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A loss-averse two-product ordering model with information updating in two-echelon inventory system
1. | School of Business, Central South University, Changsha 410083, China |
2. | School of Architecture Engineering, Jiangxi Modern Polytechnic College, Nanchang 330095, China |
This paper integrates the prospect theory with two-product ordering problem and adopts Bayesian forecasting model under Brownian motion to propose a loss-averse two-product ordering model with demand information updating in a two-echelon inventory system. We also derive all psychological perceived revenue functions for sixteen supply-demand cases as well as the expected value functions and prospect value function for the loss-averse retailer. To solve this model, a Monte Carlo algorithm is presented to estimate the high dimensional integrals with curved polyhedral integral region of unknown volume. Numerical results show that the optimal order quantities of both high-risk product and low-risk product vary across different psychological reference points, which are also affected by information updating, and the loss-averse retailer benefits considerably from information updating. All results suggest that our model provides a better description of the retailer$'$s actual ordering behavior than existing models.
References:
[1] |
L. Abdel-Malek, R. Montanari and L. C. Morales,
Exact, approximate, and generic iterative models for the multi-product newsboy problem with budget constraint, International Journal of Production Economics, 2 (2004), 189-198.
|
[2] |
V. Agrawal and S. Seshadri,
Impact of uncertainty and risk aversion on price and order quantity in the newsvendor problem, Manufacturing & Service Operations Management, 4 (2000), 410-423.
|
[3] |
S. Choi and A. Ruszczyński,
A multi-product risk-averse newsvendor with exponential utility function, European Journal of Operational Research, 214 (2011), 78-84.
|
[4] |
A. Dvoretzky, J. Kiefer and J. Wolfowitz,
The inventory problem: Ⅱ. Case of unknown distributions of demand, Econometrica: Journal of the Econometric Society, 20 (1952), 450-466.
|
[5] |
L. Eeckhoudt, C. Gollier and H. Schlesinger,
The risk-averse (and prudent) newsboy, Management Science, 5 (1995), 786-794.
|
[6] |
G. Hadley and T. M. Whitin,
Analysis of Inventory Systems, Prentice Hall, Upper Saddle River, 1994. |
[7] |
M. Joseph and K. Panos,
On the complementary value of accurate demand information and production and supplier flexibility, Manufacturing & Service Operations Management, 2 (2002), 99-113.
|
[8] |
D. Kahneman and A. Tversky,
Prospect theory: An analysis of decision under risk, Econometrica, 2 (1979), 263-292.
|
[9] |
M. Khouja,
The single-period (newsvendor) problem: Literature review and suggestions for future research, Omega, 5 (1999), 537-553.
|
[10] |
A. H. L. Lau and H. S. Lau,
Decision models for single-period products with two ordering opportunities, International Journal of Production Economics, 5 (1998), 57-70.
|
[11] |
W. Liu, S. Song and C. Wu,
Impact of loss aversion on the newsvendor game with product substitution, International Journal of Production Economics, 141 (2013), 352-359.
|
[12] |
X. Long and J. Nasiry,
Prospect theory explains newsvendor behavior: The role of reference points, Management Science, 61 (2014), 3009-3012.
|
[13] |
L. Ma, Y. Zhao, W. Xue, T. Cheng and H. Yan,
Loss-averse newsvendor model with two ordering opportunities and market information updating, International Journal of Production Economics, 140 (2012), 912-921.
|
[14] |
G. C. Mahata,
A single period inventory model for incorporating two-ordering opportunities under imprecise demand information, International Journal of Industrial Engineering Computations, 2 (2011), 385-394.
|
[15] |
J. Miltenburg and C. Pong,
Order quantities for style goods with two order opportunities and Bayesian updating of demand: Part 2-capacity constraints, International Journal of Production Research, 8 (2007), 1707-1723.
|
[16] |
J. V. Neuman and O. Morgenstern,
Theory of Games and Economic Behavior, 2$^{nd}$ edition, Princeton university press, Princeton, 1994. |
[17] |
N. C. Petruzzi and M. Dada,
Pricing and the newsvendor problem: A review with extensions, Operations Research, 2 (1999), 183-194.
|
[18] |
R. Pindyck,
Irreversible investment, capacity choice, and the value of the firm, American Economic Review, 5 (1988), 969-985.
|
[19] |
Y. Qin, R. Wang, A. J. Vakharia, Y. Chen and M. M. H. Seref,
The newsvendor problem: Review and directions for future research, European Journal of Operational Research, 213 (2011), 361-374.
|
[20] |
M. E. Schweitzer and G. P. Cachon,
Decision bias in the newsvendor problem with a known demand distribution: experimental evidence, Management Science, 3 (2000), 404-420.
|
[21] |
G. H. Tannous,
Capital budgeting for volume flexibility equipment, Decision Sciences, 2 (1996), 157-184.
