Originally posted by: arronlee11

hi~everyone:

    i have modeled a linear programming model;there are two decision variables (x and y) in my model,and these two decision variables are interger variables;

first,i solved the model with cplex directly,the total time cost isT1;

second,let x relax as a continuous variable and y is a interger variable still，when i solved the model with cplex, the time cost is T2;

third,let y relax as a continuous variable and x is a interger variable still, when i solved the model with cplex,the time cost is T3;

now i hvae serveral questions：

1、What is the size relationship among T1,T2 and T3;

2、according to the Testing by a data sets, it shows that:T1=0.5 sec,T2=95 sec,T3=0.3 sec; does the result reasonable？

It is certainly not unreasonable. Integrality restrictions let CPLEX apply some heuristics, bound-tightening rules etc. that it would not use without the integrality restrictions. Here is a simple example. Suppose that your objective is to minimize x + y, and that CPLEX has an incumbent solution with objective value 7. In scenario T1, CPLEX knows that the objective value must be an integer (it is the sum of two integers), and so if the LP relaxation of a node has objective value 6.3, any integer-feasible solution in that node must have objective value at least 7. Thus the node can be pruned. In scenario T2, the objective value is not necessarily an integer, so the incumbent with value 7 does not let you prune the node with value 6.3.

Originally posted by: arronlee11

Thank you very much for your answer.