From 6e2c5a7d4a782e5ebcced97eaf225c5fa81654bb Mon Sep 17 00:00:00 2001 From: Oscar Dowson Date: Wed, 27 Dec 2023 10:01:12 +1300 Subject: [PATCH] [docs] add modulo to tips_and_tricks.jl --- docs/src/tutorials/linear/tips_and_tricks.jl | 22 ++++++++++++++++++++ 1 file changed, 22 insertions(+) diff --git a/docs/src/tutorials/linear/tips_and_tricks.jl b/docs/src/tutorials/linear/tips_and_tricks.jl index ba7507f87f8..13b42a64f79 100644 --- a/docs/src/tutorials/linear/tips_and_tricks.jl +++ b/docs/src/tutorials/linear/tips_and_tricks.jl @@ -114,6 +114,28 @@ model = Model(); # This reformulation does not work for ``t \le \max\{x, y\}``. +# ## Modulo + +# To model ``y = x % n``, where ``n`` is a constant modulus, we use the +# relationship ``x = n \cdot z + y``, where ``z \in \mathbb{Z}_+`` is the number +# of times that ``n`` can be divided by ``x`` and ``y`` is the remainder. + +n = 4 +model = Model(); +@variable(model, x >= 0, Int) +@variable(model, 0 <= y <= n - 1, Int) +@variable(model, z >= 0, Int) +@constraint(model, x == n * z + y) + +# The modulo reformulation is often useful for subdividing a time increment into +# units of time like hours and days: + +model = Model(); +@variable(model, t >= 0, Int) +@variable(model, 0 <= hours <= 23, Int) +@variable(model, days >= 0, Int) +@constraint(model, t == 24 * days + hours) + # ## Boolean operators # Binary variables can be used to construct logical operators. Here are some