scholarly journals Polynomial algorithms for some scheduling problems with one nonrenewable resource

2021 ◽  
Author(s):  
Abderrahim SAHLI ◽  
Jacques Carlier ◽  
Aziz MOUKRIM
Keyword(s):  
Flow Shop ◽  
Precedence Constraints ◽  
Polynomial Algorithms ◽  
Interval Order ◽  
Scheduling Problems ◽  
Nonrenewable Resource ◽  
Feasible Schedule ◽  
Time Flow ◽  
Flow Shop Problem ◽  
Maximum Completion Time

This paper deals with the Extended Resource Constrained Project Scheduling Problem (ERCPSP) which is defined by events, nonrenewable resources and precedence constraints between pairs of events. The availability of a resource is depleted and replenished at the occurrence times of a set of events. The decision problem of ERCPSP consists of determining whether an instance has a feasible schedule or not. When there is only one nonrenewable resource, this problem is equivalent to find a feasible schedule that minimizes the number of resource units initially required. It generalizes the maximum cumulative cost problem and the two-machine maximum completion time flow-shop problem. In this paper, we consider this problem with some specific precedence constraints: parallel chains, series-parallel and interval order precedence constraints. For the  first two cases, polynomial algorithms based on a linear decomposition of chains are proposed. For the third case, a polynomial  algorithm is introduced to solve it. The priority between events is defined using the properties of interval orders.

scholarly journals Optimal Results and Numerical Simulations for Flow Shop Scheduling Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Tao Ren ◽  
Yuandong Diao ◽  
Xiaochuan Luo
Keyword(s):  
Local Search ◽  
Completion Time ◽  
Flow Shop ◽  
Asymptotic Optimality ◽  
Flow Shop Scheduling ◽  
Release Dates ◽  
Scheduling Problems ◽  
Improvement Strategy ◽  
Shop Scheduling ◽  
Flow Shop Problem

This paper considers them-machine flow shop problem with two objectives: makespan with release dates and total quadratic completion time, respectively. For Fm|rj|Cmax, we prove the asymptotic optimality for any dense scheduling when the problem scale is large enough. For Fm‖ΣCj2, improvement strategy with local search is presented to promote the performance of the classical SPT heuristic. At the end of the paper, simulations show the effectiveness of the improvement strategy.

scholarly journals Some Results on Shop Scheduling with S-Precedence Constraints among Job Tasks

Algorithms ◽  
2019 ◽  
Vol 12 (12) ◽  
pp. 250 ◽  
Author(s):  
Alessandro Agnetis ◽  
Fabrizio Rossi ◽  
Stefano Smriglio
Keyword(s):  
Job Shop ◽  
Flow Shop ◽  
Exact Algorithms ◽  
Precedence Constraints ◽  
Flow Shop Scheduling ◽  
Scheduling Problems ◽  
Job Tasks ◽  
Shop Scheduling ◽  
Special Cases ◽  
Complexity Status

We address some special cases of job shop and flow shop scheduling problems with s-precedence constraints. Unlike the classical setting, in which precedence constraints among the tasks of a job are finish–start, here the task of a job cannot start before the task preceding it has started. We give polynomial exact algorithms for the following problems: a two-machine job shop with two jobs when recirculation is allowed (i.e., jobs can visit the same machine many times), a two-machine flow shop, and an m-machine flow shop with two jobs. We also point out some special cases whose complexity status is open.

scholarly journals A matheuristic approach for the two-machine total completion time flow shop problem

2011 ◽  
Vol 213 (1) ◽  
pp. 67-78 ◽  
Author(s):  
Federico Della Croce ◽  
Andrea Grosso ◽  
Fabio Salassa
Keyword(s):  
Completion Time ◽  
Flow Shop ◽  
Total Completion Time ◽  
Time Flow ◽  
Flow Shop Problem

Marriage in Honeybee Optimization to Scheduling Problems

2011 ◽  
pp. 158-177
Author(s):  
Pedro Palominos ◽  
Victor Parada ◽  
Gustavo Gatica ◽  
Andrés Véjar
Keyword(s):  
Flow Shop ◽  
Solution Space ◽  
Single Machine Scheduling ◽  
Optimization Techniques ◽  
Average Error ◽  
Scheduling Problems ◽  
Bee Colony ◽  
First Case ◽  
Biological Technique ◽  
Flow Shop Problem

The biological inspired optimization techniques have proven to be powerful tools for solving scheduling problems. Marriage in Honeybee Optimization is a recent biological technique that attempts to emulate the social behavior in a bee colony and although has been applied to only a limited number of problems, it has delivered promising results. By means of this technique in this chapter the authors explore the solution space of scheduling problems by identifying an appropriate representation for each studied case. Two cases were considered: the minimization of earliness-tardiness penalties in a single machine scheduling and the permutation flow shop problem. The performance was evaluated for the first case with 280 instances from the literature. The technique performed quite well for a wide range of instances and achieved an average improvement of 1.4% for all instances. They obtained better solutions than the available upper bound for 141 instances. In the second case, they achieved an average error of 3.5% for the set of 120 test instances.

