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Novel correlation coefficients under the intuitionistic multiplicative environment and their applications to decision-making process
Optimal pricing and inventory management for a loss averse firm when facing strategic customers
1. | Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China |
2. | Department of Mathematics and Physics, Beijing Institute of Petrochemical Technology, Beijing 102617, China |
This paper considers the joint inventory and pricing decision problem that a loss averse firm with reference point selling seasonal products to strategic consumers with risk preference and decreasing value. Consumers can decide whether to buy at the full price in stage 1, or to wait till stage 2 for the salvage price. They may not get the product if the product is sold out in stage 2. The firm aims to choose a base stock policy and find an optimal price to maximize its expected utility, while consumers aim to decide whether to buy or wait strategically for optimizing their payoffs. We formulate the problem as a Stackelberg game between the firm and the strategic consumers in which the firm is the leader. By deriving the rational expectation equilibrium, we find both the optimal stocking level and the full price in our model are lower than those in the classical model without strategic consumers, by which leads to a lower profit. Furthermore, it is shown that the reimbursement contract cannot alleviate the impact of strategic behavior of customers while the firm's profit can be improved by the price commitment strategy in most cases. Numerical studies are carried out to investigate the impact of strategic customer behavior and system parameters on the firm's optimal decisions.
References:
[1] |
S. Anily and R. Hassin,
Pricing, replenishment, and timing of selling in a market with heterogeneous customers, International Journal of Production Economics, 145 (2013), 672-682.
|
[2] |
Y. Aviv and A. Pazgal,
Optimal pricing of seasonal products in the presence of forward-looking consumers, Manuf. Serv. Oper. Manag., 10 (2008), 339-359.
|
[3] |
O. Baron, M. Hu, S. Najafi-Asadolahi and Q. Qian,
Newsvendor selling to loss-averse consumers with stochastic reference points, Manuf. Serv. Oper. Manag., 17 (2015), 456-469.
|
[4] |
O. Besbes and I. Lobel,
Intertemporal price discrimination: Structure and computation of optimal policies, Management Science, 61 (2015), 92-110.
|
[5] |
J. I. Bulow,
Durable-goods monopolist, J. Political Econom, 90 (1982), 314-332.
|
[6] |
G. P. Cachon and R. Swinney,
Purchasing, pricing, and quick response in the presence of strategic consumer behavior, Management Science, 55 (2009), 497-511.
|
[7] |
G. P. Cachon and R. Swinney,
The value of fast fasion: Quick response, enhanced design, and strategic consumer behavior, Management Science, 57 (2011), 778-795.
|
[8] |
R. H. Coase,
Durability and monopoly, J. Law Econom., 15 (1972), 143-149.
|
[9] |
J. R. Correa, R. Montoya and C. Thraves,
Contingent preannounced pricing policies with strategic consumers, Operations Research, 64 (2016), 251-272.
doi: 10.1287/opre.2015.1452. |
[10] |
J. Du, J. Zhang and G. Hua,
Pricing and inventory management in the presence of strategic customer with risk preference and decreasing value, International Journal of Production Economics, 164 (2015), 160-166.
|
[11] |
L. Eeckhoudt, C. Gollier and H. Schlesinger,
The risk-averse (and prudent) newsboy, Management Science, 41 (1995), 786-794.
|
[12] |
X. D. He and X. Y. Zhou,
Portfolio choice under cumulative prospect theory: An analytical treatment, Management Science, 57 (2011), 315-331.
|
[13] |
X. D. He and X. Y. Zhou,
Myopic loss aversion, reference point, and money illusion, Quant. Finance, 14 (2014), 1541-1554.
doi: 10.1080/14697688.2014.917805. |
[14] |
P. Heidhues and B. Koszegi,
The Impact of Consumer Loss Averse on Pricing, Woking paper, University of California, Berkeley, 2005. |
[15] |
P. Heidhues and B. Koszegi,
Competition and price variation when consumers are loss averse, Amer. Econom. Rev., 98 (2008), 1245-1268.
