jsLPSolver

Simple OOP javaScript library to solve linear programs, and mixed integer linear programs

##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.

Steven manages a wood shop that makes money by charging people money to use its tools. The shop owner tells Steven that he has an extra $40,000 this year to spend on new equipment. After thinking of ways to get the new tools in the shop, Steven realizes that he only has 205 sqft to work with.

The 3 pieces of equipment Steven is most interestd in are the press, the lathe, and the drill. A new drill will cost $8,000, take up 15 sqft, and yield about $100 in profit / week. A new lathe will only cost $4,000, make about $150 / wk in profit, but it takes up 30 sqft. Finally, Steven can get a new drill for $4,500 which takes up 14 sqft; and can expect about $80 / wk from it.

What should Steven buy to maximize profit?

 models.push({
     optimize: "profit",
     opType: "max",
     constraints: {
         space: {max: 205},
         price: {max: 40000}
     },
     variables: {
                 press: {space: 15, price: 8000, profit: 100},
                 lathe: {space: 30, price: 4000, profit: 150},
                 drill: {space: 14, price: 4500, profit: 80}
             },
     ints: {
         press: 1 ,lathe: 1 ,drill: 1
     }
 });