- Email: [email protected]
Comment on ‘A simulation-based approach to price optimisation of the mixed bundling problem with capacity constraints’
Accepted Manuscript Comment on ‘A simulation-based approach to price optimisation of the mixed bundling problem with capacity constraints’ Xinggang Luo, C.K. Kwong, Jiafu Tang, Yang Yu PII:
S0925-5273(17)30178-0
DOI:
10.1016/j.ijpe.2017.06.016
Reference:
PROECO 6739
To appear in:
International Journal of Production Economics
Received Date: 11 June 2017 Accepted Date: 12 June 2017
Please cite this article as: Luo, X., Kwong, C.K., Tang, J., Yu, Y., Comment on ‘A simulation-based approach to price optimisation of the mixed bundling problem with capacity constraints’, International Journal of Production Economics (2017), doi: 10.1016/j.ijpe.2017.06.016. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Comment on 'A simulation-based approach to price optimisation of the mixed bundling problem with capacity constraints' Xinggang Luoa*, C.K. Kwongb, Jiafu Tanga and Yang Yua a
School of Management, Hangzhou Dianzi University, Hangzhou, P.R.C. Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon Hong Kong, P.R.C.
RI PT
b
Abstract: Errors on the mathematical model of Mayer et al. (2013) are pointed out and corrected.
SC
Keywords: Pricing, Bundling, Mixed-integer programming
Dr. X.G. Luo, Professor of Systems Engineering, Management School,
M AN U
Corresponding author:
Hangzhou Dianzi University, Hangzhou, Zhejiang, China
TE D
E-mail: [email protected]
AC C
EP
Tel: (8624) 83682292-12
*
Corresponding author. E-mail: [email protected].
ACCEPTED MANUSCRIPT
Comment on 'A simulation-based approach to price optimisation of the mixed bundling problem with capacity constraints' Xinggang Luoa, C.K. Kwongb, Jiafu Tanga and Yang Yua a
School of Management, Hangzhou Dianzi University, Hangzhou, P.R.C. Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon Hong Kong, P.R.C.
RI PT
b
Abstract: Errors on the mathematical model of Mayer et al. (2013) are pointed out and corrected. Keywords: pricing, bundling, mixed-integer programming
SC
There are logic errors in the mathematical modelling of Mayer et al. (2013), which may lead to wrong outputs in numeric experiments. The cases that can’t fit the
M AN U
constraints of the optimization model are highlighted in grey as shown in Table 1. Table 1. The different cases of consumers’ purchase choice
A=0
CA=0,CB>0
CA=CB=0
A>B
SELECT BUNDLE
SELECT PRODUCTS
NO PURCHASE
A=B
SELECT BUNDLE
SELECT PRODUCTS
NO PURCHASE
A
SELECT PRODUCTS
SELECT PRODUCTS
NO PURCHASE
B=0
SELECT BUNDLE
SELECT PRODUCTS
NO PURCHASE
B<0
SELECT BUNDLE
NO PURCHASE
NO PURCHASE
B>0
SELECT PRODUCTS
SELECT PRODUCTS
NO PURCHASE
SELECT BUNDLE
SELECT PRODUCTS
NO PURCHASE
SELECT BUNDLE
NO PURCHASE
NO PURCHASE
SELECT PRODUCTS
SELECT PRODUCTS
NO PURCHASE
B>0
B=0
TE D
A>0
CA>0,CB>0
SELECT PRODUCTS
PRODUCTS
NO PURCHASE
B<0
NO PURCHASE
NO PURCHASE
NO PURCHASE
B=0 B<0 B>0
EP
A<0
Note*: A-surplus of the bundle; B-surplus of products; prefix ‘C’- remaining capacity
AC C
To correct the problem, constraint (17) of Mayer et al. (2013) should be: N
N0 j J 1 N0 1 [∑ ( vi 0 − p0 n ) ⋅ γ i 0 n + ⋅ γ i 0 n − ∑∑ ( vij − p jn ) ⋅ γ ijn ] ≤ ∑ xi 0 n M n =1 M j =1 n =1 n =1
(17')
and a new constraint (21') is added as follows.
