# A Mathematical Programming Language

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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- A Mathematical Programming Language ranks in the top 10% of languages
- the A Mathematical Programming Language website
- the A Mathematical Programming Language wikipedia page
- A Mathematical Programming Language first appeared in 1985
- file extensions for A Mathematical Programming Language include ampl, mod, dat and run
- the A Mathematical Programming Language team is on twitter
- See also: linux, unix, awk, c, algebraic-modeling-language, nl, xml, excel-app
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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 November 16th, 2019