logmip1a.gms : LogMIP User's Manual Example 1a - Job Scheduling

**Description**

Three jobs (A,B,C) must be executed sequentially in three steps, but not all jobs require all the stages. The objective is to obtain the sequence of tasks which minimizes the completion time. Once a job has started it cannot be interrupted. The objective is to obtain the sequence of task, which minimizes the completion time. Ref: Raman & Grossmann, Comp. & Chem. Eng., 18, 7, p.563-578, 1994. Aldo Vecchietti, LogMIP User's Manual, 2007 http://www.logmip.ceride.gov.ar/files/pdfs/logmip_manual.pdf Keywords: extended mathematical programming, disjunctive programming, job scheduling

**References**

- Vecchietti, A, LogMIP User's Manual, 2007. http://www.logmip.ceride.gov.ar/files/pdfs/logmip_manual.pdf
- Raman, R, and Grossmann, I E, Modeling and Computational Techniques for Logic Based Integer Programming. Computers and Chemical Engineering 18, 7 (1994), 563-578.

**Small Model of Type :** EMP

**Category :** GAMS Model library

**Main file :** logmip1a.gms

```
$title LogMIP User's Manual Example 1a - Job Scheduling (LOGMIP1A,SEQ=332)
$onText
Three jobs (A,B,C) must be executed sequentially in three steps, but
not all jobs require all the stages. The objective is to obtain the
sequence of tasks which minimizes the completion time. Once a job has
started it cannot be interrupted. The objective is to obtain the
sequence of task, which minimizes the completion time.
Ref: Raman & Grossmann, Comp. & Chem. Eng., 18, 7, p.563-578, 1994.
Aldo Vecchietti, LogMIP User's Manual, 2007
http://www.logmip.ceride.gov.ar/files/pdfs/logmip_manual.pdf
Keywords: extended mathematical programming, disjunctive programming,
job scheduling
$offText
Set
I / 1*6 /
J / A, B, C /;
Positive Variable X(J), T;
Variable Z;
Equation equat1, equat2, equat3, equat4, equat5, equat6, equat7, equat8, equat9, OBJECTIVE;
equat1.. T =g= X('A') + 8;
equat2.. T =g= X('B') + 5;
equat3.. T =g= X('C') + 6;
equat4.. X('A') - X('C') =l= -5;
equat5.. X('C') - X('A') =l= -2;
equat6.. X('B') - X('C') =l= -1;
equat7.. X('C') - X('B') =l= -6;
equat8.. X('A') - X('B') =l= -5;
equat9.. X('B') - X('A') =l= 0;
OBJECTIVE.. Z =e= T;
Model PEQUE1 / all /;
X.up(J) = 20;
$onEcho > "%LM.INFO%"
disjunction bigm 25 * equat4 else equat5
disjunction bigm 26 * equat6 else equat7
disjunction bigm 25 * equat8 else equat9
* optional, if not set LOGMIP will find the modeltype suitable
modeltype mip
$offEcho
option emp = logmip;
solve PEQUE1 using emp minimizing Z;
```