A note on longest processing time algorithms for the two uniform parallel machine makespan minimization problem

2015 ◽  
Vol 19 (2) ◽  
pp. 207-211 ◽  
Author(s):  
Ivar Massabò ◽  
Giuseppe Paletta ◽  
Alex J. Ruiz-Torres
Keyword(s):  
Minimization Problem ◽  
Processing Time ◽  
Parallel Machine ◽  
Makespan Minimization

Unrelated Parallel-Machine Scheduling with Controllable Processing Times and Impact of Deteriorating Maintenance Activities under Consideration

2016 ◽  
Vol 33 (01) ◽  
pp. 1650001 ◽  
Author(s):  
Chun-Lai Liu ◽  
Jian-Jun Wang
Keyword(s):  
Processing Time ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Controllable Processing Times ◽  
Maintenance Activity ◽  
Processing Times ◽  
Unrelated Parallel Machine Scheduling ◽  
Deteriorating Maintenance ◽  
Maintenance Activities

In this paper, we study the problem of unrelated parallel machine scheduling with controllable processing times and deteriorating maintenance activity. The jobs are nonresumable. The processing time of each job is a linear function of the amount of a continuously divisible resource allocated to the job. During the planning horizon, there is at most one maintenance activity scheduled on each machine. Additionally, if the starting time of maintenance activity is delayed, the length of the maintenance activity required to perform will increase. Considering the total completion times of all jobs, the impact of maintenance activity in the form of the variation in machine load and the amounts of compression, we need to determine the job sequence on each machine, the location of maintenance activities and processing time compression of each job simultaneously. Accordingly, a polynomial time solution to the problem is provided.

scholarly journals Decomposition approaches for parallel machine scheduling of step-deteriorating jobs to minimize total tardiness and energy consumption

2021 ◽  
Author(s):  
Xiao Wu ◽  
Peng Guo ◽  
Yi Wang ◽  
Yakun Wang
Keyword(s):  
Energy Consumption ◽  
Tabu Search ◽  
Processing Time ◽  
Deteriorating Jobs ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Total Tardiness ◽  
Master Problem ◽  
Starting Time ◽  
Extra Energy

AbstractIn this paper, an identical parallel machine scheduling problem with step-deteriorating jobs is considered to minimize the weighted sum of tardiness cost and extra energy consumption cost. In particular, the actual processing time of a job is assumed to be a step function of its starting time and its deteriorating threshold. When the starting time of a job is later than its deteriorating threshold, the job faces two choices: (1) maintaining its status in holding equipment and being processed with a base processing time and (2) consuming an extra penalty time to finish its processing. The two work patterns need different amounts of energy consumption. To implement energy-efficient scheduling, the selection of the pre-processing patterns must be carefully considered. In this paper, a mixed integer linear programming (MILP) model is proposed to minimize the total tardiness cost and the extra energy cost. Decomposition approaches based on logic-based Benders decomposition (LBBD) are developed by reformulating the studied problem into a master problem and some independent sub-problems. The master problem is relaxed by only making assignment decisions. The sub-problems are to find optimal schedules in the job-to-machine assignments given by the master problem. Moreover, MILP and heuristic based on Tabu search are used to solve the sub-problems. To evaluate the performance of our methods, three groups of test instances were generated inspired by both real-world applications and benchmarks from the literature. The computational results demonstrate that the proposed decomposition approaches can compute competitive schedules for medium- and large-size problems in terms of solution quality. In particular, the LBBD with Tabu search performs the best among the suggested four methods.

scholarly journals USULAN PENJADWALAN PRODUKSI PRODUK ST 37777 PT EBAKO NUSANTARA PADA DEPARTEMEN SMOOTHMILLING UNTUK MEMINIMASI MAKESPAN

2018 ◽  
Vol 13 (1) ◽  
pp. 61
Author(s):  
Mellysa Asmawar
Keyword(s):  
Production Process ◽  
Processing Time ◽  
Manufacturing Industry ◽  
Job Scheduling ◽  
Makespan Minimization ◽  
Central Java ◽  
Short Processing Time ◽  
Jobshop Scheduling ◽  
Machine Work

