Maximizing the robustness for simple assembly lines with fixed cycle time and limited number of workstations

Abstract

International audienc

Solving robust bin-packing problems with a branch-and-price approach

“…Theorem 1 ( Rossi et al (2016) ) . The stability radius ρ for a given feasible solution is calculated as follows:…”

“…As a consequence, the notations ρ 1 and ρ ∞ will be used for 1 and ∞ , respectively. The integer programming formulation of RBP 1 , RBP ∞ and RBP rr is based on the following three theorems, which are demonstrated by Rossi et al (2016) , by Sotskov et al (2006) and by Pirogov (2019) , respectively.…”

“…Only a subset of tasks with uncertain processing times can be identified by decision makers at the line design stage. In order to overcome this difficulty, Rossi, Gurevsky, Battaïa, and Dolgui (2016) , motivated by the work of Sotskov, Dolgui, and Portmann (2006) , proposed a new approach, based on the stability radius optimization. For any given solution, its stability radius is obtained as the maximal magnitude of variations from their nominal values of the uncertain task times for which the solution feasibility (or optimality) is preserved.…”

“…In this paper, we develop a branch-and-price method applied to the problems, which are inverse to those addressed in Rossi et al (2016) . By considering a BP problem, therefore excluding precedence constraints, the problem consists of allocating a given set of items to a minimum number of bins so that the stability radius of the solution is not less than a specified threshold, which determines a desired level of robustness.…”

Multi-objective Approach and Model for Transfer Line Reconfigurations

“…The design objective is often to minimize the total line cost (Battaïa et al, 2012ab), however, other performance criteria can be also considered, for example the robustness of the obtained solution (Gurevsky et al, 2012;Gurevsky et al, 2013a;Gurevsky et al, 2013b;Rossi et al, 2016;Sotskov et al, 2019). In contrast, the reconfiguration problem is characterized by a different objective which is to minimize the cost incurred by the modifications of the line.…”