be constructed per unit of time. All points of the network are accessible for construction at any time. For each pair of vertices, a due date is given. It is required to find a construction schedule that minimizes the maximum lateness of all pairs of vertices, where the lateness of a pair is the difference between the time when the pair becomes connected by an already constructed path and the pair's due date. We introduce the problem and analyze its structural properties, present a mixed-integer linear programming formulation, develop a number of lower bounds that are integrated in a branch-and-bound algorithm, and discuss results of computational experiments both for instances based on randomly generated networks and for instances based on 2010 Chilean earthquake data.
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Freire, A. S., Moreno, E., & Yushimito, W. F. (2016). A branch-and-bound algorithm for the maximum capture problem with random utilities. Eur. J. Oper. Res., 252(1), 204–212.
Abstract: The MAXIMUM CAPTURE PROBLEM WITH RANDOM UTILITIES seeks to locate new facilities in a competitive market such that the captured demand of users is maximized, assuming that each individual chooses among all available facilities according to the well-know a random utility model namely the multinomial logit. The problem is complex mostly due to its integer nonlinear objective function. Currently, the most efficient approaches deal with this complexity by either using a nonlinear programing solver or reformulating the problem into a Mixed-Integer Linear Programing (MILP) model. In this paper, we show how the best MILP reformulation available in the literature can be strengthened by using tighter coefficients in some inequalities. We also introduce a new branch-and-bound algorithm based on a greedy approach for solving a relaxation of the original problem. Extensive computational experiments are presented, bench marking the proposed approach with other linear and non-linear relaxations of the problem. The computational experiments show that our proposed algorithm is competitive with all other methods as there is no method which outperforms the others in all instances. We also show a large-scale real instance of the problem, which comes from an application in park-and-ride facility location, where our proposed branch-and-bound algorithm was the most effective method for solving this type of problem. (C) 2015 Elsevier B.V. All rights reserved.
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Letelier, O. R., Clautiaux, F., & Sadykov, R. (2022). Bin Packing Problem with Time Lags. INFORMS J. Comput., Early Access.
Abstract: We introduce and motivate several variants of the bin packing problem where bins are assigned to time slots, and minimum and maximum lags are required between some pairs of items. We suggest two integer programming formulations for the general problem: a compact one and a stronger formulation with an exponential number of variables and constraints. We propose a branch-cut-and-price approach that exploits the latter formulation. For this purpose, we devise separation algorithms based on a mathematical characterization of feasible assignments for two important special cases of the problem: when the number of possible bins available at each period is infinite and when this number is limited to one and time lags are nonnegative. Computational experiments are reported for instances inspired from a real-case application of chemical treatment planning in vineyards, as well as for literature instances for special cases of the problem. The experimental results show the efficiency of our branch-cutand-price approach, as it outperforms the compact formulation on newly proposed instances and is able to obtain improved lower and upper bounds for literature instances. Summary of Contribution: The paper considers a new variant of the bin packing problem, which is one of the most important problems in operations research. A motivation for introducing this variant is given, as well as a real-life application. We present a novel and original exact branch-cut-and-price algorithm for the problem. We implement this algorithm, and we present the results of extensive computational experiments. The results show a very good performance of our algorithm. We give several research directions that can be followed by subsequent researchers to extend our contribution to more complex and generic problems.
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Pereira, J., & Ritt, M. (2023). Exact and heuristic methods for a workload allocation problem with chain precedence constraints. Eur. J. Oper. Res., 309(1), 387–398.
Abstract: Industrial manufacturing is often organized in assembly lines where a product is assembled on a se-quence of stations, each of which executes some of the assembly tasks. A line is balanced if the maximum total execution time of any station is minimal. Commonly, the task execution order is constrained by precedences, and task execution times are independent of the station performing the task. Here, we con -sider a recent variation, called the “(Calzedonia) Workload Allocation Problem” (WAP), where the prece-dences form a chain, and the execution time of a task depends on the worker executing it. This problem was recently proposed by Battarra et al. (2020) and it is a special case of the Assembly Line Worker As-signment and Balancing Problem Miralles et al. (2007) where precedence relations are arbitrary. In this paper we consider the computational complexity of the problem and prove its NP-hardness. To solve the problem, we provide different lower bounds and exact and heuristic procedures. The performance of the proposed methods is tested on previously proposed instances and on new, larger instances with the same characteristics. The results show that the proposed methods can solve instances with up to about 40 0 0 tasks and 29 workers, doubling the size of the instances that previously could be solved to optimality.
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