AbstrakProses produksi ST 37777 di PT Ebako Nusantara menggunakan jadwal yang didasarkan oleh proses-proses yang dilakukan dengan menggunakan data historis yang telah ada dari proses produksi yang telah dilakukan. PT Ebako Nusantara merupakan industri manufaktur yang bergerak di bidang furnitur yang berlokasi di Terboyo, Semarang, Jawa Tengah. Dalam proses produksi ST 37777, terdapat 11 mesin dan 16 job dimana setiap job memiliki urutan mesin yang berbeda. Penjadwalan yang ada untuk produk tipe ST 37777 dengan tipe jobshop belum menerapkan suatu ketetapan dalam penentuan waktu dan urutan pengerjaan mesin yang efektif sehingga masih banyak job yang selesai terlambat. Untuk itu diperlukan suatu penjadwalan mesin yang efektif sehingga dapat memenuhi waktu produksi pesanan sesuai dengan yang telah disepakati. Penjadwalan jobshop diperlukan untuk memaksimumkan efisiensi dan utilitas sumber daya di lantai produksi. Penentuan jadwal mesin ini bertujuan meminimasi makespan dengan menggunakan Software WINQSB modul job schedulling. Metode yang digunakan adalah metode Short Processing Time. Hasil penjadwalan menggunakan Software WINQSB diperoleh makespan menjadi 15 jam dengan hasil penjadwalan tersebut tidak ada job yang terlambat dan semua job dikerjakan berurutan. AbstractThe production process of ST 37777 in PT Ebako Nusantara uses a schedule based on the processes performed using existing historical data from the production process that has been done. PT Ebako Nusantara is a manufacturing industry engaged in furnitur located in Terboyo, Semarang, Central Java. In the production process ST 37777, there are 11 machines and 16 jobs where each job has a different sequence of machines. The existing scheduling for ST 37777 type product with jobshop type has not been applied a determination in the timing and sequence of effective machine work so that many jobs are finished too late. For that required an effective engine scheduling so that it can meet the production time of orders in accordance with the agreed. Jobshop scheduling is needed to maximize efficiency and resource utilities on the production floor. Determination of this machine schedule aims to minimize the makespan using WINQSB Software job scheduling module. The method used is the method of Short Processing Time. The scheduling result using WINQSB software obtained makespan to 15 hours with scheduling result no job is late and all job done in sequence. Keywords: Jobshop Scheduling; Short Processing Time; Makespan Minimization

scholarly journals Parallel-Batch Scheduling with Two Models of Deterioration to Minimize the Makespan

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Cuixia Miao
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Processing Time ◽  
Parallel Machine ◽  
Batch Scheduling ◽  
Approximation Schemes ◽  
Time Approximation ◽  
Identical Parallel Machine ◽  
Parallel Machine Problem ◽  
Machine Problem

We consider the bounded parallel-batch scheduling with two models of deterioration, in which the processing time of the first model ispj=aj+αtand of the second model ispj=a+αjt. The objective is to minimize the makespan. We presentO(n log n)time algorithms for the single-machine problems, respectively. And we propose fully polynomial time approximation schemes to solve the identical-parallel-machine problem and uniform-parallel-machine problem, respectively.

Minimizing the Makespan and Flowtime in Two-Machine Stochastic Open Shops

1996 ◽  
Vol 10 (4) ◽  
pp. 557-567
Author(s):  
Tian-Shyug Lee ◽  
Georgia-Ann Klutke
Keyword(s):  
Processing Time ◽  
Parallel Machine ◽  
Open Shop ◽  
Two Machines

In this paper, we present some new results on the makespan and flowtime in a two-parallel machine open shop. A set of n jobs is to be processed on two machines, the order of processing being immaterial. For the case where the machines are identical, and the jobs are nonoverlapping ordered, we show that the sequences that stochastically minimize the makespan are longest processing time first-shortest processing time first (LPT-SPT). Within this class of sequences, we show that the SPT sequence stochastically minimizes the flowtime.

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