TomSym UIMP - Production Scheduling Problem

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

TomSym implementation of GAMS Example (UIMP,SEQ=11)

A company manufactures nuts, bolts and washers using three different machines that can be operated in normal or overtime production mode. The company needs to plan operations for the next two periods.

Ellison, E F D, and Mitra, P, UIMP - User Interface for Mathematical Programming. ACM Transactions on Mathematical Software 8, 2 (1982).

i: time periods (summer, winter) j: production mode (normal, overtime) k: products (nuts, bolts, washers) l: machines (m1, m2, m3)

% Machine hours (hours per unit), mh(l,k)
mh = [ 4  4  6
       7  6  6
       3  0  0 ];

% Addfactors for mh(i,j)
mhadd = [ 0  -1
          1   0 ];

%  Availability  (hours)
av = [ 100  80
       100  90
        40  30 ];

% Machine hours required
t = zeros(2,2,3,3);
for i=1:2
    for j=1:2
        for k=1:3
            for l=1:3
                t(i,j,k,l) = mh(l,k);
                if mh(l,k) > 0
                    t(i,j,k,l) = t(i,j,k,l)+mhadd(i,j);
                end
            end
        end
    end
end
t(2,2,3,1) = 5;

% Machine hours available;
a = zeros(2,2,3);
a(1,:,:) = av';
a(2,:,:) = av'+10;

% Production cost data
tc = [ 2 3 4
       4 3 2
       1 0 0 ];

% Addfactors for tc
tcadd = [ 0 1
          1 2 ];

% Production cost
c = zeros(2,2,3,3);
for i=1:2
    for j=1:2
        for k=1:3
            for l=1:3
                c(i,j,k,l) = tc(l,k);
                if tc(l,k) > 0
                    c(i,j,k,l) = c(i,j,k,l)+tcadd(i,j);
                end
            end
        end
    end
end

% Selling price
p = [ 10 10  9
      11 11 10 ];

% Demand
d = [ 25 30 30
      30 25 25 ];

% Storage cost
s = ones(3,1);

% Storage capacity
h = [20;20;0];

% Production
toms 3x3 x11 x12 x21 x22

% Products stored
toms 2x3 y

% Products sold
toms 2x3 z

%  Positive Variables: x, y
cbnd = {x11 >= 0, x12 >= 0, x21 >= 0, x22 >= 0, y >= 0};

% m3 can only produce nuts
cbnd = {cbnd{:}, x11(2:3,3) <= 0, x12(2:3,3) <= 0, ...
    x21(2:3,3) <= 0, x22(2:3,3) <= 0};

cost = 0;
for i=1:2
    for k=1:3
        cost = cost + s(k)*y(i,k);
        if i == 1
            cost = cost + sum(squeeze(c(1,1,k,:)).*x11(k,:)'+...
                squeeze(c(1,2,k,:)).*x12(k,:)');
        else
            cost = cost + sum(squeeze(c(2,1,k,:)).*x21(k,:)'+...
                squeeze(c(2,2,k,:)).*x22(k,:)');
        end
    end
end

revenue = sum(sum(p.*z));

profit = revenue - cost;

eq1 = {};
for l=1:3
    eq1 = {eq1{:}, sum(squeeze(t(1,1,:,l)).*x11(:,l)) <= a(1,1,l)};
    eq1 = {eq1{:}, sum(squeeze(t(1,2,:,l)).*x12(:,l)) <= a(1,2,l)};
    eq1 = {eq1{:}, sum(squeeze(t(2,1,:,l)).*x21(:,l)) <= a(2,1,l)};
    eq1 = {eq1{:}, sum(squeeze(t(2,2,:,l)).*x22(:,l)) <= a(2,2,l)};
end

eq2 = {};
for i=1:2
    for k=1:3
        if i>1
            eq2 = {eq2; sum(x21(k,:)+x22(k,:))...
                + y(i-1,k) == z(i,k) + y(i,k)};
        else
            eq2 = {eq2; sum(x11(k,:)+x12(k,:))...
                == z(i,k) + y(i,k)};
        end
    end
end

eq3 = {z >= d; y <= [h'; h']};

options = struct;
options.scale = 'manual';
options.name = 'max_revenue';
solution1 = ezsolve(-revenue,{cbnd, eq1, eq2, eq3},[],options);
options.name = 'max_profit';
solution = ezsolve(-profit,{cbnd, eq1, eq2, eq3},[],options);

disp(' ');
disp('Maximum revenue:');
disp(subs(revenue,solution1));

disp('Maximum profit:');
disp(subs(profit,solution));

Problem type appears to be: lp
Time for symbolic processing: 0.17434 seconds
Starting numeric solver
===== * * * =================================================================== * * *
TOMLAB - TOMLAB Development license  999007. Valid to 2011-12-31
=====================================================================================
Problem: ---  1: max_revenue                    f_k   -2251.190476190476100000
                                              f(x_0)      0.000000000000000000

Solver: CPLEX.  EXIT=0.  INFORM=1.
CPLEX Dual Simplex LP solver
Optimal solution found

FuncEv   20 Iter   20 
Elapsed time: 0.002000 sec. 
Problem type appears to be: lp
Time for symbolic processing: 0.22328 seconds
Starting numeric solver
===== * * * =================================================================== * * *
TOMLAB - TOMLAB Development license  999007. Valid to 2011-12-31
=====================================================================================
Problem: ---  1: max_profit                     f_k   -1571.047619047619000000
                                              f(x_0)      0.000000000000000000

Solver: CPLEX.  EXIT=0.  INFORM=1.
CPLEX Dual Simplex LP solver
Optimal solution found

FuncEv   22 Iter   22 
Elapsed time: 0.003000 sec. 
 
Maximum revenue:
  2.2512e+003
Maximum profit:
  1.5710e+003