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- javascript-lp-solver
- javascript-lp-solver/src/solver
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Readme
jsLPSolver
A linear programming solver for the rest of us!
##What Can I do with it? You can solve problems that fit the following fact pattern like this one from this site.
On June 24, 1948, the former Soviet Union blocked all land and water routes through East Germany to Berlin. A gigantic airlift was organized using American and British planes to supply food, clothing and other supplies to more than 2 million people in West Berlin.
The cargo capacity was 30,000 cubic feet for an American plane and 20,000 cubic feet for a British plane. To break the Soviet blockade, the Western Allies had to maximize cargo capacity, but were subject to the following restrictions: No more than 44 planes could be used. The larger American planes required 16 personnel per flight; double that of the requirement for the British planes. The total number of personnel available could not exceed 512. The cost of an American flight was $9000 and the cost of a British flight was $5000. The total weekly costs could note exceed $300,000. Find the number of American and British planes that were used to maximize cargo capacity.
##So How Would I Do This?
Part of the reason I built this library is that I wanted to do as little thinking / setup as possible
to solve the actual problem. Instead of tinkering with arrays to solve this problem, you would create a
model in a JavaScript object, and solver it through the object's solve function; like this:
var solver = new Solver,
results,
model = {
"optimize": "capacity",
"opType": "max",
"constraints": {
"plane": {"max": 44},
"person": {"max": 512},
"cost": {"max": 300000}
},
"variables": {
"brit": {
"capacity": 20000,
"plane": 1,
"person": 8,
"cost": 5000
},
"yank": {
"capacity": 30000,
"plane": 1,
"person": 16,
"cost": 9000
}
},
};
results = solver.Solve(model);
console.log(results);which should yield the following:
{feasible: true, brit: 24, yank: 20, result: 1080000}##What If I Want Only Integers
Say you live in the real world and partial results aren't realistic, or are too messy.
You run a small custom furniture shop and make custom tables and dressers.
Each week you're limited to 300 square feet of wood, 110 hours of labor, and 400 square feet of storage.
A table uses 30sf of wood, 5 hours of labor, requires 30sf of storage and has a gross profit of $1,200. A dresser uses 20sf of wood, 10 hours of work to put together, requires 50 square feet to store and has a gross profit of $1,600.
How much of each do you product to maximize profit, given that partial furniture isn't allowed in this dumb word problem?
var solver = require("./src/solver"),
model = {
"optimize": "profit",
"opType": "max",
"constraints": {
"wood": {"max": 300},
"labor": {"max": 110},
"storage": {"max": 400}
},
"variables": {
"table": {"wood": 30,"labor": 5,"profit": 1200,"table": 1, "storage": 30},
"dresser": {"wood": 20,"labor": 10,"profit": 1600,"dresser": 1, "storage": 50}
},
"ints": {"table": 1,"dresser": 1}
}
console.log(solver.Solve(model));
// {feasible: true, result: 1440-0, table: 8, dresser: 3}##How Fast is it?
Below are the results from my home made suite of variable sized LP(s)
{ Relaxed: { variables: 2, time: 0.004899597 },
Unrestricted: { constraints: 1, variables: 2, time: 0.001273972 },
'Chevalier 1': { constraints: 5, variables: 2, time: 0.000112002 },
Artificial: { constraints: 2, variables: 2, time: 0.000101994 },
'Wiki 1': { variables: 3, time: 0.000358714 },
'Degenerate Min': { constraints: 5, variables: 2, time: 0.000097377 },
'Degenerate Max': { constraints: 5, variables: 2, time: 0.000085829 },
'Coffee Problem': { constraints: 2, variables: 2, time: 0.000296747 },
'Computer Problem': { constraints: 2, variables: 2, time: 0.000066585 },
'Generic Business Problem': { constraints: 2, variables: 2, time: 0.000083135 },
'Generic Business Problem 2': { constraints: 2, variables: 2, time: 0.000040413 },
'Chocolate Problem': { constraints: 2, variables: 2, time: 0.000058503 },
'Wood Shop Problem': { constraints: 2, variables: 2, time: 0.000045416 },
'Integer Wood Problem': { constraints: 3, variables: 2, ints: 2, time: 0.002406691 },
'Berlin Air Lift Problem': { constraints: 3, variables: 2, time: 0.000077362 },
'Integer Berlin Air Lift Problem': { constraints: 3, variables: 2, ints: 2, time: 0.000823271 },
'Infeasible Berlin Air Lift Problem': { constraints: 5, variables: 2, time: 0.000411828 },
'Integer Wood Shop Problem': { constraints: 2, variables: 3, ints: 3, time: 0.001610363 },
'Integer Sports Complex Problem': { constraints: 6, variables: 4, ints: 4, time: 0.001151579 },
'Integer Chocolate Problem': { constraints: 2, variables: 2, ints: 2, time: 0.000109692 },
'Integer Clothing Shop Problem': { constraints: 2, variables: 2, ints: 2, time: 0.000382191 },
'Integer Clothing Shop Problem II': { constraints: 2, variables: 4, ints: 4, time: 0.000113927 },
'Shift Work Problem': { constraints: 6, variables: 6, time: 0.000127012 },
'Monster Problem': { constraints: 576, variables: 552, time: 0.054285454 },
monster_II: { constraints: 842, variables: 924, ints: 112, time: 0.649073406 } }##Incorporating a "Big-Boy" Solver
Part of the reason that I build this library is because I hate setting up tableaus. Unfortunately, I'm not a CS wizard, and this solver probably should not be used for real calculation intensive problems. However, I'm in the process of building out functionality to convert a JSON object into a tableau. Its in a pretty primitive state right now, but if you
var awesome = solver.ReformatLP(model);
fs = require("fs");
fs.writeFile("model.lp", fs);you can convert a JSON model into a string that can be used by LP_Solve.