|
[16] |
P. Heidhues and B. Koszegi,
Regular prices and sales, Theor. Econom., 9 (2014), 217-251.
doi: 10.3982/TE1274. |
[17] |
D. Kahneman and A. Tversky,
Prospect theory: An analysis of decision under risk, Econometrica, 47 (1979), 263-291.
|
[18] |
B. Keren and J. S. Pliskin,
A benchmark solution for the risk-averse newsvendor problem, Eur. J. Oper. Res., 37 (2006), 1463-1650.
|
[19] |
V. Kobberling and P. P. Wakker,
An index of loss aversion, J. of Economic Theory, 122 (2005), 119-131.
doi: 10.1016/j.jet.2004.03.009. |
[20] |
B. Koszegi and M. Rabin,
A model of reference-dependent preferences, Quart. J. Econ., 121 (2006), 1133-1165.
|
[21] |
J. Li, N. Granedos and S. Netessine,
Are consumers strategic? structural estimation from the air travel industry, Management Science, 60 (2014), 2114-2137.
|
[22] |
Q. Liu and G. J. van Ryzin,
Strategic capacity rationing to induce early purchases, Management Science, 54 (2008), 1115-1131.
|
[23] |
X. Y. Long and J. Nasiry,
Prospect theory explain newsvendor behavior: The role of reference points, Management Science, 60 (2014), 1057-1062.
|
[24] |
J. F. Muth,
Rational expectations and the theory of price movements, Econometrica, 29 (1961), 315-335.
|
[25] |
M. Nagarajan and S. Shechter,
Prospect theory and the newsvendor problem, Management Science, 60 (2014), 1057-1062.
|
[26] |
M. Pervin, S. K. Roy and G. W. Weber,
Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration, Annals of Operations Research, 253 (2016), 1-24.
|
[27] |
M. Pervin, S. K. Roy and G. C. Mahata,
An inventory model with demand declining market for deteriorating items under trade credit policy, International Journal of Management Science and Engineering Management, 11 (2016), 243-251.
|
[28] |
M. Pervin, S. K. Roy and G. W. Weber,
A Two-echelon inventory model with stock-dependent demand and variable holding cost for deteriorating items, Numerical Algebra, Control and Optimization, 7 (2017), 21-50.
doi: 10.3934/naco.2017002. |
[29] |
Porteus and L. Evan, Foundations of Stochastic Inventory Theory, Stanford University Press, 2002.
![]() |
[30] |
P. Ray and M. Jenamani,
Mean-variance analysis of souring decision under disruption risk, Eur. J. Oper. Res., 250 (2015), 679-689.
doi: 10.1016/j.ejor.2015.09.028. |
[31] |
J. Rubio-Herrero, M. Baykal-Gursoy and A. Jaskiewicz,
A price setting newsvendor problem under mean-variance criteria, Eur. J. Oper. Res., 247 (2015), 575-587.
doi: 10.1016/j.ejor.2015.06.006. |
[32] |
Z. J. Shen and X. Su,
Customer behavior modeling in revenue management and auctions: A review and new research opportunities, Production and Operations Management, 16 (2007), 713-728.
|
[33] |
Y. Shi, X. Y. Cui, J. Yao and D. Li,
Dynamic trading with reference point adaptation and loss aversion, Operations Research, 63 (2015), 789-806.
doi: 10.1287/opre.2015.1399. |
[34] |
X. Su,
Intertemporal pricing with strategic customer behavior, Management Science, 53 (2007), 726-741.
|
[35] |
X. Su and F. Zhang,
Strategic customer behavior, commitment, and supply chain performance, Management Science, 54 (2008), 1759-1773.
|
[36] |
N. L. Stokey,
Rational expectation and durable goods pricing, The Bell Journal of Economics, 12 (1981), 112-128.
doi: 10.2307/3003511. |
[37] |
C. X. Wang, S. Webster and N. Surech,
Would a risk-averse newsvendor order less at a highter selling price?, Eur. J. Oper. Res., 196 (2009), 544-553.