|
[22] |
R. H. Thaler, A. Tversky, D. Kahneman and A Schwartz,
The effect of myopia and loss aversion on risk taking: An experimental test, The Quarterly Journal of Economics, 112 (1997), 647-661.
|
[23] |
C. X. Wang and S. Webster,
The loss-averse newsvendor problem, Omega, 37 (2009), 93-105.
|
[24] |
C. X. Wang,
The loss-averse newsvendor game, International Journal of Production Economics, 124 (2010), 448-452.
|
[25] |
Q. Zhang, D. Zhang, Y. Tsao and J. Luo,
Optimal ordering policy in a two-stage supply chain with advance payment for stable supply capacity, International Journal of Production Economics, 177 (2016), 34-43.
|
[26] |
Y. Zhou, X. Chen, X. Xu and C. Yu,
A multi-product newsvendor problem with budget and loss constraints, International Journal of Information Technology & Decision Making, 5 (2005), 1093-1110.
|
[27] |
Y. Zhou, W. Qiu and Z. Wang,
Product-portfolio Ordering Analysis with Update Information in the Two-echelon: Risk Decision-making Model, Systems Engineering-Theory & Practice, 28 (2008), 9-16.
|
[28] |
Y. Zhou, R. Ying, X. Chen and Z. Wang,
Two-product newsboy problem based on prospect theory, Journal of Management Sciences in China, 11 (2013), 17-29.
|
show all references
The reviewing process was handled by Changjun Yu.
References:
[1] |
L. Abdel-Malek, R. Montanari and L. C. Morales,
Exact, approximate, and generic iterative models for the multi-product newsboy problem with budget constraint, International Journal of Production Economics, 2 (2004), 189-198.
|
[2] |
V. Agrawal and S. Seshadri,
Impact of uncertainty and risk aversion on price and order quantity in the newsvendor problem, Manufacturing & Service Operations Management, 4 (2000), 410-423.
|
[3] |
S. Choi and A. Ruszczyński,
A multi-product risk-averse newsvendor with exponential utility function, European Journal of Operational Research, 214 (2011), 78-84.
|
[4] |
A. Dvoretzky, J. Kiefer and J. Wolfowitz,
The inventory problem: Ⅱ. Case of unknown distributions of demand, Econometrica: Journal of the Econometric Society, 20 (1952), 450-466.
|
[5] |
L. Eeckhoudt, C. Gollier and H. Schlesinger,
The risk-averse (and prudent) newsboy, Management Science, 5 (1995), 786-794.
|
[6] |
G. Hadley and T. M. Whitin,
Analysis of Inventory Systems, Prentice Hall, Upper Saddle River, 1994. |
[7] |
M. Joseph and K. Panos,
On the complementary value of accurate demand information and production and supplier flexibility, Manufacturing & Service Operations Management, 2 (2002), 99-113.
|
[8] |
D. Kahneman and A. Tversky,
Prospect theory: An analysis of decision under risk, Econometrica, 2 (1979), 263-292.
|
[9] |
M. Khouja,
The single-period (newsvendor) problem: Literature review and suggestions for future research, Omega, 5 (1999), 537-553.
|
[10] |
A. H. L. Lau and H. S. Lau,
Decision models for single-period products with two ordering opportunities, International Journal of Production Economics, 5 (1998), 57-70.
|
[11] |
W. Liu, S. Song and C. Wu,
Impact of loss aversion on the newsvendor game with product substitution, International Journal of Production Economics, 141 (2013), 352-359.
|
[12] |
X. Long and J. Nasiry,
Prospect theory explains newsvendor behavior: The role of reference points, Management Science, 61 (2014), 3009-3012.
|
[13] |
L. Ma, Y. Zhao, W. Xue, T. Cheng and H. Yan,
Loss-averse newsvendor model with two ordering opportunities and market information updating, International Journal of Production Economics, 140 (2012), 912-921.
|
[14] |
G. C. Mahata,
A single period inventory model for incorporating two-ordering opportunities under imprecise demand information, International Journal of Industrial Engineering Computations, 2 (2011), 385-394.
|
[15] |
J. Miltenburg and C. Pong,
Order quantities for style goods with two order opportunities and Bayesian updating of demand: Part 2-capacity constraints, International Journal of Production Research, 8 (2007), 1707-1723.
|
[16] |
J. V. Neuman and O. Morgenstern,
Theory of Games and Economic Behavior, 2$^{nd}$ edition, Princeton university press, Princeton, 1994. |
[17] |
N. C. Petruzzi and M. Dada,
Pricing and the newsvendor problem: A review with extensions, Operations Research, 2 (1999), 183-194.
|
[18] |
R. Pindyck,
Irreversible investment, capacity choice, and the value of the firm, American Economic Review, 5 (1988), 969-985.
|
[19] |
Y. Qin, R. Wang, A. J. Vakharia, Y. Chen and M. M. H. Seref,
The newsvendor problem: Review and directions for future research, European Journal of Operational Research, 213 (2011), 361-374.
