Add to Exercise 13-7(a)-

(f) the following:

(g) Compute the subgradient direction of Algorithm 13C at your solution of (f)

and take a step using lambda = 500 to update the dual solution. Then re-solve the Lagrangian relaxation. Did the value improve?

(h) Repeat (g) by taking a second step from the solution of

(f) using stepsize lambda

= 250 to update the dual solution, and comment on the result.

(i) Is it possible that the dualization of

(b) can produce a bound better than the LP relaxation of the full model? Explain.

(j) Now formulate an alternative Lagrangian relaxation dualizing the first two main constraints and keeping the 3rd and 4th.

(k) Can that new dualization ever produce a bound better than the LP relaxation of the full model? Explain.