TomSym LogMIP User's Manual Example 1a - Job Scheduling

This page is part of the TomSym Manual. See TomSym Manual.

TomSym implementation of GAMS Example (LOGMIP1A,SEQ=332)

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.

toms 6x1 I
toms 3x1 J X

% Binary variables
toms 6x1 integer Y
cbnd1 = {0 <= Y <= 1};

toms T

% X and T are positive
cbnd2 = {0 <= X; 0 <= T};

eq1 = {T >= X(1) + 8
    T >= X(2) + 5
    T >= X(3) + 6};

eq2 = {X(1)-X(3) <= -5
    X(3)-X(1) <= -2
    X(2)-X(3) <= -1
    X(3)-X(2) <= -6
    X(1)-X(2) <= -5
    X(2)-X(1) <= 0};

objective = T;

cbnd3 = {X <= 20};

% Disjunction
eq3 = {(X(1)-X(3))*Y(1) <= -5*Y(1)
    (X(3)-X(1))*Y(2) <= -2*Y(2)
    (X(2)-X(3))*Y(3) <= -1*Y(3)
    (X(3)-X(2))*Y(4) <= -6*Y(4)
    (X(1)-X(2))*Y(5) <= -5*Y(5)
    (X(2)-X(1))*Y(6) <= 0*Y(6)};

eq4 = {Y(1) + Y(2) == 1
    Y(3) + Y(4) == 1
    Y(5) + Y(6) == 1};

options = struct;
options.solver = 'minlpBB';
constr = {cbnd1;cbnd2;cbnd3; eq1;eq3;eq4};
solution = ezsolve(objective,constr,[],options);

Problem type appears to be: minlp
Time for symbolic processing: 0.40735 seconds
Starting numeric solver
===== * * * =================================================================== * * *
TOMLAB - TOMLAB Development license  999007. Valid to 2011-12-31
=====================================================================================
Problem: ---  1:                                f_k      11.000000000000000000
                                              f(x_0)      0.000000000000000000

Solver: minlpBB.  EXIT=0.  INFORM=0.
Dense Branch and Bound MINLP
Optimal integer solution found

FuncEv    5 GradEv    5 HessEv    4 ConstrEv    3 ConJacEv    3 ConHessEv    3 Iter    1 
CPU time: 0.015600 sec. Elapsed time: 0.024000 sec.