The Variable-Sized Bin Packing Problem with Color Constraints (VSBPP-CC) is a generalization of the classical one-dimensional Bin Packing Problem, where bins of different capacities are available for packing a set of items each characterized by a weight and a color. The objective is to pack all the items while minimizing the total residual capacity, and such that each bin contains at most two different colors. In this paper we consider a special case of VSBPP-CC where each color is assigned to only one item. We first describe the problem, its practical context and survey related works. We then propose several original mathematical formulations for the problem. Preliminary computational results show the efficiency of our formulations, mainly the so-called matching formulation, in solving CSPLIB-based instances.

Railway infrastructure maintenance is of fundamental importance in order to ensure a good service in terms of punctuality, safety and efficiently operation of trains on railway track and also for passenger comfort. Track maintenance covers a large amount of different activities such as inspections, repairs, replacement of failed components or modules and renewals. In this paper, we address the problem of scheduling the preventive railway maintenance activities. The goal is to prevent track failure probability and breakdowns to guarantee a stable and safe service in specified conditions. These activities ensure the increasing of the system reliability and its availability but require considerable resources and large costs, which can be minimized by scheduling the maintenance operations. This problem is proven to be NP-hard, and consequently the development of heuristic and meta-heuristic approaches to solve it is well justified. Thus, we propose an ant colony optimization (ACO) method based on opportunities to deal with this problem. The performance of our proposed ACO algorithm is tested by numerical experiments on a large number of randomly generated instances. A comparison with optimal solutions are presented. The results show the effectiveness of our proposed method.

In our research, we are interested in the three-dimensional multiple-bin-size bin packing problem (MBSBPP). We deal with the real word application of cutting mousse blocks proposed by a Tunisian industrial company. First, we present the general context related to our optimization problem. Second we formulate it as a mathematical problem without considering the guillotine constraint, and then we tested it on small instances taken from the industry. Thereafter, we propose and test a lower bound for large instances from the same industrial company. Finally, some computational results are presented.

This paper considers a two-stage robotic flow shop scheduling problem. The objective is to minimize the makespan. The problem consists of two dedicated machines at the first stage and one common machine at the second stage. Each job is defined by two operations processed on the two-stages in series. Depending on its type, each job is executed on a dedicated machine at the first stage, then it is transported, by a robot or a conveyor, to be executed on the common machine at the second stage. We propose two mixed-integer program (MIP) models to solve this problem which is NP-Hard. These two models can be improved using valid inequalities based on three lower bounds. In addition, due to the NP-hardness of this case, a heuristic is developed to solve approximately large-size problems. The results indicate that the obtained solutions are of high quality and the corresponding CPU time is acceptable.