Optimal scheduling of unit-time tasks on two uniform processors under tree-like precedence constraints

1989 ◽  
Vol 33 (6) ◽  
pp. 423-437 ◽  
Author(s):  
W. Kubiak
Keyword(s):  
Precedence Constraints ◽  
Optimal Scheduling ◽  
Uniform Processors

Minimizing expected makespans on uniform processor systems

1987 ◽  
Vol 19 (01) ◽  
pp. 177-201 ◽  
Author(s):  
E. G. Coffman ◽  
L. Flatto ◽  
M. R. Garey ◽  
R. R. Weber
Keyword(s):  
Optimal Scheduling ◽  
Problem Size ◽  
Bellman Equations ◽  
Similar Threshold ◽  
General Bound ◽  
Execution Times ◽  
Identical Rate ◽  
Expected Makespan ◽  
Uniform Processors

We study the problem of scheduling n given jobs on m uniform processors to minimize expected makespan (maximum finishing time). Job execution times are not known in advance, but are known to be exponentially distributed, with identical rate parameters depending solely on the executing processor. For m = 2 and 3, we show that there exist optimal scheduling rules of a certain threshold type, and we show how the required thresholds can be easily determined. We conjecture that similar threshold rules suffice for m > 3 but are unable to prove this. However, for m > 3 we do obtain a general bound on problem size that permits Bellman equations to be used to construct an optimal scheduling rule for any given set of m rate parameters, with the memory required to represent that scheduling rule being independent of the number of remaining jobs.

Minimizing expected makespans on uniform processor systems

1987 ◽  
Vol 19 (1) ◽  
pp. 177-201 ◽  
Author(s):  
E. G. Coffman ◽  
L. Flatto ◽  
M. R. Garey ◽  
R. R. Weber
Keyword(s):  
Optimal Scheduling ◽  
Problem Size ◽  
Bellman Equations ◽  
Similar Threshold ◽  
General Bound ◽  
Execution Times ◽  
Identical Rate ◽  
Expected Makespan ◽  
Uniform Processors

We study the problem of scheduling n given jobs on m uniform processors to minimize expected makespan (maximum finishing time). Job execution times are not known in advance, but are known to be exponentially distributed, with identical rate parameters depending solely on the executing processor. For m = 2 and 3, we show that there exist optimal scheduling rules of a certain threshold type, and we show how the required thresholds can be easily determined. We conjecture that similar threshold rules suffice for m > 3 but are unable to prove this. However, for m > 3 we do obtain a general bound on problem size that permits Bellman equations to be used to construct an optimal scheduling rule for any given set of m rate parameters, with the memory required to represent that scheduling rule being independent of the number of remaining jobs.

Aplikasi Metode Hungarian Dalam Optimalisasi Waktu Penugasan Karyawan dan Keuntungan Produksi Home Industry

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Empya Charlie ◽  
Siti Rusdiana ◽  
Rini Oktavia
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Solution ◽  
Optimal Scheduling ◽  
Total Work ◽  
Work Time ◽  
Hungarian Method ◽  
Total Work Time

Penelitian ini bertujuan untuk mengoptimalkan penjadwalan karyawan di CV. Karya Indah Bordir dalam melakukan tugas-tugas tertentu menggunakan metode Hungaria, serta menganalisis sensitivitas solusi optimal jika ada pengurangan waktu karyawan untuk menyelesaikan tugas-tugas. Metode Hongaria diterapkan pada proses bordir yang melibatkan 11 karyawan dan 10 tugas. Hasil penjadwalan yang optimal meminimalkan waktu produksi bordir perusahaan. Hasil penjadwalan optimal yang ditemukan adalah: karyawan 1 mengerjakan tas Mambo, karyawan 2 mengerjakan tas Elli, karyawan 3 mengerjakan tas Lonjong, karyawan 4 mengerjakan tas Tampang bunga, karyawan 6 mengerjakan tas Ransel, karyawan 7 mengerjakan tas Tima, karyawan 8 mengerjakan tas Keong, karyawan 9 mengerjakan tas Alexa, karyawan 10 mengerjakan tas Luna, dan karyawan 11 mengerjakan tas Mikha, dengan total waktu kerja adalah 13,7 jam. Setelah metode Hongaria diterapkan, CV. Karya Indah Bordir mendapat peningkatan pendapatan sebanyak 9,09%. Analisis sensitivitas dilakukan dengan mengurangi waktu karyawan dalam menyulam tas. Hasil analisis sensitivitas adalah beberapa batasan untuk variabel basis dan non basis untuk mempertahankan solusi optimal.   This research has a purpose to optimize the scheduling of employees in CV. Karya Indah Bordir in doing certain tasks using Hungarian method, as well as analyzing the sensitivity of the optimal solution if there is a reduction on the employees time to finish the tasks. The Hungarian method was applied on the embroidery process involving 11 employees and 10 tasks. The optimal scheduling result minimize the time of the embroidery production of the company. The optimal scheduling result found is: employee 1 does the Mambo bag, employee 2 does the Elli bag, employee 3 does the Lonjong bag, employee 4 does the Tampang bunga bag, employee 6 does the Ransel, employee 7 does the Tima bag, employee 8 does the Keong bag, employee 9 does the Alexa bag, employees 10 does the Luna bag, and employee 11 does the Mikha bag, with the total work time is 13,7 hours. After the Hungarian method was applied, CV. Karya Indah Bordir got the increasing revenue as much as 9,09 %. The sensitivity analysis was conducted by reducing the time of the employees take in embroidery the bags. The results of the sensitivity analysis are some boundaries for basis and non basis variables to maintain the optimal solution. 

Optimal Scheduling and Control of Ingot Handling in a Steelmaking Environment

1983 ◽  
Author(s):  
Stanley F. Bullington ◽  
Yong-Zai Lu ◽  
Colin L. Moodie ◽  
Theodore J. Williams
Keyword(s):  
Optimal Scheduling ◽  
And Control
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