Mbot at 13:34, 8 November 2011

2011-11-08T13:34:06Z

← Older revision		Revision as of 08:34, 8 November 2011
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	<pre>		<pre>
	Problem type appears to be: lp		Problem type appears to be: lp
	Time for symbolic processing: 0.~~008625~~ seconds		Time for symbolic processing: 0.0080349 seconds
	Starting numeric solver		Starting numeric solver
	===== * * * =================================================================== * * *		===== * * * =================================================================== * * *
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	FuncEv 6 Iter 6		FuncEv 6 Iter 6
	~~CPU time: 0.015600 sec.~~ Elapsed time: 0.002000 sec.		Elapsed time: 0.002000 sec.
	Problem type appears to be: lp		Problem type appears to be: lp
	Time for symbolic processing: 0.~~031684~~ seconds		Time for symbolic processing: 0.029608 seconds
	Starting numeric solver		Starting numeric solver
	===== * * * =================================================================== * * *		===== * * * =================================================================== * * *

Mbot at 21:25, 2 November 2011

2011-11-02T21:25:22Z

← Older revision		Revision as of 16:25, 2 November 2011
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	Unitary processing times		Unitary processing times

			<pre>
	+--------+-------------------+		+--------+-------------------+
	\| \| Lines \|		\| \| Lines \|
Line 17:		Line 18:
	\| P4 \|0.9\|1.1\|1.0\|0.9\|1.0\|		\| P4 \|0.9\|1.1\|1.0\|0.9\|1.0\|
	+--------+---+---+---+---+---+		+--------+---+---+---+---+---+
			</pre>

	Possible transfers of personnel		Possible transfers of personnel

			<pre>
	+------+-------------------+------------------+		+------+-------------------+------------------+
	\| \| Destination \| \|		\| \| Destination \| \|
Line 31:		Line 34:
	\| L5 \|yes\|yes\|yes\| no\| -\| 300 \|		\| L5 \|yes\|yes\|yes\| no\| -\| 300 \|
	+------+---+---+---+---+---+------------------+		+------+---+---+---+---+---+------------------+
			</pre>

	==Variables==		==Variables==

			<pre>
	profit Profit per product		profit Profit per product
	capacity Hours at each site		capacity Hours at each site
Line 39:		Line 44:
	transfermat Transfer matrix		transfermat Transfer matrix
	maxtransfer Maximum hours to transfer		maxtransfer Maximum hours to transfer
			</pre>

	==Reference==		==Reference==

Mbot: Created page with "{{Part Of Manual|title=the TomSym Manual|link=TomSym Manual}} ==Problem description== The company Line Production decides to plan the production of four of its produ..."

2011-11-02T21:02:29Z

Created page with "{{Part Of Manual|title=the TomSym Manual|link=TomSym Manual}} ==Problem description== The company Line Production decides to plan the production of four of its produ..."

New page

{{Part Of Manual|title=the TomSym Manual|link=[[TomSym|TomSym Manual]]}}

==Problem description==

The company Line Production decides to plan the production of four of its products (P1, P2, P3, P4) on its five production lines (L1 to L5). The company gains net profits of $ 7 for the products P1 and P4, $ 8 for P2, and $ 9 for P3. The maximum times during which the five production lines may operate are different during the planning period. The maximum capacities for L1 to L5 are 4500 hours, 5000 hours, 4500 hours, 1500 hours, and 2500 hours respectively. The table below lists the processing time in hours necessary for the production of one unit of every product on every production line. Which quantities of P1 to P4 should be produced to maximize the total profit? If subsequently a transfer of personnel (and hence of working hours) is authorized between production lines during the planning period as shown in the second table below, which is the maximum profit? How many hours are transfered and under what conditions?

Unitary processing times

+--------+-------------------+
| | Lines |
+--------+---+---+---+---+---+
|Products| L1| L2| L3| L4| L5|
+--------+---+---+---+---+---+
| P1 |1.3|0.9|2.0|0.3|0.9|
| P2 |1.8|1.7|1.4|0.6|1.1|
| P3 |1.3|1.2|1.3|1.0|1.4|
| P4 |0.9|1.1|1.0|0.9|1.0|
+--------+---+---+---+---+---+

Possible transfers of personnel

+------+-------------------+------------------+
| | Destination | |
+------+---+---+---+---+---+Maximum number of |
|Origin| L1| L2| L3| L4| L5|transferable hours|
+------+---+---+---+---+---+------------------+
| L1 | -|yes|yes|yes| no| 400 |
| L2 | no| -|yes| no|yes| 800 |
| L3 |yes|yes| -|yes| no| 500 |
| L4 | no| no| no| -|yes| 200 |
| L5 |yes|yes|yes| no| -| 300 |
+------+---+---+---+---+---+------------------+

==Variables==

profit Profit per product
capacity Hours at each site
timemat Time to produce products
transfermat Transfer matrix
maxtransfer Maximum hours to transfer

