title: Scipy Optimizer or heuristic approach, which to choose for bottleneck capacity
body: <p>I am not able to formulate the below problem into <code>scipy's</code> <code>linprog</code> or <code>minimize</code> due to complex constraint condition. So wanted to check if there are other modules that allow below format of block constraints.</p>
  <p><a href="https://i.stack.imgur.com/QsxNJ.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/QsxNJ.png" alt="here" /></a></p>
  <p>Since, this also checks for the bottleneck capacity(which is taken care of by constraints in <code>B14</code>) my check was whether we should go for direct solvers or take a heuristic approach where we assign random numbers and keep re-balancing towards the slowest process. Iterating till numbers seem to converge ?.</p>
  <p>Details of the problem :</p>
  <p><code>Objective</code> : F9, F10, F11 each individually and such that all are almost same(it's a constraint) - Background is that consider p1,p2 and p3 as serial processes and so I want maximum throughput from each and the same.(factoring bottleneck)</p>
  <p><code>Variables</code> : C6:E8. These are percentage allocation and hence should be between (0,1)(bound)</p>
  <p><code>Constraint</code> : i)Mentioned in 'objective' - the total output for each process should be the same.
  i.e. F9 = F10 = F11.</p>
  <p>ii)Also sum of allocation for a specific machine should be 100%. i.e. sum(C6:C8) = 1, sum(D6:D8) = 1 and sum(E6:E8) = 1</p>
  <p>I need help in formulating the first constraint. How can I add a equation to ensure equality of those 3 cells(F9:F11) ?</p>