|
[20] |
M. E. Schweitzer and G. P. Cachon,
Decision bias in the newsvendor problem with a known demand distribution: experimental evidence, Management Science, 3 (2000), 404-420.
|
[21] |
G. H. Tannous,
Capital budgeting for volume flexibility equipment, Decision Sciences, 2 (1996), 157-184.
|
[22] |
R. H. Thaler, A. Tversky, D. Kahneman and A Schwartz,
The effect of myopia and loss aversion on risk taking: An experimental test, The Quarterly Journal of Economics, 112 (1997), 647-661.
|
[23] |
C. X. Wang and S. Webster,
The loss-averse newsvendor problem, Omega, 37 (2009), 93-105.
|
[24] |
C. X. Wang,
The loss-averse newsvendor game, International Journal of Production Economics, 124 (2010), 448-452.
|
[25] |
Q. Zhang, D. Zhang, Y. Tsao and J. Luo,
Optimal ordering policy in a two-stage supply chain with advance payment for stable supply capacity, International Journal of Production Economics, 177 (2016), 34-43.
|
[26] |
Y. Zhou, X. Chen, X. Xu and C. Yu,
A multi-product newsvendor problem with budget and loss constraints, International Journal of Information Technology & Decision Making, 5 (2005), 1093-1110.
|
[27] |
Y. Zhou, W. Qiu and Z. Wang,
Product-portfolio Ordering Analysis with Update Information in the Two-echelon: Risk Decision-making Model, Systems Engineering-Theory & Practice, 28 (2008), 9-16.
|
[28] |
Y. Zhou, R. Ying, X. Chen and Z. Wang,
Two-product newsboy problem based on prospect theory, Journal of Management Sciences in China, 11 (2013), 17-29.
|

| | | | | | | |
200 | 123.69 | 400 | 63.72 | 200 | 57.44 | 400 | 59.79 |
| | | | | | | |
200 | 123.69 | 400 | 63.72 | 200 | 57.44 | 400 | 59.79 |
| | | | | |
0 | 271 | 281 | 427 | 429 | 3283.9 |
1000 | 270 | 278 | 426 | 428 | 2475.8 |
2000 | 265 | 273 | 421 | 427 | 1347.2 |
3000 | 270 | 268 | 413 | 427 | 643.9 |
4000 | 298 | 280 | 410 | 403 | -235.7 |
5000 | 315 | 285 | 460 | 305 | -785.4 |
8000 | 335 | 290 | 459 | 303 | -1436.7 |
10000 | 333 | 285 | 457 | 302 | -2578.8 |
30000 | 331 | 283 | 455 | 301 | -3521.6 |
50000 | 333 | 288 | 454 | 300 | -4076.4 |
| | | | | |
0 | 271 | 281 | 427 | 429 | 3283.9 |
1000 | 270 | 278 | 426 | 428 | 2475.8 |
2000 | 265 | 273 | 421 | 427 | 1347.2 |
3000 | 270 | 268 | 413 | 427 | 643.9 |
4000 | 298 | 280 | 410 | 403 | -235.7 |
5000 | 315 | 285 | 460 | 305 | -785.4 |
8000 | 335 | 290 | 459 | 303 | -1436.7 |
10000 | 333 | 285 | 457 | 302 | -2578.8 |
30000 | 331 | 283 | 455 | 301 | -3521.6 |
50000 | 333 | 288 | 454 | 300 | -4076.4 |
| | | | | |
0 | 40 | 23 | 15 | 25 | 8.5853 |
1000 | 36 | 22 | 14 | 25 | 0.1422 |
2000 | 37 | 23 | 16 | 23 | -32.983 |
3000 | 39 | 24 | 18 | 21 | -421.655 |
4000 | 41 | 25 | 20 | 20 | -1674.67 |
5000 | 43 | 25 | 22 | 18 | -1975.9 |
8000 | 45 | 28 | 23 | 15 | -3452.9 |
10000 | 43 | 27 | 25 | 13 | -3987.0 |
30000 | 41 | 25 | 26 | 12 | -5436.9 |
50000 | 43 | 27 | 27 | 11 | -6475.8 |
| | | | | |
0 | 40 | 23 | 15 | 25 | 8.5853 |
1000 | 36 | 22 | 14 | 25 | 0.1422 |
2000 | 37 | 23 | 16 | 23 | -32.983 |
3000 | 39 | 24 | 18 | 21 | -421.655 |
4000 | 41 | 25 | 20 | 20 | -1674.67 |
5000 | 43 | 25 | 22 | 18 | -1975.9 |
8000 | 45 | 28 | 23 | 15 | -3452.9 |
10000 | 43 | 27 | 25 | 13 | -3987.0 |
30000 | 41 | 25 | 26 | 12 | -5436.9 |
50000 | 43 | 27 | 27 | 11 | -6475.8 |
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