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### Tinkering: using AMPL/Gurobi to allocate parts in a play

Now and then Rey and I do play readings with friends. Usually there are rather more roles than there are readers, so "one man in his time plays many parts", which works fine until you end up playing two roles in the same scene and having to have an extended conversation with yourself.

So you want to cast roles in a way that avoids that kind of overlap, and you probably also want to make sure the different readers each get a decent share of the lines. You

AMPL (A Mathematical Programming Language) is similar to MiniZinc, which I posted about a while back: it's designed for specifying optimisation/constraint problems and then passing them to a solver of one's choice.

It's very much a declarative language: instead of giving the computer a set of steps to follow, you give it a set of requirements and then let it figure out how to satisfy those requirements. (This still feels like magic to me.)

AMPL and other optimisation languages usually take input in two parts: a "model" which is a generic description of the problem and requirements, and "data" which defines a specific instance of the problem.

So, here's some AMPL code:

In the unlikely event that anybody other than me actually wants to use this, you can download a free demo from AMPL (unlimited duration, restricts to about 300 variables i.e. number of actors x number of parts should be less than 300).

The demo comes bundled with a selection of top-notch and open-source commercial solvers, all free to use subject to that size restriction. By default it uses the MINOS solver, which is nice for generic nonlinear problems but doesn't handle integer constraints; since those are important here you'll want to use "options solver gurobi" (or cplex or xpress).

So you want to cast roles in a way that avoids that kind of overlap, and you probably also want to make sure the different readers each get a decent share of the lines. You

*could*do this by hand, but since I'm currently teaching myself AMPL, I thought it'd be a fun challenge to program a solution.AMPL (A Mathematical Programming Language) is similar to MiniZinc, which I posted about a while back: it's designed for specifying optimisation/constraint problems and then passing them to a solver of one's choice.

It's very much a declarative language: instead of giving the computer a set of steps to follow, you give it a set of requirements and then let it figure out how to satisfy those requirements. (This still feels like magic to me.)

AMPL and other optimisation languages usually take input in two parts: a "model" which is a generic description of the problem and requirements, and "data" which defines a specific instance of the problem.

So, here's some AMPL code:

**( The model )****( The data: )**In the unlikely event that anybody other than me actually wants to use this, you can download a free demo from AMPL (unlimited duration, restricts to about 300 variables i.e. number of actors x number of parts should be less than 300).

The demo comes bundled with a selection of top-notch and open-source commercial solvers, all free to use subject to that size restriction. By default it uses the MINOS solver, which is nice for generic nonlinear problems but doesn't handle integer constraints; since those are important here you'll want to use "options solver gurobi" (or cplex or xpress).