doi: 10.1016/j.ejor.2008.04.002. |
[38] |
J. Wu, J. Li, S. Y. Wang and T. C. E. Cheng,
Mean-variance analysis of the newsvendor model with stockout cost, Omega, 37 (2009), 724-730.
|
[39] |
R. Yin, Y. Aviv, A. Pazgal and C. S. Tang,
Optimal markdown pricing: Implications of inventory display formats in the presence of strategic customers, Management Science, 55 (2009), 1391-1408.
|
[40] |
P. H. Zipkin,
Foundations of Inventory Management, McGraw-Hill/Irwin, 2000. |
show all references
References:
[1] |
S. Anily and R. Hassin,
Pricing, replenishment, and timing of selling in a market with heterogeneous customers, International Journal of Production Economics, 145 (2013), 672-682.
|
[2] |
Y. Aviv and A. Pazgal,
Optimal pricing of seasonal products in the presence of forward-looking consumers, Manuf. Serv. Oper. Manag., 10 (2008), 339-359.
|
[3] |
O. Baron, M. Hu, S. Najafi-Asadolahi and Q. Qian,
Newsvendor selling to loss-averse consumers with stochastic reference points, Manuf. Serv. Oper. Manag., 17 (2015), 456-469.
|
[4] |
O. Besbes and I. Lobel,
Intertemporal price discrimination: Structure and computation of optimal policies, Management Science, 61 (2015), 92-110.
|
[5] |
J. I. Bulow,
Durable-goods monopolist, J. Political Econom, 90 (1982), 314-332.
|
[6] |
G. P. Cachon and R. Swinney,
Purchasing, pricing, and quick response in the presence of strategic consumer behavior, Management Science, 55 (2009), 497-511.
|
[7] |
G. P. Cachon and R. Swinney,
The value of fast fasion: Quick response, enhanced design, and strategic consumer behavior, Management Science, 57 (2011), 778-795.
|
[8] |
R. H. Coase,
Durability and monopoly, J. Law Econom., 15 (1972), 143-149.
|
[9] |
J. R. Correa, R. Montoya and C. Thraves,
Contingent preannounced pricing policies with strategic consumers, Operations Research, 64 (2016), 251-272.
doi: 10.1287/opre.2015.1452. |
[10] |
J. Du, J. Zhang and G. Hua,
Pricing and inventory management in the presence of strategic customer with risk preference and decreasing value, International Journal of Production Economics, 164 (2015), 160-166.
|
[11] |
L. Eeckhoudt, C. Gollier and H. Schlesinger,
The risk-averse (and prudent) newsboy, Management Science, 41 (1995), 786-794.
|
[12] |
X. D. He and X. Y. Zhou,
Portfolio choice under cumulative prospect theory: An analytical treatment, Management Science, 57 (2011), 315-331.
|
[13] |
X. D. He and X. Y. Zhou,
Myopic loss aversion, reference point, and money illusion, Quant. Finance, 14 (2014), 1541-1554.
doi: 10.1080/14697688.2014.917805. |
[14] |
P. Heidhues and B. Koszegi,
The Impact of Consumer Loss Averse on Pricing, Woking paper, University of California, Berkeley, 2005. |
[15] |
P. Heidhues and B. Koszegi,
Competition and price variation when consumers are loss averse, Amer. Econom. Rev., 98 (2008), 1245-1268.
|
[16] |
P. Heidhues and B. Koszegi,
Regular prices and sales, Theor. Econom., 9 (2014), 217-251.
doi: 10.3982/TE1274. |
[17] |
D. Kahneman and A. Tversky,
Prospect theory: An analysis of decision under risk, Econometrica, 47 (1979), 263-291.
|
[18] |
B. Keren and J. S. Pliskin,
A benchmark solution for the risk-averse newsvendor problem, Eur. J. Oper. Res., 37 (2006), 1463-1650.
|
[19] |
V. Kobberling and P. P. Wakker,
An index of loss aversion, J. of Economic Theory, 122 (2005), 119-131.
doi: 10.1016/j.jet.2004.03.009. |
[20] |
B. Koszegi and M. Rabin,
A model of reference-dependent preferences, Quart. J. Econ., 121 (2006), 1133-1165.
