In this paper, we consider the basic makespan minimization problem on identical parallel machines. The aim of this study is to solve to optimality the hard instances of the literature. We present an integer linear program based on an innovative arc-flow model inspired from the duality between the bin packing problem and the parallel-machine scheduling problem. The proposed mathematical model is tested on a large set of hard instances. The results of computational experiments attest the efficiency of the new approach and prove that it outperforms the existing ones. In addition to its efficiency, the proposed method is simple and easy to use.

Personal rapid transit (PRT) is a public and automated transport system in which a fleet of small driverless vehicles operate in order to transport passengers between a set of stations through a network of guided ways. Each customer is carried from one station to another directly with no stop in intermediate stations. This mode of transport can result in a high level of unused capacity due to the empty moves of the vehicles. In this paper, we model the problem of minimizing the energy consumed by the PRT system while assuming predeterministic list of orders; then we solve it using some constructive heuristics. Experiments are run on 1320 randomly generated test problems with various sizes. Our algorithms are shown to give good results over large trip instances.

Fixed point theory is a very important tool in mathematics and applied sciences. Latterly, many application examples have been presented for communication network and computer science fields. The proposed schema can be considered as a theoretical foundation for such a type of applications. In this paper, we introduce the notion of the G _m -contraction to generalize and extend the notion of G-contraction. We investigate the existence and uniqueness of the fixed point for such contractions in M-metric space endowed with a graph. Our results extend and generalize various results in the existing literature, in particular the results of Jachymski. Some examples are included, which illustrate the results proved herein.

Time, quality, and cost are the most critical performance indicators in project management. It has always been considered a tough challenge for project managers to optimize them simultaneously. This study aims at establishing a simulation-based Integer Linear Programming tool that helps project managers, at the preliminary stages, to assess the risks related to the feasibility and profitability of the projects within the framework of a stochastic discrete time-cost-quality tradeoff problem. Computational experiments on a wide range of benchmark instances from the literature were performed, and the results were compared with those of the deterministic version of the problem. The proposed approach is able to assess the impact of the stochastic behavior of the duration and quality of the tasks on the cost, duration and quality of the whole project. Moreover, the simplicity and the reduced time required for the computation of large size networks revealed to be very promising for giving a practical solution for real-life projects.