DESCRIPTION
- Basic Linear Programming examples in z3.
- Reflecting different domains like Engineering, Statistics, Medicine, etc.
- Testing how we can make better solutions to the standard problems compared to other software.
Examples
ExampleLP1: Chocolate Problem
Shannon's Chocolates produces semisweet chocolate chips and milk chocolate chips at its plants in
Wichita, KS and Moore, OK. The Wichita plant produces 3000 pounds of semisweet chips and 2000
pounds of milk chocolate chips each day at a cost of $1000, while the Moore plant produces 1000
pounds of semisweet chips and 6000 pounds of milk chocolate chips each day at a cost of $1500.
Shannon has an order from Food Box Supermarkets for at least 30,000 pounds of semisweet chips and
60,000 pounds of milk chocolate chips. How should Shannon schedule its production so that it can fill
the order at minimum cost? What is the minimum cost?
var solver = require('javascript-lp-solver'),
results,
model = {
"name": "Chocolate Problem",
"optimize": "cost",
"opType": "min",
"constraints": {
"semisweet": {
"min": 30000
},
"milk chocolate": {
"min": 60000
}
},
"variables": {
"Kansas": {
"semisweet": 3000,
"milk chocolate": 2000,
"cost": 1000
},
"Oklahoma": {
"semisweet": 1000,
"milk chocolate": 6000,
"cost": 1500
}
}
};
console.log(solver.Solve(model));
{ feasible: true,
result: 18750,
bounded: true,
Kansas: 7.5,
Oklahoma: 7.5 }
ExampleLP2: Coffee Problem
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?
var solver = require('javascript-lp-solver'),
results,
model = {
"name": "Coffee Problem",
"optimize": "profit",
"opType": "max",
"constraints": {
"costa": {
"max": 200
},
"ethiopian": {
"max": 330
}
},
"variables": {
"yusip": {
"costa": 0.5,
"ethiopian": 0.5,
"profit": 3.5
},
"exotic": {
"costa": 0.25,
"ethiopian": 0.75,
"profit": 4
}
}
};
console.log(solver.Solve(model));
{ feasible: true,
result: 1985,
bounded: true,
yusip: 270,
exotic: 260 }
ExampleLP3: Farmer Problem
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?
var solver = require('javascript-lp-solver'),
results,
model = {
"name": "farmer Problem",
"optimize": "profit",
"opType": "max",
"constraints": {
"storage": {
"max": 15000
},
"expense": {
"max": 4000
},
"plant": {
"max": 75
}
},
"variables": {
"wheat": {
"storage": 120,
"expense": 110,
"plant": 1,
"profit": 143
},
"barley": {
"storage": 210,
"expense": 30,
"plant": 1,
"profit": 60
}
}
};
console.log(solver.Solve(model));
{ feasible: true,
result: 6315.625,
bounded: true,
wheat: 21.875,
barley: 53.125 }
ExampleLP4: SAS Manufacturing Problem
http://support.sas.com/documentation/cdl/en/imlug/66845/HTML/default/viewer.htm#imlug_genstatexpls_sect011.htm
Consider the following product mix example (Hadley, 1962). A shop that has three machines, A, B, and C, turns
out four different products. Each product must be processed on each of the three machines (for example, lathes,
drills, and milling machines). The following table shows the number of hours required by each product on each
machine:
The weekly time available on each of the machines is 2,000, 8,000, and 5,000 hours, respectively. The
products contribute 5.24, 7.30, 8.34, and 4.18 to profit, respectively. What mixture of products can be
manufactured to maximize profit?
var solver = require('javascript-lp-solver'),
results,
model = {
"name": "Manufacturing Problem",
"optimize": "profit",
"opType": "max",
"constraints": {
"timea": {
"max": 2000
},
"timeb": {
"max": 8000
},
"timec": {
"max": 5000
}
},
"variables": {
"m1": {
"timea": 1.5,
"timeb": 1,
"timec": 1.5,
"profit": 5.24
},
"m2": {
"timea": 1,
"timeb": 5,
"timec": 3,
"profit": 7.3
},
"m3": {
"timea": 2.4,
"timeb": 1,
"timec": 3.5,
"profit": 8.34
},
"m4": {
"timea": 1,
"timeb": 3.5,
"timec": 1,
"profit": 4.18
}
},
};
console.log(solver.Solve(model));
{ feasible: true,
result: 12737.05882353,
bounded: true,
m1: 294.11764706,
m4: 58.82352941,
m2: 1500 }