|
[21] |
J. Li, N. Granedos and S. Netessine,
Are consumers strategic? structural estimation from the air travel industry, Management Science, 60 (2014), 2114-2137.
|
[22] |
Q. Liu and G. J. van Ryzin,
Strategic capacity rationing to induce early purchases, Management Science, 54 (2008), 1115-1131.
|
[23] |
X. Y. Long and J. Nasiry,
Prospect theory explain newsvendor behavior: The role of reference points, Management Science, 60 (2014), 1057-1062.
|
[24] |
J. F. Muth,
Rational expectations and the theory of price movements, Econometrica, 29 (1961), 315-335.
|
[25] |
M. Nagarajan and S. Shechter,
Prospect theory and the newsvendor problem, Management Science, 60 (2014), 1057-1062.
|
[26] |
M. Pervin, S. K. Roy and G. W. Weber,
Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration, Annals of Operations Research, 253 (2016), 1-24.
|
[27] |
M. Pervin, S. K. Roy and G. C. Mahata,
An inventory model with demand declining market for deteriorating items under trade credit policy, International Journal of Management Science and Engineering Management, 11 (2016), 243-251.
|
[28] |
M. Pervin, S. K. Roy and G. W. Weber,
A Two-echelon inventory model with stock-dependent demand and variable holding cost for deteriorating items, Numerical Algebra, Control and Optimization, 7 (2017), 21-50.
doi: 10.3934/naco.2017002. |
[29] |
Porteus and L. Evan, Foundations of Stochastic Inventory Theory, Stanford University Press, 2002.
![]() |
[30] |
P. Ray and M. Jenamani,
Mean-variance analysis of souring decision under disruption risk, Eur. J. Oper. Res., 250 (2015), 679-689.
doi: 10.1016/j.ejor.2015.09.028. |
[31] |
J. Rubio-Herrero, M. Baykal-Gursoy and A. Jaskiewicz,
A price setting newsvendor problem under mean-variance criteria, Eur. J. Oper. Res., 247 (2015), 575-587.
doi: 10.1016/j.ejor.2015.06.006. |
[32] |
Z. J. Shen and X. Su,
Customer behavior modeling in revenue management and auctions: A review and new research opportunities, Production and Operations Management, 16 (2007), 713-728.
|
[33] |
Y. Shi, X. Y. Cui, J. Yao and D. Li,
Dynamic trading with reference point adaptation and loss aversion, Operations Research, 63 (2015), 789-806.
doi: 10.1287/opre.2015.1399. |
[34] |
X. Su,
Intertemporal pricing with strategic customer behavior, Management Science, 53 (2007), 726-741.
|
[35] |
X. Su and F. Zhang,
Strategic customer behavior, commitment, and supply chain performance, Management Science, 54 (2008), 1759-1773.
|
[36] |
N. L. Stokey,
Rational expectation and durable goods pricing, The Bell Journal of Economics, 12 (1981), 112-128.
doi: 10.2307/3003511. |
[37] |
C. X. Wang, S. Webster and N. Surech,
Would a risk-averse newsvendor order less at a highter selling price?, Eur. J. Oper. Res., 196 (2009), 544-553.
doi: 10.1016/j.ejor.2008.04.002. |
[38] |
J. Wu, J. Li, S. Y. Wang and T. C. E. Cheng,
Mean-variance analysis of the newsvendor model with stockout cost, Omega, 37 (2009), 724-730.
|
[39] |
R. Yin, Y. Aviv, A. Pazgal and C. S. Tang,
Optimal markdown pricing: Implications of inventory display formats in the presence of strategic customers, Management Science, 55 (2009), 1391-1408.
