A Mathematical Programming Language, aka A Mathematical Programming Language, is an actively used programming language created in 1985. A Mathematical Programming Language (AMPL) is an algebraic modeling language to describe and solve high-complexity problems for large-scale mathematical computing (i.e., large-scale optimization and scheduling-type problems). It was developed by Robert Fourer, David Gay, and Brian Kernighan at Bell Laboratories. AMPL supports dozens of solvers, both open source and commercial software, including CBC, CPLEX, FortMP, Gurobi, MINOS, IPOPT, SNOPT, KNITRO, and LGO. Read more on Wikipedia...

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### Example code from the web:

```set PROD;  # products

param rate {PROD} > 0;     # tons produced per hour
param avail >= 0;          # hours available in week

param profit {PROD};       # profit per ton
param market {PROD} >= 0;  # limit on tons sold in week

var Make {p in PROD} >= 0, <= market[p]; # tons produced

maximize Total_Profit: sum {p in PROD} profit[p] * Make[p];

# Objective: total profits from all products

subject to Time: sum {p in PROD} (1/rate[p]) * Make[p] <= avail;

# Constraint: total of hours used by all
# products may not exceed hours available```

### Example code from Linguist:

```# A toy knapsack problem from the LocalSolver docs written in AMPL.

set I;
param Value{I};
param Weight{I};
param KnapsackBound;
var Take{I} binary;

maximize TotalValue: sum{i in I} Take[i] * Value[i];
s.t. WeightLimit: sum{i in I} Take[i] * Weight[i] <= KnapsackBound;

data;

param:
I: Weight Value :=
0    10     1
1    60    10
2    30    15
3    40    40
4    30    60
5    20    90
6    20   100
7     2    15;

param KnapsackBound := 102;
```

### Example code from Wikipedia:

```set Plants;
set Markets;

# Capacity of plant p in cases
param Capacity{p in Plants};

# Demand at market m in cases
param Demand{m in Markets};

# Distance in thousands of miles
param Distance{Plants, Markets};

# Freight in dollars per case per thousand miles
param Freight;

# Transport cost in thousands of dollars per case
param TransportCost{p in Plants, m in Markets} :=
Freight * Distance[p, m] / 1000;

# Shipment quantities in cases
var shipment{Plants, Markets} >= 0;

# Total transportation costs in thousands of dollars
minimize cost:
sum{p in Plants, m in Markets} TransportCost[p, m] * shipment[p, m];

# Observe supply limit at plant p
s.t. supply{p in Plants}: sum{m in Markets} shipment[p, m] <= Capacity[p];

# Satisfy demand at market m
s.t. demand{m in Markets}: sum{p in Plants} shipment[p, m] >= Demand[m];

data;

set Plants := seattle san-diego;
set Markets := new-york chicago topeka;

param Capacity :=
seattle   350
san-diego 600;

param Demand :=
new-york 325
chicago  300
topeka   275;

param Distance : new-york chicago topeka :=
seattle        2.5      1.7     1.8
san-diego      2.5      1.8     1.4;

param Freight := 90;```

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Last updated August 9th, 2020

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