Andrew and Hartwig, Please find below a pointer to an interesting article that compares various formulations for non-convex piecewise linear cost functions. The formulation affects the run time of the usually hard to solve MIP models. Non-convex and concave cost functions occur quite often in supply chain modelling, e.g. transportation costs with scale/utilization effects.
Croxton, K. L., Gendron, B. and Magnanti, T. L., "A comparison of mixed-integer programming models for non-convex piecewise linear cost minimization problems," Management Sci., v49, pp. 1268-1273, 2003. Best regards, Ivo van Baren 2007/8/9, Andrew Makhorin <[EMAIL PROTECTED]>: > > > I would like to know if it is possible with GLPK to solve problems > > with a piecewise linear objective function. > > It is possible. However, you need to reformulate your problem, > because glpk does not support non-linear objective and constraints. > A standard way to model a piecewise objective is using SOS2 > constraints, which, in turn, can be modeled as follows: > http://lists.gnu.org/archive/html/help-glpk/2007-06/msg00005.html > > > I currently work on a model for supply chain planning which uses a > > term in the objective funktion with is equal to zero as long as the > > value of a decision variable is greater than a given constant value, > > and wich is equal to the product of a cost constant and the > > difference of the constant and the decision variable. > > > I use ILOG OPL Studio for developing the model and CPLEX for solving > > it. > > Please note that glpk is much weaker than cplex in the sense of > ability to solve large or hard MIPs. > > > Recently I got the hint to look for GLPK, so I made it running on my > > PC and ported the model. Everything is fine except the piecewise > > objective term. > > > (In ILOG OPL I modeled it with a function within the objective > > function: > > > maximize sum(...) ... + cost * maxl(0, constant - Variable); ) > > > BTW: is there any GUI for GLPK which has similar functionality like > > OPL Studio for CPLEX? > > Unfortunately, not. > > > > > > _______________________________________________ > Help-glpk mailing list > [email protected] > http://lists.gnu.org/mailman/listinfo/help-glpk >
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