Scheduling jobs with normally distributed processing times on parallel machines

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/68407700:21730/22:00350475

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Scheduling jobs with normally distributed processing times on parallel machines

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Scheduling jobs with normally distributed processing times on parallel machines

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

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

Projekt

<a href="/cs/project/EF15_003%2F0000466" target="_blank" >EF15_003/0000466: Umělá inteligence a uvažování</a><br>

Návaznosti

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

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

European Journal of Operational Research

ISSN

0377-2217

e-ISSN

1872-6860

Svazek periodika

297

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

20

Strana od-do

422-441

Kód UT WoS článku

000716386200003

EID výsledku v databázi Scopus

2-s2.0-85108953462