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Errata to “A robust optimization model for stochastic logistic problems”
ARTICLE IN PRESS
Int. J. Production Economics 98 (2005) 108–109 www.elsevier.com/locate/ijpe
Erratum
Errata to ‘‘A robust optimization model for stochastic logistic problems’’ [International Journal of Production Economics, 64 (2000) 385–397] Ali Yasar Department of Decision Sciences and Engineering Systems, Rensselaer Polytechnic Institute, 110 Eighth St. Troy, NY 12180, USA Received 1 October 2004; accepted 1 February 2005
Abstract This errata points out several errors in various optimization models and an inconsistent numerical result in ChianSon Yu, Han-Lin Li [International Journal of Production Economics 64 (2000) 385–397]. r 2005 Elsevier B.V. All rights reserved. Keywords: Goal programming; Robust optimization; Stochastic programming; Logistic problem
S X
Equation errors
ps
s¼1
XX i
k
cik xik þ
ps
i
s¼1
On p. 389 (2.21): S X
XX
X k
csk xk þ
XX k
! ckj xkj
j
ys
cik xik þ
k
X
csk xk þ
XX
k
k
ckj xkj
j
ys for each s. On p. 390 (2.22): ! XX X XX cik xik þ csk xk þ ckj xkj ys i
should be
k
k
k
j
should be XX DOI of original article: 10.1016/S0925-5273(99)00074-2 Tel.: +1 518 276 8098; fax: +1 518 276 8227. E-mail address: [email protected].
!
i
cik xik þ
k
for each s.
0925-5273/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2005.02.009
X k
csk xk þ
XX k
j
! ckj xkj ys
ARTICLE IN PRESS Erratum / Int. J. Production Economics 98 (2005) 108–109
On p. 390 (2.23): X xkj Dsj gsj dsj
should be l
k
should be X xkj Dsj gsj dsj .
109
4 X
ps ðTC þ PC þ ICÞ
s¼1
k
4 X
! ps ðTC þ PC þ ICÞ þ 2ys .
s¼1
On p. 390 (2.24): X xkj dsj gsj þ Dsj k
should be gsj þ Dsj
X
On p. 394 (4.15): 4 X
ps ½ðTC þ PC þ ICÞ þ ys 0
s¼1
xkj dsj .
should be
k
On p. 391 constraint (3.3) should be for each s. On p. 393 (4.9):
4 X
ps ½ðTC þ PC þ ICÞ þ ys 0.
s¼1
z12 þ z22 Ds2 gs2 ¼ dþ s2 ds3
should be z12 þ z22 Ds2 gs2 ¼ dþ s2 ds2 .
On p. 394 (4.13): l
4 X
ps ðTC þ PC þ ICÞ
s¼1
4 X s¼1
ps ½ðTC þ PC þ ICÞ þ 2ys
Inconsistent results The solution for the two equivalent models (which are given on pp. 393 and 394) is given in Table 2 on p. 395. The results in Table 2 are inconsistent with the constraints in the optimization models. For example, models contain the following constraint: y1 340 (4.6), yet in Table 2 we see that y1 ¼ 500.
Int. J. Production Economics 98 (2005) 108–109 www.elsevier.com/locate/ijpe
Erratum
Errata to ‘‘A robust optimization model for stochastic logistic problems’’ [International Journal of Production Economics, 64 (2000) 385–397] Ali Yasar Department of Decision Sciences and Engineering Systems, Rensselaer Polytechnic Institute, 110 Eighth St. Troy, NY 12180, USA Received 1 October 2004; accepted 1 February 2005
Abstract This errata points out several errors in various optimization models and an inconsistent numerical result in ChianSon Yu, Han-Lin Li [International Journal of Production Economics 64 (2000) 385–397]. r 2005 Elsevier B.V. All rights reserved. Keywords: Goal programming; Robust optimization; Stochastic programming; Logistic problem
S X
Equation errors
ps
s¼1
XX i
k
cik xik þ
ps
i
s¼1
On p. 389 (2.21): S X
XX
X k
csk xk þ
XX k
! ckj xkj
j
ys
cik xik þ
k
X
csk xk þ
XX
k
k
ckj xkj
j
ys for each s. On p. 390 (2.22): ! XX X XX cik xik þ csk xk þ ckj xkj ys i
should be
k
k
k
j
should be XX DOI of original article: 10.1016/S0925-5273(99)00074-2 Tel.: +1 518 276 8098; fax: +1 518 276 8227. E-mail address: [email protected].
!
i
cik xik þ
k
for each s.
0925-5273/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2005.02.009
X k
csk xk þ
XX k
j
! ckj xkj ys
ARTICLE IN PRESS Erratum / Int. J. Production Economics 98 (2005) 108–109
On p. 390 (2.23): X xkj Dsj gsj dsj
should be l
k
should be X xkj Dsj gsj dsj .
109
4 X
ps ðTC þ PC þ ICÞ
s¼1
k
4 X
! ps ðTC þ PC þ ICÞ þ 2ys .
s¼1
On p. 390 (2.24): X xkj dsj gsj þ Dsj k
should be gsj þ Dsj
X
On p. 394 (4.15): 4 X
ps ½ðTC þ PC þ ICÞ þ ys 0
s¼1
xkj dsj .
should be
k
On p. 391 constraint (3.3) should be for each s. On p. 393 (4.9):
4 X
ps ½ðTC þ PC þ ICÞ þ ys 0.
s¼1
z12 þ z22 Ds2 gs2 ¼ dþ s2 ds3
should be z12 þ z22 Ds2 gs2 ¼ dþ s2 ds2 .
On p. 394 (4.13): l
4 X
ps ðTC þ PC þ ICÞ
s¼1
4 X s¼1
ps ½ðTC þ PC þ ICÞ þ 2ys
Inconsistent results The solution for the two equivalent models (which are given on pp. 393 and 394) is given in Table 2 on p. 395. The results in Table 2 are inconsistent with the constraints in the optimization models. For example, models contain the following constraint: y1 340 (4.6), yet in Table 2 we see that y1 ¼ 500.