This paper studies the multi-resource-constrained unrelated parallel machine scheduling problem under various operational constraints with the objective of minimising maximum completion time among ...

Constraint programming approach for multi-resource-constrained unrelated parallel machine scheduling problem with sequence-dependent setup times

In this paper we study the periodic maintenance problem: given a set of m machines and a horizon of T periods, find indefinitely repeating itself maintenance schedule such that at most one machine can be serviced at each period. In addition, all the machines must be serviced at least once for any cycle. In each period the machine i generates a servicing cost bi or an operating cost which depends on the last period in which i was serviced. The operating cost of each machine i in a period equals ai times the number of periods since the last servicing of that machine. The main objective is to find a cyclic maintenance schedule of a periodicity T that minimizes total cost. To solve this problem we propose a new Mixed Integer programming formulation and a new heuristic method based on general Variable neighborhood search called Nested general variable neighborhood search. The performance of this heuristic is shown through an extensive experimentation on a diverse set of problem instances.

Nested general variable neighborhood search for the periodic maintenance problem

This paper addresses the problem of scheduling independent jobs on identical parallel machines with a single server to minimise the makespan. We propose mixed integer programming (MIP) formulations...

Mathematical formulations for the parallel machine scheduling problem with a single server

Parallel machine scheduling (PMS) is a common setting in many manufacturing facilities, in which each job is allowed to be processed on one of the machines of the same type. It involves scheduling $n$ jobs on $m$ machines to minimize certain objective functions. For preemptive scheduling, most problems are not only NP-hard but also difficult in practice. Moreover, many unexpected events, such as machine failure and requirement change, are inevitable in the practical production process, meaning that rescheduling is required for static scheduling methods. Deep reinforcement learning (DRL), which combines deep learning and reinforcement learning, has achieved promising results in several domains and has shown the potential to solve large Markov decision process (MDP) optimization tasks. Moreover, PMS problems can be formulated as an MDP problem, inspiring us to devise a DRL method to deal with PMS problems in a dynamic environment. We develop a novel DRL-based PMS method, called DPMS, in which the developed model considers the characteristics of PMS to design states and the reward. The actions involve dispatching rules, so DPMS can be considered a meta-dispatching-rule system that can efficiently select a sequence of dispatching rules based on the current environment or unexpected events. The experimental results demonstrate that DPMS can yield promising results in a dynamic environment by learning from the interactions between the agent and the environment. Furthermore, we conduct extensive experiments to analyze DPMS in the context of developing a DRL to deal with dynamic PMS problems.

Dynamic Parallel Machine Scheduling With Deep Q-Network

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. 

https://link.springer.com/content/pdf/10.1007/s11590-022-01925-2.pdf

General variable neighborhood search for the parallel machine scheduling problem with two common servers

This paper considers the problem of scheduling a set of independent jobs on an arbitrary number of identical parallel machines with setup consideration and a makespan objective. The setup operations are performed by one available server. We propose two mixed integer programming (MIP) formulations to solve optimally this problem. The performance of each model is compared with another MIP proposed in the literature. It turns out that our formulation based on time-indexed variables outperforms the other models.

MIP formulations for identical parallel machine scheduling problem with single server

In this paper, we study the m identical parallel machines scheduling problem with a single server to minimize the schedule length (makespan). Each job requires a prior set-up which must be performed by a single server. For this strongly $\mathcal {NP}$-hard problem, a variable neighborhood search is proposed. We conduct a comparative analysis with existing algorithms using previously solved instances from the literature. The results indicate that the algorithm presented in this paper is effective and efficient regarding the quality of the solution: the obtained objective function values are very close to lower bounds.

Variable Neighborhood Search for Identical Parallel Machine Scheduling Problem with a Single Server

This paper considers the problem of scheduling a set of n independent jobs on m identical parallel machines with setup times constraints. Immediately before processing, each job must be loaded on a common server to perform the setup operation. During the loading operation, both the machine and the server are occupied. Two greedy heuristics are developed for (m ≥ 2) in order to minimize respectively the server waiting time and the machine idle time. These heuristics generalize those proposed in the literature for the case of two machines. The computational results show the efficiency of the proposed heuristics.

Greedy heuristics for identical parallel machine scheduling problem with single server to minimize the makespan

Proposition of a Quantified Method for the Individual Competence Assessment in Manufacturing Industry

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