==Reference==

Applications of optimization... Gueret, Prins, Seveaux

<source lang="matlab">
% Marcus Edvall, Tomlab Optimization Inc, E-mail: tomlab@tomopt.com
% Copyright (c) 2005-2009 by Tomlab Optimization Inc., $Release: 7.2.0$
% Written Oct 7, 2005. Last modified Apr 8, 2009.
</source>

==Problem setup==

<source lang="matlab">
profit = [7 8 9 7]';
capacity = [4500 5000 4500 1500 2500]';

timemat = [ 1.3 0.9 2.0 0.3 0.9;...
1.8 1.7 1.4 0.6 1.1;...
1.3 1.2 1.3 1.0 1.4;...
0.9 1.1 1.0 0.9 1.0];

transfermat = [0 1 1 1 0;...
0 0 1 0 1;...
1 1 0 1 0;...
0 0 0 0 1;...
1 1 1 0 0];

maxtransfer = [400 800 200 500 300]';

p = length(profit); %products

produce = tom('produce',p,1);

% No variables are binary
bnds = {produce >= 0};

% Capacity constraint
con = {timemat'*produce <= capacity};

% Objective
objective = -profit'*produce;
constraints = {bnds, con};
options = struct;
options.solver = 'cplex';
options.name = 'Prod Planning with Personnel Assign';
sol1 = ezsolve(objective,constraints,[],options);

l = length(capacity);
hours = tom('hours',l,1);
transfer = tom('transfer',l,l);

% No variables are binary
bnds = {produce >= 0, hours >= 0, transfer >= 0};

% Line constraint
con = {timemat'*produce <= hours};

% Line transfer constraint
con2 = {hours == capacity + sum(transfermat.*transfer,1)' - ...
sum(transfermat.*transfer,2)};

% Line max transfer constraint
con3 = {sum(transfermat.*transfer,2) <= maxtransfer};

% Objective
objective = -profit'*produce;
constraints = {bnds, con, con2, con3};
options = struct;
options.solver = 'cplex';
options.name = 'Prod Planning with Personnel Assign';
sol2 = ezsolve(objective,constraints,[],options);

PriLev = 1;
if PriLev > 0
disp('without transfer')
x1 = sol1.produce;
for i = 1:length(x1)
if x1(i) > 0
disp([' produce ' num2str(x1(i)) ' units of P' num2str(i) ])
end
end
disp('with transfer')
x2 = sol2.produce;
for i = 1:length(x2),
if x2(i) > 0,
disp([' produce ' num2str(x2(i)) ' units of P' num2str(i) ])
end
end
transfer = sol2.transfer;
for i = 1:size(transfer,1),
idx = find(transfer(i,:));
for j = 1: length(idx),
disp([' transfer ' num2str(transfer(i,idx(j))) ...
' hours from ' num2str(i) ' to ' num2str(idx(j)) ])
end
end
hours = sol2.hours;
for j = 1:length(hours),
disp([' work ' num2str(hours(j)) ' hours at L' num2str(j) ])
end
end

% MODIFICATION LOG
%
% 051205 med Created.
% 060117 per Added documentation.
% 060126 per Moved disp to end
% 060131 per Really moved disp to end
% 090325 med Converted to tomSym
</source>

<pre>
Problem type appears to be: lp
Time for symbolic processing: 0.008625 seconds
Starting numeric solver
===== * * * =================================================================== * * *
TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31
=====================================================================================
Problem: --- 1: Prod Planning with Personnel Assign f_k -18882.978723404256000000
f(x_0) 0.000000000000000000

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

FuncEv 6 Iter 6
CPU time: 0.015600 sec. Elapsed time: 0.002000 sec.
Problem type appears to be: lp
Time for symbolic processing: 0.031684 seconds
Starting numeric solver
===== * * * =================================================================== * * *
TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31
=====================================================================================
Problem: --- 1: Prod Planning with Personnel Assign f_k -23431.085043988263000000
sum(|constr|) 0.000000000000682121
f(x_k) + sum(|constr|) -23431.085043988263000000
f(x_0) 0.000000000000000000

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

FuncEv 10 Iter 10
Elapsed time: 0.002000 sec.
without transfer
produce 1542.5532 units of P1
produce 1010.6383 units of P2
with transfer
produce 702.346 units of P1
produce 942.8152 units of P2
produce 554.2522 units of P3
produce 854.8387 units of P4
transfer 400 hours from 1 to 4
transfer 800 hours from 2 to 5
transfer 200 hours from 3 to 4
work 4100 hours at L1
work 4200 hours at L2
work 4300 hours at L3
work 2100 hours at L4
work 3300 hours at L5

</pre>

TomSym Production Planning with Personnel Assignment - Revision history

Mbot at 13:34, 8 November 2011

Mbot at 21:25, 2 November 2011

Mbot: Created page with "{{Part Of Manual|title=the TomSym Manual|link=TomSym Manual}} ==Problem description== The company Line Production decides to plan the production of four of its produ..."