γ ijn ≤ xi 0 n + xijn ≤ γ i 0 n + γ ijn
(21')
References [1] Mayer S, Klein R, Seiermann S. A simulation-based approach to price optimisation of the mixed bundling problem with capacity constraints [J]. International Journal of Production Economics, 2013, 145(2):584-598.
S0925-5273(17)30178-0
DOI:
10.1016/j.ijpe.2017.06.016
Reference:
PROECO 6739
To appear in:
International Journal of Production Economics
Received Date: 11 June 2017 Accepted Date: 12 June 2017
Please cite this article as: Luo, X., Kwong, C.K., Tang, J., Yu, Y., Comment on ‘A simulation-based approach to price optimisation of the mixed bundling problem with capacity constraints’, International Journal of Production Economics (2017), doi: 10.1016/j.ijpe.2017.06.016. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Comment on 'A simulation-based approach to price optimisation of the mixed bundling problem with capacity constraints' Xinggang Luoa*, C.K. Kwongb, Jiafu Tanga and Yang Yua a
School of Management, Hangzhou Dianzi University, Hangzhou, P.R.C. Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon Hong Kong, P.R.C.
RI PT
b
Abstract: Errors on the mathematical model of Mayer et al. (2013) are pointed out and corrected.
SC
Keywords: Pricing, Bundling, Mixed-integer programming
Dr. X.G. Luo, Professor of Systems Engineering, Management School,
M AN U
Corresponding author:
Hangzhou Dianzi University, Hangzhou, Zhejiang, China
TE D
E-mail: [email protected]
AC C
EP
Tel: (8624) 83682292-12
*
Corresponding author. E-mail: [email protected].
ACCEPTED MANUSCRIPT
Comment on 'A simulation-based approach to price optimisation of the mixed bundling problem with capacity constraints' Xinggang Luoa, C.K. Kwongb, Jiafu Tanga and Yang Yua a
School of Management, Hangzhou Dianzi University, Hangzhou, P.R.C. Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon Hong Kong, P.R.C.
RI PT
b
Abstract: Errors on the mathematical model of Mayer et al. (2013) are pointed out and corrected. Keywords: pricing, bundling, mixed-integer programming
SC
There are logic errors in the mathematical modelling of Mayer et al. (2013), which may lead to wrong outputs in numeric experiments. The cases that can’t fit the
M AN U
constraints of the optimization model are highlighted in grey as shown in Table 1. Table 1. The different cases of consumers’ purchase choice
A=0
CA=0,CB>0
CA=CB=0
A>B
SELECT BUNDLE
SELECT PRODUCTS
NO PURCHASE
A=B
SELECT BUNDLE
SELECT PRODUCTS
NO PURCHASE
A
SELECT PRODUCTS
SELECT PRODUCTS
NO PURCHASE
B=0
SELECT BUNDLE
SELECT PRODUCTS
NO PURCHASE
B<0
SELECT BUNDLE
NO PURCHASE
NO PURCHASE
B>0
SELECT PRODUCTS
SELECT PRODUCTS
NO PURCHASE
SELECT BUNDLE
SELECT PRODUCTS
NO PURCHASE
SELECT BUNDLE
NO PURCHASE
NO PURCHASE
SELECT PRODUCTS
SELECT PRODUCTS
NO PURCHASE
B>0
B=0
TE D
A>0
CA>0,CB>0
SELECT PRODUCTS
PRODUCTS
NO PURCHASE
B<0
NO PURCHASE
NO PURCHASE
NO PURCHASE
B=0 B<0 B>0
EP
A<0
Note*: A-surplus of the bundle; B-surplus of products; prefix ‘C’- remaining capacity
AC C
To correct the problem, constraint (17) of Mayer et al. (2013) should be: N
N0 j J 1 N0 1 [∑ ( vi 0 − p0 n ) ⋅ γ i 0 n + ⋅ γ i 0 n − ∑∑ ( vij − p jn ) ⋅ γ ijn ] ≤ ∑ xi 0 n M n =1 M j =1 n =1 n =1
(17')
and a new constraint (21') is added as follows.
γ ijn ≤ xi 0 n + xijn ≤ γ i 0 n + γ ijn
(21')
References [1] Mayer S, Klein R, Seiermann S. A simulation-based approach to price optimisation of the mixed bundling problem with capacity constraints [J]. International Journal of Production Economics, 2013, 145(2):584-598.