Constraint Satisfaction – Product Mix – Wood Paneling Example

Don’t get me started…. It’s amazing that Operations Research / Optimization / Contraint Satisfaction have come so far ( the Holy Grail of Computing ), yet so very few IT personnel even know about it….

% minizinc product mix model from http://www.solver.com/stepbystep.htm
% 2012 Jason Filley (jason@snakelegs.org)



%%%% parameters
int: glue = 5800;		% glue (quarts)
int: pressing = 730;	% pressing time (hours)
int: pine = 29200;		% pine chips (pounds)
int: oak = 32500;		% oak chips (pounds)


constraint assert(glue >= 0,"Invalid datafile: " ++
	"glue must be non-negative.");
constraint assert(pressing >= 0,"Invalid datafile: " ++
	"pressing must be non-negative.");
constraint assert(pine >= 0,"Invalid datafile: " ++
	"pine must be non-negative.");
constraint assert(oak >= 0,"Invalid datafile: " ++
	"oak must be non-negative.");

	
%%%% decision variables
var 0..100: tahoe;
var 0..100: pacific;
var 0..100: savannah;
var 0..100: aspen;


%%%% constraints

% glue
constraint  50*tahoe + 50*pacific + 100*savannah + 50*aspen <= glue;

% pressing time
constraint  5*tahoe + 15*pacific + 10*savannah + 5*aspen <= pressing;

% pine chips
constraint  500*tahoe + 400*pacific + 250*savannah + 200*aspen <= pine;

% oak chips
constraint  500*tahoe + 750*pacific + 250*savannah + 500*aspen <= oak;



%%%% objective function -- maximize profit
var 0..100000: profit;
profit = 450*tahoe + 1150*pacific + 800*savannah + 400*aspen;
solve maximize profit;


output ["Tahoe: ", show(tahoe), "\n",
		"Pacific: ", show(pacific), "\n",
		"Savannah: ", show(savannah), "\n",
		"Aspen: ", show(aspen), "\n",
		"Profit: ", show(profit), "\n"];

% minizinc.exe product_mix_wood_paneling.mzn
% Tahoe: 23
% Pacific: 15
% Savannah: 39
% Aspen: 0
% Profit: 58800
% ----------