By Robert Fourer

AMPL is a language for large-scale optimization and mathematical programming difficulties in creation, distribution, mixing, scheduling, and plenty of different functions. Combining customary algebraic notation and a strong interactive command surroundings, AMPL makes it effortless to create versions, use a large choice of solvers, and think about suggestions. notwithstanding versatile and handy for fast prototyping and improvement of versions, AMPL additionally deals the rate and generality wanted for repeated large-scale construction runs. This ebook, written by way of the creators of AMPL, is a whole advisor for modelers in any respect degrees of expertise. It starts with an educational on known linear programming versions, and offers all of AMPL's beneficial properties for linear programming with huge examples. extra chapters disguise community, nonlinear, piecewise-linear, and integer programming; database and spreadsheet interactions; and command scripts. so much chapters comprise workouts. obtain unfastened types of AMPL and several other solvers from www.ampl.com for experimentation, overview, and schooling. the website additionally lists owners of the economic model of AMPL and diverse solvers.

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**Example text**

To promote variety, the weekly diet must contain between 2 and 10 packages of each food. The amount of sodium and calories in each package is also given; total sodium must not exceed 40,000 mg, and total calories must be between 16,000 and 24,000. All of these changes can be made through a few modifications to the data, as shown in Figure 2-3. Putting this new data in file diet2 . 89 1. 99 1. 20000 20000 20000 20000 40000 24000 n_min 700 700 700 700 0 16000 param amt (tr) A BEEF 60 CHK 8 FISH 8 HAM 40 MCH 15 MTL 70 SPG 25 TUR 60 f_max .

This interpretation is related to the concept of an economic equilibrium, as we will explain in Chapter 19. In still another, quite different application, the inputs are work schedules, and the outputs correspond to hours worked on cenain days of a month. 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.

D) It looks a little strange that the attribute amounts for research octane are negative. What is the limit constraint for this attribute really saying? 2 Diet and Other Input Models: Minimizing Costs To complement the profit-maximizing models of Chapter I, we now consider linear programming models in which the objective is to minimize costs. Where the constraints of maximization models tend to be upper limits on the availability of resources, the constraints in minimization models are more likely to be lower limits on the amounts of certain "qualities" in the solution.