title: Either or constraint WITH ONE POINT IN COMMON in linear programming operations-research
body: <p>suppose we have a quantity variable x (which is upperbounded by n), and a logic variable y which is equal to</p>
  <p>y = 1 if x >= s; where s is a generic number</p>
  <p>y = 0 otherwise => if x is strictly lesser than s => if x &lt; s</p>
  <br>
  Surfing around on the internet I found out this clear explanation https://youtu.be/iQ3PlKKorXA?t=35 which turned out to be the common pattern about either-or constraint. Therefore following the video, the solution would be:
  <br>
  <p>s - x &lt;= (1 - y)*n </p>
  <p>x - s &lt;= y*n</p>
  <p>And yet x could be equal to s in both the cases.
  <br>How can we fix this?</p>