General variable neighborhood search for the parallel machine scheduling problem with two common servers
Abdelhak Elidrissi, Rachid Benmansour, Angelo Sifaleras
Abstract
Abstract We address in this paper the parallel machine scheduling problem with a shared loading server and a shared unloading server. Each job has to be loaded by the loading server before being processed on one of the available machines and unloaded immediately by the unloading server after its processing. The objective function involves the minimization of the overall completion time, known as the makespan. This important problem raises in flexible manufacturing systems, automated material handling, healthcare, and many other industrial fields, and has been little studied up to now. To date, research on it has focused on the case of two machines. The regular case of this problem is considered. A mixed integer programming formulation based on completion time variables is suggested to solve small-sized instances of the problem. Due to its $$\mathcal{NP}\mathcal{}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>NP</mml:mi> <mml:mrow/> </mml:mrow> </mml:math> -hardness, we propose two greedy heuristics based on the minimization of the loading, respectively unloading, server waiting time, and an efficient General Variable Neighborhood Search (GVNS) algorithm. In the computational experiments, the proposed methods are compared using 120 new and publicly available instances. It turns out that, the proposed GVNS with an initial solution-finding mechanism based on the unloading server waiting time minimization significantly outperforms the other approaches.