----------------------------------------------------------------------------- -- | -- Module : Documentation.SBV.Examples.Optimization.Production -- Copyright : (c) Levent Erkok -- License : BSD3 -- Maintainer: erkokl@gmail.com -- Stability : experimental -- -- Solves a simple linear optimization problem ----------------------------------------------------------------------------- module Documentation.SBV.Examples.Optimization.Production where import Data.SBV -- | Taken from -- -- A company makes two products (X and Y) using two machines (A and B). -- -- - Each unit of X that is produced requires 50 minutes processing time on machine -- A and 30 minutes processing time on machine B. -- -- - Each unit of Y that is produced requires 24 minutes processing time on machine -- A and 33 minutes processing time on machine B. -- -- - At the start of the current week there are 30 units of X and 90 units of Y in stock. -- Available processing time on machine A is forecast to be 40 hours and on machine B is -- forecast to be 35 hours. -- -- - The demand for X in the current week is forecast to be 75 units and for Y is forecast -- to be 95 units. -- -- - Company policy is to maximise the combined sum of the units of X and the units of Y -- in stock at the end of the week. -- -- How much of each product should we make in the current week? -- -- We have: -- -- >>> optimize Lexicographic production -- Optimal model: -- X = 45 :: Integer -- Y = 6 :: Integer -- stock = 1 :: Integer -- -- That is, we should produce 45 X's and 6 Y's, with the final maximum stock of just 1 expected! production :: Goal production = do x <- sInteger "X" -- Units of X produced y <- sInteger "Y" -- Units of X produced -- Amount of time on machine A and B let timeA = 50 * x + 24 * y timeB = 30 * x + 33 * y constrain \$ timeA .<= 40 * 60 constrain \$ timeB .<= 35 * 60 -- Amount of product we'll end up with let finalX = x + 30 finalY = y + 90 -- Make sure the demands are met: constrain \$ finalX .>= 75 constrain \$ finalY .>= 95 -- Policy: Maximize the final stock maximize "stock" \$ (finalX - 75) + (finalY - 95)