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.
Fred's Coffee sells two blends of beans: Yusip Blend and Exotic Blend. Yusip Blend is one-half Costa Rican beans and one-half Ethiopian beans. Exotic Blend is one-quarter Costa Rican beans and three-quarters Ethiopian beans. Profit on the Yusip Blend is $3.50 per pound, while profit on the Exotic Blend is $4.00 per pound. Each day Fred receives a shipment of 200 pounds of Costa Rican beans and 330 pounds of Ethiopian beans to use for the two blends.
How many pounds of each blend should be prepared each day to maximize profit? What is the maximum profit?
##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: "profit",
opType: "max",
constraints: {
"Costa Rican" : {max: 200},
"Etheopian": {max: 330}
},
variables: {
"Yusip": {"Costa Rican" : 0.5, "Etheopian": 0.5, profit: 3.5},
"Exotic": {"Costa Rican" : 0.25, "Etheopian": 0.75, profit: 4}
}
};
results = solver.solve(model);
console.log(results);which should yield the following:
{feasible: true, Yusip: 270, Exotic: 260, result: 1985}
##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
}
});