122. SPBIGM - SP Big M Coefficient

The SPBIGM parameter is used by the Stochastic Programming (SP) solver in constructing forcing constraints that may be required in the deterministic models generated by the solver.  Forcing constraints are generally added to force binary variables to 1 when some activity occurs.  For example, suppose x is a continuous variable and z is a binary variable.  A forcing constraint that would drive z to 1 whenever x is positive would be:

 x M * z

where M is some large number. M in this case is the SPBIGM parameter.  

There are two things to note about M.  First, if M is too small, a forcing constraint can become infeasible, making the entire model infeasible.  In general, M should be at least as large as the largest possible value for x so as not to introduce an infeasibility.  However, from an algorithmic point of view, M should not be too large.  If M is unrealistically large, it will be tougher for the integer solver to converge, plus  it also introduces the potential round off error.

The default setting for M should be sufficient for most models.  However, if your SP model is infeasible for no known reason, you may want to try increasing M. On the other hand, if your SP is running slow, you may want to try reducing M.

The SPBIGM parameter defaults to a value of 1.e8.