Scheduling jobs with normally distributed processing times on parallel machines

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F22%3A00350475" target="_blank" >RIV/68407700:21230/22:00350475 - isvavai.cz</a>

Alternative codes found

RIV/68407700:21730/22:00350475

Result on the web

<a href="https://doi.org/10.1016/j.ejor.2021.05.011" target="_blank" >https://doi.org/10.1016/j.ejor.2021.05.011</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ejor.2021.05.011" target="_blank" >10.1016/j.ejor.2021.05.011</a>

Result language

angličtina

Original language name

Scheduling jobs with normally distributed processing times on parallel machines

Original language description

We consider a stochastic parallel machine scheduling problem, where the jobs have uncertain processing time described by a normal probability distribution. The objective is to maximize the probability that all the jobs are completed before a common due date. The considered problem has many practical applications, but it is notoriously known to be difficult as it involves several non-linearities which complicates its analysis and solution. In this work, we have developed novel lower and upper bounds on the objective function. The upper bound is computed via a solution to a problem where a subset of machines is represented as a single machine having a modified due date. Furthermore, we study lower and upper bounds on the number of jobs that must be scheduled on a machine in an optimal schedule. Subsequently, we use the bounds to construct an efficient branch-and-price algorithm where the pricing problem is found to be related to an inflatable stochastic Knapsack problem. An advantage of the branch-and-price algorithm is a constraint branching mechanism that mitigates symmetries in the solution space. The performance evaluation of the proposed algorithm shows that our algorithm outperforms the state-of-the-art method. In this paper, we also study a special case of the problem assuming two machines. We developed a scalable method whose efficiency arises from the concavity of the relaxed objective function and a fast procedure to recover optimal integer solution from it. These improvements allowed us to solve instances with 500 jobs within a few seconds.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/EF15_003%2F0000466" target="_blank" >EF15_003/0000466: Artificial Intelligence and Reasoning</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2022

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

European Journal of Operational Research

ISSN

0377-2217

e-ISSN

1872-6860

Volume of the periodical

297

Issue of the periodical within the volume

2

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

20

Pages from-to

422-441

UT code for WoS article

000716386200003

EID of the result in the Scopus database

2-s2.0-85108953462