Industry 5.0 emphasizes human-centered production environments, promoting collaboration between humans and smart machines. This shift introduces new scheduling challenges due to the stochastic nature of human behavior—challenges that traditional deterministic models cannot adequately address. This paper studies a stochastic dual-resource allocation problem in a flow shop setting, where worker behavior impacts production outcomes through random breaks. We model worker states using Markov chains and apply a Sample Average Approximation method to minimize the expected makespan for a given number of jobs. Numerical experiments demonstrate the effectiveness of our approach. We also study the impact of the behavior of the workers on the overall production performance.

In this paper, we study the Constrained-Routing and Spectrum Assignment (C-RSA) problem. Consider an undirected, loopless, and connected graph${G}$. Let$\mathbb{S}$be an optical spectrum of available contiguous frequency slots, and${K}$be a set of traffic demands. The C-RSA is to assign for each demand${k\,\in \,K}$a path in${G}$between its origin-destination nodes, and an interval of contiguous frequency slots in$\mathbb{S}$while respecting some technological constraints, and optimizing some linear objective function. First, we propose an extended integer linear programming formulation for the C-RSA. A column generation algorithm is developed to solve its linear relaxation. We also describe several valid inequalities for the polytope associated with this formulation, and address the related separation problems. Using these results, we derive a Branch-and-Cut-and-Price algorithm, along with computational results are presented using large-scale instances.

Network design problems have been largely studied in the last decades due to the ubiquity of IT communication in our daily life. We address in this paper the k-edge-connected hop-constrained network design problem (kHNDP) which is known to be NP-hard. In this paper, we present a hybrid parallel approach for solving the kHNDP based on a Lagrangian relaxation algorithm, a greedy algorithm, and a genetic algorithm. Computational results obtained with our algorithms are compared with those from CPLEX.

In this article, we study the k-edge-connected L-hop-constrained network design problem. Given a weighted graph , a set D of pairs of nodes, two integers and , the problem consists in finding a minimum weight subgraph of G containing at least k edge-disjoint paths of length at most L between every pair . We consider the problem in the case where L = 2, 3 and . We first discuss integer programming formulations introduced in the literature. Then, we introduce new integer programming formulations for the problem that are based on the transformation of the initial undirected graph into directed layered graphs. We present a theoretical comparison of these formulations in terms of LP-bound. Finally, these formulations are tested using CPLEX and compared in a computational study for k = 3, 4, 5. © 2015 Wiley Periodicals, Inc. NETWORKS, 67(2), 148–169 2016

Given a weighted undirected graph G with a set of pairs of terminals (si, ti), , and an integer , the two node-disjoint hop-constrained survivable network design problem is to find a minimum weight subgraph of G such that between every si and ti there exist at least two node-disjoint paths of length at most L. This problem has applications in the design of survivable telecommunication networks with QoS-constraints. We discuss this problem from a polyhedral point of view. We present several classes of valid inequalities along with necessary and/or sufficient conditions for these inequalities to be facet defining. We also discuss separation routines for these classes of inequalities, and propose a Branch-and-Cut algorithm for the problem when L = 3, as well as some computational results. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 67(4), 316–337 2016

Abstract In this article, we consider the k‐edge connected subgraph problem from a polyhedral point of view. We introduce further classes of valid inequalities for the associated polytope and describe sufficient conditions for these inequalities to be facet defining. We also devise separation routines for these inequalities and discuss some reduction operations that can be used in a preprocessing phase for the separation. Using these results, we develop a Branch‐and‐Cut algorithm and present some computational results. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010