. Linear programming based algorithms for preemptive and non-preemptive RCPSP. Eur. Journal of Oper. Res., 2007Res., , 182, pp.1012Res., -1022 Linear Programming based algorithms for preemptive and non-preemptive RCPSP Abstract: In this paper, the RCPSP (Resource Constrained Project Scheduling Problem) is solved using a linear programming model. Each activity may or may not be preemptive. Each variable is associated to a subset of independent activities (antichains). The properties of the model are first investigated. In particular, conditions are given that allow a solution of the linear program to be a feasible schedule. From these properties, an algorithm based on neighbourhood search is derived. One neighbour solution is obtained through one Simplex pivoting, if this pivoting preserves feasibility. Methods to get out of local minima are provided. The solving methods are tested on the PSPLIB instances in a preemptive setting and prove efficient. They are used when preemption is forbidden with less success, and this difference is discussed.
In this article, we address a real life optimization problem, the rail track inspection scheduling problem. This problem consists of scheduling railway network inspection tasks. The objective is to minimize the total deadhead distance while performing all inspection tasks. Different 0-1 integer formulations for the problem are presented. A heuristic based on both Benders and Dantzig-Wolfe decompositions is proposed to solve this rich arc routing problem. Its performance is analyzed on a real life dataset provided by the French national railway company. The proposed algorithm is compared to a dynamic programming-based heuristic. Its ability to schedule the inspection tasks of 1 year on a sparse graph with thousand nodes and arcs is assessed.
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