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Machine scheduling Job 1Job 3 Job 4 Job 5Machine 1 Machine 2 time 0C max Job 2.

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Presentation on theme: "Machine scheduling Job 1Job 3 Job 4 Job 5Machine 1 Machine 2 time 0C max Job 2."— Presentation transcript:

1 Machine scheduling Job 1Job 3 Job 4 Job 5Machine 1 Machine 2 time 0C max Job 2

2 Machine scheduling Job 1Job 3 Job restrictions: Job 4 Job 5Machine 1 Machine 2 time 0C max Objective functions:Machine environments: Job 2

3 Machine scheduling Job 1Job 3 Job restrictions: Job 4 Job 5Machine 1 Machine 2 time 0C max Objective functions:Machine environments: - release dates - deadlines - precedence constraints - preemptions Job 2

4 Machine scheduling Job 1Job 3 Job restrictions: Job 4 Job 5Machine 1 Machine 2 time 0C max Objective functions:Machine environments: - release dates - deadlines - precedence constraints - preemptions - makespan - average completion time - F(C 1,C 2,...,C n ) Job 2

5 Machine scheduling Job 1Job 3 Job restrictions: Job 4 Job 5Machine 1 Machine 2 time 0C max Objective functions:Machine environments: - release dates - deadlines - precedence constraints - preemptions - makespan - average completion time - F(C 1,C 2,...,C n ) -Identical machines: p j for all jobs j - Unrelated machines: p ij for all mach. i and jobs j Job 2

6 On-line optimization M1M1 M2M t = 0

7 On-line optimization M1M1 M2M

8 On-line optimization M1M1 M2M t = 1

9 On-line optimization M1M1 M2M On-line solution

10 On-line optimization M1M1 M2M M1M1 M2M2 On-line solution Optimal solution

11 On-line optimization M1M Single machine, preemption allowed, min. total completion time: Σ j C j Shortest remaining processing time rule gives optimal schedule. t = 0

12 On-line optimization M1M Single machine, preemption allowed, min. total completion time: Σ j C j Shortest remaining processing time rule gives optimal schedule. t = 1

13 On-line optimization M1M Single machine, preemption allowed, min. total completion time: Σ j C j Shortest remaining processing time rule gives optimal schedule. t = 1

14 On-line optimization M1M Single machine, preemption allowed, min. total completion time: Σ j C j Shortest remaining processing time rule gives optimal schedule. t = 3

15 On-line optimization M1M Single machine, preemption allowed, min. total completion time: Σ j C j Shortest remaining processing time rule gives optimal schedule.

16 On-line optimization Competitive analysis An algorithm A is called α-competitive (α>= 1) if for every instance I and feasible solution X An algorithm A is called competitive if there exists a constant α>=1 such that A is α-competitive.

17 On-line optimization Metrical service systems - k servers in metric space M - Requests arrive one by one - A request r is a subset of M - Move one server to r - Goal: minimize tot. travelled distance

18 Metrical service systems Caching problem n main memorycache...., 23, 2, 17, 4 requests 3

19 Metrical service systems Caching problem n main memorycache...., 23, 2, 17, 4 requests Algorithms: -FIFO -LIFO -LFU 12 n

20 Metrical service systems Scheduling -Single machine with k possible states -Switching between state x and state y costs d xy -processing job j in state x costs p xj


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