Principles of Mathematics in Operations Research

258 Solutions

Min (xia + x2a + x3a) H 1- {xip + x2p + x3p)

s.t.

(xla + xig) - (xlb + xlf) = 0\

(x2a + X2 9 ) - (x 2 b + x 2 f) = 0 > node 1

(X3a + XZg) - (x3b + X 3 f) = 0 J

(zip) - (xio) = 10

(x2p) - {x2o) = —10 ^ node OP

(x3p) - (x3o) = 0

Xla + X2a + X3a < 10

b)

xip + x2p + x3p < 10

xia,--- ,x3p>0 (integer)

Min ]T Y

Ck

rfp

k pevk

s.t.

Y fp =

D

<<

Pf=Vk

Y Y ^fr ^

U

• k P£Vk
  fp < V-P
  fP>0 (integer)
  We have (huge number of) K2m variables, m + K constraints and K1m
  simple bounds other than the nonnegativity constraints. The following sets
  the relation between the decision variables of the two formulations whose
  constraints are isomorphic:

xak = Y taPfP' fp = m^YXak (aPPlied recursively).

P£Vk k