Re: [Help-glpk] Modelling Advice Request - Project Tasks

[Yingjie Lan]

> I solved your enclosed model in 350sec.
> using SCIP (Answer was "5" ) with no special
> settings.

Seems NEOS SCIP can be hooked up to many different solvers (including GLPK), I 
wonder which solver are you using behind SCIP?

> 
> * if position[a] > position[b], then before[a,b] = 0
> * if position[a] < position[b], then before[a,b] = 1
> 

Big-M: M = 15 - 1 given 15 tasks. 

position[b] - position[a] <= M * before[a,b]
position[a] - position[b] <= M * before[b,a]
before[a,b]+before[b,a] == 1


> 
> /* 
> The project consists of 15 tasks. Completion of any of
> these tasks will save time on other tasks in the project as
> follows:
> 
> 
> Task 1 savings: 2 hours on task 2: 2 hours on task 4: 1
> hours on task 9
> Task 2 savings: 2 hours on task 1: 3 hours on task 15
> Task 3 savings: 4 hours on task 1: 1 hours on task 5
> Task 4 savings: 1 hours on task 1: 1 hours on task 3: 2
> hours on task 5: 1 hours on task 10
> 
> Task 5 savings: 1 hours on task 2: 1 hours on task 10: 1
> hours on task 13: 1 hours on task 14: 1 hours on task 15
> Task 6 savings: 1 hours on task 4: 1 hours on task 8: 2
> hours on task 11: 1 hours on task 15
> Task 7 savings: 2 hours on task 2: 3 hours on task 15
> 
> Task 8 savings: 4 hours on task 5: 1 hours on task 11
> Task 9 savings: 1 hours on task 2: 2 hours on task 3: 1
> hours on task 11: 1 hours on task 13
> Task 10 savings: 4 hours on task 11: 1 hours on task 15
> Task 11 savings: 1 hours on task 1: 1 hours on task 3: 1
> hours on task 8: 1 hours on task 10: 1 hours on task 12
> 
> Task 12 savings: 3 hours on task 1: 1 hours on task 4: 1
> hours on task 11
> Task 13 savings: 2 hours on task 3: 3 hours on task 12
> Task 14 savings: 1 hours on task 3: 1 hours on task 6: 1
> hours on task 7: 1 hours on task 8: 1 hours on task 12
> 
> Task 15 savings: 2 hours on task 6: 2 hours on task 12: 1
> hours on task 13
> */

can reduce the before[,] variables somehow,
create variable pair: before[a,b] and before[b,a]
only if task a, b are related in savings.

Cheers,

Yingjie