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Assuming that the value $C + 0.5$ is valid, you could model this by simply adding the constraint $$x \leq C + 0.5$$ Otherwise, you define a constant say $\epsilon = 10^{-7}$ and do $$x \leq C + 0.5 … answered Oct 12 '19 by Claudio Contardo You could simply write$$y(i) - y(i - 1) \ge 0, \qquad i=2,...,N
answered Mar 12 '20 by Claudio Contardo
It is not possible, and the reason is that for them to give you the dual, they also need to give you the binding cutting planes at each node. Much of Gurobi's (and CPLEX's as well) magic relies on the …
answered Mar 13 '20 by Claudio Contardo
As others already said, the PCSPP described resorts to a simple SPP with potentially negative costs. It would still be solvable in poly time if no cycles of negative weight are present. Otherwise, you …
answered Jul 5 '19 by Claudio Contardo
In DP Bertsekas Network Optimization (that can be downloaded for free) there's an exercise at Page 104 (Finding an initial price vector) where you can find a method for solving shortest paths in dynam …
answered Feb 4 '20 by Claudio Contardo
The optimal solution is 15/3 for the three variables. Any other assignment is such that at least one of the variables takes a value larger than 15/3.
answered Feb 4 '20 by Claudio Contardo
You seem to be mixing up two related but different attributes: time windows and route duration. Duration is the time elapsed since the beginning of a route, and depends on the starting time as you men …
answered Jul 3 '19 by Claudio Contardo
Indeed, as you pointed out already, checking time windows feasibility is only doable in linear time for a given, static, route. However, you may exploit preprocessing techniques and partial paths con …
answered Jul 9 '19 by Claudio Contardo
You may find a partial answer to your question in the following article (forthcoming in OR) by JP Vielma and J Huchette https://arxiv.org/abs/1708.00050 In that paper, the authors consider the problem …
answered Aug 20 '20 by Claudio Contardo
Stabilization methods are tricky. Dual optimal inequalities are you best chance to obtain significant speed ups. Basically they prevent a bunch of useless dual values by exploiting problem-specific st …
answered May 31 '19 by Claudio Contardo
As Rob said, one option is to initialize your CG with a set of columns coming from a feasible solution. The rationale behind is to start from a set of near-optimal (from a MP perspective!) columns. As …
answered Apr 7 '20 by Claudio Contardo
I will give you a little more insight based on my latest experience solving minimax (or maximin) integer programs. Sorry I will be a bit self-citing here. Indeed, the main reason that can explain the …
answered Jun 3 '19 by Claudio Contardo
An exact method will (typically within a bounded number of steps) provide a proven optimal solution. This is, a solution x* and a guarantee that no other feasible solution has an objective better than …
answered Jul 9 '19 by Claudio Contardo
In Montreal we have Louis M Rousseau whose father Jean Marc Rousseau was also a professor until he quit academua to start his own company (GIRO). From Chile there is Gabriel Weintraub, professor at S …
answered Jun 11 '19 by Claudio Contardo
Assuming that the $c_i$ and $q$ are all positive you may add one binary variable $y_i$ for every $i=1,\cdots,n$ then you may do \begin{align}c_i x_i &\geq q y_i \quad\forall i\\\sum_i y_i &\geq 1\end{ …
answered Nov 14 '19 by Claudio Contardo

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