logmip1a.gms : LogMIP User's Manual Example 1a - Job Scheduling
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, http://www.logmip.ceride.gov.ar/
References:
- Vecchietti, A, LogMIP User's Manual, 2007. http://www.logmip.ceride.gov.ar/eng/documentation/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 Types: LOGMIP mip
<![CDATA[
$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, http://www.logmip.ceride.gov.ar/
$offtext
SET I /1*6/,
J /A,B,C/;
BINARY VARIABLES Y(i);
POSITIVE VARIABLES X(J),T;
VARIABLE Z;
EQUATIONS equat1, equat2, equat3, equat4, equat5, equat6,
equat7, equat8, equat9, DUMMY, 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;
DUMMY.. SUM(I, Y(I)) =G= 0;
OBJECTIVE.. Z =E= T;
MODEL PEQUE1 /ALL/;
X.UP(J)=20.;
$ONECHO > "%lm.info%"
DISJUNCTION D1,D2,D3;
D1 IS IF Y('1') THEN equat4;
ELSIF Y('2') THEN equat5; ENDIF;
D2 IS IF Y('3') THEN equat6;
ELSIF Y('4') THEN equat7; ENDIF;
D3 IS IF Y('5') THEN equat8;
ELSIF Y('6') THEN equat9; ENDIF;
$OFFECHO
OPTION MIP=LMBIGM;
SOLVE PEQUE1 USING MIP MINIMIZING Z;
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