Scheduling in parallel machines with two servers: the restrictive case
Rachid Benmansour, Angelo Sifaleras
In this paper we study the Parallel machine scheduling problem with Two Servers in the Restrictive case (PTSR). Before its processing, the job must be loaded on a common loading server. After a machine completes processing one job, an unloading server is needed to remove the job from the machine. During the loading, respectively the unloading, operation, both the machine and the loading, respectively the unloading, server are occupied. The objective function involves the minimization of the makespan. A Mixed Integer Linear Programming (MILP) model is proposed for the solution of this difficult problem. Due to the NP-hardness of the problem, a Variable Neighborhood Search (VNS) algorithm is proposed. The proposed VNS algorithm is compared against a state-of-the-art solver using a randomly generated data set. The results indicate that, the obtained solutions computed in a short amount of CPU time are of high quality. Specifically, the VNS solution approach outperformed IBM CPLEX Optimizer for instances with 15 and 20 jobs.
Max-Diversity Orthogonal Regrouping of MBA Students using a GRASP/VND Heuristic
Franco Robledo, Pablo Romero, Pablo Sartor, Sebastián Laborde
Students from Master in Business Administration (MBA) programs are usually split into teams. Many schools rotate the teams at the beginning of every term, so that each student works with a different set of peers during every term. Diversity within every team is desirable regarding gender, major, age and other criteria. Achieving diverse teams while avoiding -or minimizing- the repetition of student pairs is a time-consuming complex task for MBA Directors. The Max-Diversity Orthogonal Regrouping (MDOR) problem is here introduced, where the goal is to maximize a global notion of diversity, considering multiple stages (i.e., terms) and intra-diversity within the teams. A hybrid GRASP/VND heuristic combined with Tabu Search is developed for its resolution. Its effectiveness has been tested in real-life groups from the MBA program offered at IEEM Business School, Universidad de Montevideo, Uruguay, with a notorious gain regarding team diversity and repetition level.