doi: 10.3934/jimo.2017069

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

3. 

School of Business Central South University, Changsha 410083, China

* Corresponding author: shenzhen@csu.edu.cn

The reviewing process was handled by Changjun Yu.

Received  December 2015 Revised  December 2016 Published  June 2017

Fund Project: The Paper is supported by NNSF grants (No. 71221061, 71210003, 71431006, 71471178, 71171201, 71671189) and NCET grant( No. NCET-11-0524)

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.

Citation: Yanju Zhou, Zhen Shen, Renren Ying, Xuanhua Xu. A loss-averse two-product ordering model with information updating in two-echelon inventory system. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2017069
References:
[1]

L. Abdel-MalekR. 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. DvoretzkyJ. 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. EeckhoudtC. 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. LiuS. 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. MaY. ZhaoW. XueT. 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. QinR. WangA. J. VakhariaY. 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. ThalerA. TverskyD. 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. ZhangD. ZhangY. 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. ZhouX. ChenX. 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. ZhouW. 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. ZhouR. YingX. 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

References:
[1]

L. Abdel-MalekR. 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. DvoretzkyJ. 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. EeckhoudtC. 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. LiuS. 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. MaY. ZhaoW. XueT. 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. QinR. WangA. J. VakhariaY. 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. ThalerA. TverskyD. 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. ZhangD. ZhangY. 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. ZhouX. ChenX. 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. ZhouW. 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. ZhouR. YingX. Chen and Z. Wang, Two-product newsboy problem based on prospect theory, Journal of Management Sciences in China, 11 (2013), 17-29.

Figure 1.  The Time Line of the Event
Table 1.  Updated Demand Information Values of Two products
$\ u^{IU}_{A1}\ $ $\ \sigma^{IU2}_{A1}\ $ $\ u^{IU}_{A2}\ $ $\ \sigma^{IU2}_{A2}\ $ $\ u^{IU}_{B1}\ $ $\ \sigma^{IU2}_{B1}\ $ $\ u^{IU}_{B2}\ $ $\ \sigma^{IU2}_{B2}\ $
200123.6940063.7220057.4440059.79
$\ u^{IU}_{A1}\ $ $\ \sigma^{IU2}_{A1}\ $ $\ u^{IU}_{A2}\ $ $\ \sigma^{IU2}_{A2}\ $ $\ u^{IU}_{B1}\ $ $\ \sigma^{IU2}_{B1}\ $ $\ u^{IU}_{B2}\ $ $\ \sigma^{IU2}_{B2}\ $
200123.6940063.7220057.4440059.79
Table 2.  Optimal Order Quantity with Different Psychological Reference Points and Information Updating
$\ \pi_0\ $ $\ x^{*}_{A1}\ $ $\ x^{*}_{B1}\ $ $\ x^{*}_{A2}\ $ $\ x^{*}_{B2}\ $ $\ U^*(\mathbf{x^*})\ $
02712814274293283.9
10002702784264282475.8
20002652734214271347.2
3000270268413427643.9
4000298280410403-235.7
5000315285460305-785.4
8000335290459303-1436.7
10000333285457302-2578.8
30000331283455301-3521.6
50000333288454300-4076.4
$\ \pi_0\ $ $\ x^{*}_{A1}\ $ $\ x^{*}_{B1}\ $ $\ x^{*}_{A2}\ $ $\ x^{*}_{B2}\ $ $\ U^*(\mathbf{x^*})\ $
02712814274293283.9
10002702784264282475.8
20002652734214271347.2
3000270268413427643.9
4000298280410403-235.7
5000315285460305-785.4
8000335290459303-1436.7
10000333285457302-2578.8
30000331283455301-3521.6
50000333288454300-4076.4
Table 3.  Optimal Order Quantity with Different Psychological Reference Points and No Information Updating
$\ \pi_0\ $ $\ x^{*}_{A1}\ $ $\ x^{*}_{B1}\ $ $\ x^{*}_{A2}\ $ $\ x^{*}_{B2}\ $ $\ U^*(\mathbf{x^*})\ $
0402315258.5853
1000362214250.1422
200037231623-32.983
300039241821-421.655
400041252020-1674.67
500043252218-1975.9
800045282315-3452.9
1000043272513-3987.0
3000041252612-5436.9
5000043272711-6475.8
$\ \pi_0\ $ $\ x^{*}_{A1}\ $ $\ x^{*}_{B1}\ $ $\ x^{*}_{A2}\ $ $\ x^{*}_{B2}\ $ $\ U^*(\mathbf{x^*})\ $
0402315258.5853
1000362214250.1422
200037231623-32.983
300039241821-421.655
400041252020-1674.67
500043252218-1975.9
800045282315-3452.9
1000043272513-3987.0
3000041252612-5436.9
5000043272711-6475.8
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