1)flow time - min
Task
Processing time
1
8
2
4
3
7
4
3
5
6
6
5
Algorithm: increasing processing time
2) max lateness or tardiness -> min
Task
Processing
tme
Deadline
1
4
15
2
7
16
3
2
8
4
6
21
5
3
9
Algorithm: increrasing deadline
3) minimisation of the late tasks number
Algorithm:
1.
Put task 1. in sequence S
2.
If the end of sequence S falls after the deadline of its last element, drop the longest element of S;
3.
If there are still tasks which have not been considered, put the next task into S and go to step 2.
Otherwise STOP, solotion: S, then the rest in any order.
Task
PT
Deadline
1
2
3
2
4
5
3
2
6
1
4
2
6
5
3
7
6
1
8
4) minimisation of makespan, flowshop, waiting possible
Task
PT M1
Pt M2
1
4
5
2
4
1
3
10
4
4
6
10
5
2
3
Johnson algorithm:
1.
Find minimim of PT
2.
If this min is on M2, place the task in the end (from the inner side), if o M1, in the beginning (from the
inner side) , eliminate the element
3.
If the table is empty, STOP, otherwise Step 1
5) minimisation of makespan, flowshop, waiting impossible
Task
PT M1
PT M2
1
5
5
2
4
5
3
4
4
4
3
5
A travelling salesman problem algorithm, a(i,j)=max(PTM2(i)-PTM1(j),0)
6) minimisation of makespan, jobshop, waiting possible
Task
PT M1
PT M2
Sequence
1
3
2
1,2
2
2
1
1,2
3
1
2
1,2
4
1
1
1,2
2
5
2
4
2,1
6
4
8
2,1
7
3
9
2,1
8
1
1
9
2
1
10
2
2
11
1
2
Algorithm:
1) For tasks 1,2 i 1 Johnson algorithm: P1
2) Dla task 2,1 i 2 Johnson algorithm: P2
3) On M1 P1P2, on M2 P2P1.
7) minimisation of makespan, flowshop, waiting possible
Zadanie
PT M1
PT M2
PT M3
1
5
5
3
2
4
5
2
3
4
4
5
4
3
5
7
Algorytm:
1) „Create” two machines: L1 (M1 + M2) i L2 (M2 + M3)
2) apply the Johnson algorithm
3) Draw the 3 machines schedule with the obtained order.
8) job shop – simulation
3
Task
Arrival
sequence and PT
1
0
L(10) - D(20) - G(35)
2
0
D(25) - L(20) - G(30) - M(15)
3
20
D(10) - M(10)
4
30
L(15) - G(10) - M(20)
LP.
RULE
TYPE
DESCRIPTION
1
Earliest
release date
Static
Time job is released to the
shop
2
Shortest
processing
time
Static
Processing time of
operation for which job is
waiting
3
Total work
Static
Sum of all processing
times
4
Earliest due
date
Static
Due date of job
5
Least work
remaining
Static
Sum of all processing
times for oparations not
yet performed
6
Fewest
operations
remaining
Static
Number of operations yet
to be performed
7
Work in next
queue
Dynamic
Amount of work awaiting
the next machine in a job's
processing time
Dynamic
Time remaining until due
date minus remaining
processing time
Dynamic
Slack time divided by the
number of operations
remaining
Dynamic
Time remaining until due
date divided by days
required to complete job
8
Slack time
9
Slack/
remaining
operations
10
4
Critical ratio