TomSym Cane Sugar Production - Revision history

Mbot at 13:32, 8 November 2011

2011-11-08T13:32:58Z

← Older revision		Revision as of 09:32, 8 November 2011
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	<pre>		<pre>
	Problem type appears to be: mip		Problem type appears to be: mip
	Time for symbolic processing: 0.~~01895~~ seconds		Time for symbolic processing: 0.018829 seconds
	Starting numeric solver		Starting numeric solver
	===== * * * =================================================================== * * *		===== * * * =================================================================== * * *
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	FuncEv 19		FuncEv 19
	Elapsed time: 0.003000 sec.		CPU time: 0.015600 sec. Elapsed time: 0.003000 sec.
	To minimize loss (1602) use this schema		To minimize loss (1602) use this schema
	at 8.00:		at 8.00:

Mbot at 21:24, 2 November 2011

2011-11-02T21:24:07Z

← Older revision		Revision as of 17:24, 2 November 2011
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	Table: Properties of the lots of cane sugar		Table: Properties of the lots of cane sugar

			<pre>
	Lot 1 2 3 4 5 6 7 8 9 10 11		Lot 1 2 3 4 5 6 7 8 9 10 11
	Loss (kg/h) 43 26 37 28 13 54 62 49 19 28 30		Loss (kg/h) 43 26 37 28 13 54 62 49 19 28 30
	Life span (h) 8 8 2 8 4 8 8 8 8 8 8		Life span (h) 8 8 2 8 4 8 8 8 8 8 8
			</pre>

	Every lot may be processed by any of the three, fully equivalent production lines of the sugar house. The processing of a lot takes two hours. It must be finished at the latest at the end of the life span of the wagon load. The manager of the sugar house wishes to determine a production schedule for the currently available lots that minimizes the total loss of sugar.		Every lot may be processed by any of the three, fully equivalent production lines of the sugar house. The processing of a lot takes two hours. It must be finished at the latest at the end of the life span of the wagon load. The manager of the sugar house wishes to determine a production schedule for the currently available lots that minimizes the total loss of sugar.
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	==Variables==		==Variables==

			<pre>
	proclines the number of processing lines		proclines the number of processing lines
	proctime time in hours to process a wagon		proctime time in hours to process a wagon
	loss loss of sugar in kg per hour		loss loss of sugar in kg per hour
	lifespan how long the sugar in a wagon will last		lifespan how long the sugar in a wagon will last
			</pre>

	==Reference==		==Reference==

Mbot: Created page with "{{Part Of Manual|title=the TomSym Manual|link=TomSym Manual}} ==Problem description== The harvest of cane sugar in Australia is highly mechanized. The sugar cane is ..."

2011-11-02T21:01:04Z

Created page with "{{Part Of Manual|title=the TomSym Manual|link=TomSym Manual}} ==Problem description== The harvest of cane sugar in Australia is highly mechanized. The sugar cane is ..."

New page

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

==Problem description==

The harvest of cane sugar in Australia is highly mechanized. The sugar cane is immediately transported to a sugar house in wagons that run on a network of small rail tracks. The sugar content of a wagon load depends on the field it has been harvested from and on the maturity of the sugar cane. Once harvested, the sugar content decreases rapidly through fermentation and the wagon load will entirely lose its value after a certain time. At this moment, eleven wagons all loaded with the same quantity have arrived at the sugar house. They have been examined to find out the hourly loss and the remaining life span (in hours) of every wagon, these data are summarized in the following table.

Table: Properties of the lots of cane sugar

Lot 1 2 3 4 5 6 7 8 9 10 11
Loss (kg/h) 43 26 37 28 13 54 62 49 19 28 30
Life span (h) 8 8 2 8 4 8 8 8 8 8 8

Every lot may be processed by any of the three, fully equivalent production lines of the sugar house. The processing of a lot takes two hours. It must be finished at the latest at the end of the life span of the wagon load. The manager of the sugar house wishes to determine a production schedule for the currently available lots that minimizes the total loss of sugar.

==Variables==

proclines the number of processing lines
proctime time in hours to process a wagon
loss loss of sugar in kg per hour
lifespan how long the sugar in a wagon will last

==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">
proclines = 3;
proctime = 2;
loss = [43;26;37;28;13;54;62;49;19;28;30];
lifespan = [8;8;2;8;4;8;8;8;8;8;8];

n1 = length(loss);
n2 = ceil(n1/proclines);

proc = tom('proc',n1,n2,'int');

% All slots are integers
intcons = {0 <= proc <= 1};

% Production constraint, all lots processed
prodcons1 = {sum(proc,2) == 1};

% Production constraint, No more than proclines concurrently running
prodcons2 = {sum(proc,1) <= proclines};

% Maximum slot number for a lot
slotcons = {sum(proc.*repmat(1:n2,n1,1),2) <= lifespan/proctime};

% Objective
objective = sum(sum(repmat(1:n2,n1,1).*repmat(loss,1,n2).*proctime.*proc));

constraints = {intcons, prodcons1, prodcons2, slotcons};
options = struct;
options.solver = 'cplex';
options.name = 'Cane Sugar Production';
sol = ezsolve(objective,constraints,[],options);

f_k = subs(objective,sol);

PriLev = 1;
if PriLev > 0
lots = length(lifespan);
timeslots = ceil(lots/proclines(1)); % even a fraction means work
temp = sol.proc;

disp(['To minimize loss (' num2str(f_k) ') use this schema'])

for time = 1:timeslots,
disp(['at ' num2str((time-1)*proctime(1)+8) '.00:'])
idx = find(temp(:,time));
disp([' process the lots ' num2str(idx') ])
end
disp(['at ' num2str((time)*proctime(1)+8) '.00:'])
disp( ' harvesting completed')
end

% MODIFICATION LOG
%
% 051007 med Created
% 051208 med Lifespan factor wrong
% 060109 per lifespan(9) changed to 8
% 060109 per Added documentation.
% 060125 per Moved disp to end
% 090308 med Converted to tomSym
</source>

<pre>
Problem type appears to be: mip
Time for symbolic processing: 0.01895 seconds
Starting numeric solver
===== * * * =================================================================== * * *
TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31
=====================================================================================
Problem: --- 1: Cane Sugar Production f_k 1602.000000000000000000
f(x_0) 0.000000000000000000

Solver: CPLEX. EXIT=0. INFORM=101.
CPLEX Branch-and-Cut MIP solver
Optimal integer solution found

FuncEv 19
Elapsed time: 0.003000 sec.
To minimize loss (1602) use this schema
at 8.00:
process the lots 3 6 7
at 10.00:
process the lots 1 5 8
at 12.00:
process the lots 4 10 11
at 14.00:
process the lots 2 9
at 16.00:
harvesting completed

</pre>