scholarly journals The Lagrangean Relaxation for the Flow Shop Scheduling Problem with Precedence Constraints, Release Dates and Delivery Times

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Marcelus Fabri ◽  
Helena Ramalhinho ◽  
Mauricio C. de Souza ◽  
Martin G. Ravetti
Keyword(s):  
Flow Shop ◽  
Mathematical Problem ◽  
Lagrangean Relaxation ◽  
Precedence Constraints ◽  
Flow Shop Scheduling ◽  
Computational Time ◽  
Release Dates ◽  
Delivery Times ◽  
Flow Shop Problem ◽  
Feasible Solutions

This work aims to present a methodology to support a company in the automotive business on scheduling the jobs on its final processes. These processes are: (i) checking the final product and (ii) loading the dispatch trucks. These activities are usually found in the outbound area of any manufacturing company. The problem faced is defined as the flow shop problem with precedence constraints, release dates, and delivery times. The major objective is to minimize the latest date a client receives its products. We present a time-indexed integer mathematical model to compute feasible solutions for the presented problem. Moreover, we take advantage of the Lagrangean Relaxation procedure to compute valid lower and upper bounds. The experiments were held based on the company’s premises. As a conclusion, the results showed that the methodology proposed was able to compute feasible solutions for all the instances tested. Also, the Lagrangean Relaxation approach was able to calculate better bounds in a shorter computational time than the Mathematical problem for the more complicated instances.

scholarly journals Hybrid Ant Colony Optimization-Genetics Algorithm to Minimize Makespan Flow Shop Scheduling

2018 ◽  
Vol 7 (2.2) ◽  
pp. 40
Author(s):  
Jonas Franky R. Panggabean
Keyword(s):  
Flow Shop ◽  
Harmony Search ◽  
Flow Shop Scheduling ◽  
Greedy Heuristic ◽  
Scheduling Problems ◽  
Shop Scheduling ◽  
Ga Algorithm ◽  
Dataset Size ◽  
Constructive Heuristics ◽  
Maximum Completion Time

Flow shop scheduling is a scheduling model in which the job to be processed entirely flows in the same product direction / path. In other words, jobs have routing work together. Scheduling problems often arise if there is n jobs to be processed on the machine m, which must be specified which must be done first and how to allocate jobs on the machine to obtain a scheduled production process. In research of Zini, H and ElBernoussi, S. (2016) NEH Heuristic and Stochastic Greedy Heuristic (SG) algorithms. This paper presents modified harmony search (HS) for flow shop scheduling problems with the aim of minimizing the maximum completion time of all jobs (makespan). To validate the proposed algorithm this computational test was performed using a sample dataset of 60 from the Taillard Benchmark. The HS algorithm is compared with two constructive heuristics of the literature namely the NEH heuristic and stochastic greedy heuristic (SG). The experimental results were obtained on average for the dataset size of 20 x 5 to 50 x 10, that the ACO-GA algorithm has a smaller makespan than the other two algorithms, but for large-size datasets the ACO-GA algorithm has a greater makespan of both algorithms with difference of 1.4 units of time.

AN IMPROVED APPROXIMATION ALGORITHM FOR THE TWO-MACHINE FLOW SHOP SCHEDULING PROBLEM WITH AN INTERSTAGE TRANSPORTER

2007 ◽  
Vol 18 (03) ◽  
pp. 565-591 ◽  
Author(s):  
ALAN J. SOPER ◽  
VITALY A. STRUSEVICH
Keyword(s):  
Approximation Algorithm ◽  
Flow Shop ◽  
Optimal Schedule ◽  
Flow Shop Scheduling ◽  
Polynomial Algorithms ◽  
Linear Programs ◽  
Scheduling Problem ◽  
Shop Scheduling ◽  
Integer Linear Programs ◽  
Flow Shop Problem

We study the two-machine flow shop problem with an uncapacitated interstage transporter. The jobs have to be split into batches, and upon completion on the first machine, each batch has to be shipped to the second machine by a transporter. The best known heuristic for the problem is a [Formula: see text]–approximation algorithm that outputs a two-shipment schedule. We design a [Formula: see text]–approximation algorithm that finds schedules with at most three shipments, and this ratio cannot be improved, unless schedules with more shipments are created. This improvement is achieved due to a thorough analysis of schedules with two and three shipments by means of linear programming. We formulate problems of finding an optimal schedule with two or three shipments as integer linear programs and develop strongly polynomial algorithms that find solutions to their continuous relaxations with a small number of fractional variables.

The two-machine total completion time flow shop problem

1996 ◽  
Vol 90 (2) ◽  
pp. 227-237 ◽  
Author(s):  
F. Della Croce ◽  
V. Narayan ◽  
R. Tadei
Keyword(s):  
Completion Time ◽  
Flow Shop ◽  
Total Completion Time ◽  
Time Flow ◽  
Flow Shop Problem
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