By Robert Fourer

ISBN-10: 0534388094

ISBN-13: 9780534388096

AMPL is a language for large-scale optimization and mathematical programming difficulties in construction, distribution, mixing, scheduling, and lots of different functions. Combining customary algebraic notation and a strong interactive command atmosphere, AMPL makes it effortless to create versions, use a wide selection of solvers, and look at recommendations. although versatile and handy for fast prototyping and improvement of versions, AMPL additionally bargains the rate and generality wanted for repeated large-scale construction runs. This booklet, written via the creators of AMPL, is a whole consultant for modelers in any respect degrees of expertise. It starts with an instructional on typical linear programming types, and provides all of AMPL's positive aspects for linear programming with large examples. extra chapters hide community, nonlinear, piecewise-linear, and integer programming; database and spreadsheet interactions; and command scripts. so much chapters comprise workouts. obtain loose types of AMPL and a number of other solvers from www.ampl.com for experimentation, review, and schooling. the website additionally lists owners of the economic model of AMPL and diverse solvers.

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**Sample text**

How would you declare the constraints? 7 AMPL INTERFACES 23 How much of each car should be produced, and what is the maximum profit? You should find that your solution specifies a fractional amount of one of the cars. As a practical matter, how could you make use of this solution? (d) If you maximize the total number of cars produced instead of the total profit, how many more cars do you make? How much less profit? (e) Each kind of car achieves a certain fuel efficiency, and the manufacturer is required by law to maintain a certain ‘‘fleet average’’ efficiency.

Tayyabkhan, Managerial Planning with Linear Programming: In Process Industry Operations. John Wiley & Sons (New York, NY, 1978). A detailed account of a variety of profit-maximizing applications, with emphasis on the petroleum and petrochemical industries. Vasˇek Chva´ tal, Linear Programming, W. H. Freeman (New York, NY, 1983). A concise and economical introduction to theoretical and algorithmic topics in linear programming. ’’ Management Science 4 (1958) pp. 415–449. An application to all stages of steelmaking — from coal and ore through finished products — from the early days of linear programming.

For a particular work schedule j, io [i j] is the number of hours that a person following schedule j will work on day i (zero if none). cos t [j I is the monthly salary for a person following schedule j, and X [j] is the number of workers assigned that schedule. Under this interpretation, the objective becomes the total cost of the monthly payroll, while the constraints say that for each day i, the total number of workers assigned to work that day must lie between the limits out_min [i) and out_max [i].

### AMPL: A Modeling Language for Mathematical Programming by Robert Fourer

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