|
[40] |
P. H. Zipkin,
Foundations of Inventory Management, McGraw-Hill/Irwin, 2000. |





Contributions | Risk preference of Customers | Decreasing value | Loss aversion |
Su & Zhang (2008) | - | - | - |
Liu & Van (2008) | - | - | |
Aviv & Pazgal (2008) | - | - | |
Du, Zhang & Hua (2015) | - | ||
This paper |
Contributions | Risk preference of Customers | Decreasing value | Loss aversion |
Su & Zhang (2008) | - | - | - |
Liu & Van (2008) | - | - | |
Aviv & Pazgal (2008) | - | - | |
Du, Zhang & Hua (2015) | - | ||
This paper |
Notation | Description |
The full price of unit product in classical model, the model with strategic customers and the model with reimbursement contract, respectively in period 1 | |
The stocking quantity in classical model, the model with strategic customers and the model with reimbursement contract, respectively | |
Decision variables denoting stocking quantity and full price, respectively | |
Nonnegative and independent random variable, which indicates customers' demand | |
Cumulative distribution function, characterizing the demand, and tail distribution is |
|
Partial expectation of random |
|
Salvage price in period 2 | |
Unit procurement cost of the product to the firm | |
Customers' valuation for the unit production | |
Customers' reservation price or maximum price which the customers are willing to pay | |
The firm's belief over customers' reservation price | |
Customers' belief from obtaining the product on the salvage market | |
The decreasing rate ( |
|
Customers' risk preference ( |
|
The firm's loss aversion ( |
|
Expectation operator | |
Utility function of the firm | |
The maximum and minimal function between |
Notation | Description |
The full price of unit product in classical model, the model with strategic customers and the model with reimbursement contract, respectively in period 1 | |
The stocking quantity in classical model, the model with strategic customers and the model with reimbursement contract, respectively | |
Decision variables denoting stocking quantity and full price, respectively | |
Nonnegative and independent random variable, which indicates customers' demand | |
Cumulative distribution function, characterizing the demand, and tail distribution is |
|
Partial expectation of random |
|
Salvage price in period 2 | |
Unit procurement cost of the product to the firm | |
Customers' valuation for the unit production | |
Customers' reservation price or maximum price which the customers are willing to pay | |
The firm's belief over customers' reservation price | |
Customers' belief from obtaining the product on the salvage market | |
The decreasing rate ( |
|
Customers' risk preference ( |
|
The firm's loss aversion ( |
|
Expectation operator | |
Utility function of the firm | |
The maximum and minimal function between |
465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | |||
298.9421 | 162.4174 | 304.5730 | 175.2384 | 309.4728 | 185.7115 | ||||||
403.3333 | 403.3333 | 402.8578 | 402.8578 | 401.5556 | 401.5556 | ||||||
465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | |||
394.9592 | 260.6531 | 94.1742 | 395.8801 | 264.8910 | 105.3170 | 396.6050 | 268.5129 | 113.9793 | |||
403.3333 | 403.3333 | 403.3333 | 402.8578 | 402.8578 | 402.8578 | 401.5556 | 401.5556 | 401.5556 | |||
465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | |||
388.0647 | 235.1442 | 46.7179 | 388.5513 | 237.8978 | 54.9701 | 388.8571 | 240.1336 | 60.9781 | |||
403.3333 | 403.3333 | 403.3333 | 402.8578 | 402.8578 | 402.8578 | 401.5556 | 401.5556 | 401.5556 | |||
384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | |||
256.3412 | 154.3494 | 264.0884 | 169.3020 | 270.0823 | 180.6548 | ||||||
333.3333 | 333.3333 | 332.4099 | 332.4099 | 330 | 330 | ||||||
384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | |||
323.4039 | 212.4169 | 84.3076 | 324.9323 | 218.7253 | 96.7836 | 325.7676 | 223.4203 | 105.7881 | |||
333.3333 | 333.3333 | 333.3333 | 332.4099 | 332.4099 | 332.4099 | 330 | 330 | 330 | |||
384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | |||
313.9245 | 180.8531 | 36.9033 | 314.7191 | 185.1787 | 45.1564 | 314.8643 | 188.0670 | 50.7402 | |||
333.3333 | 333.3333 | 333.3333 | 332.4099 | 332.4099 | 332.4099 | 330 | 330 | 330 | |||
311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | |||
214.7582 | 138.5999 | 223.2811 | 153.8583 | 228.8967 | 164.4633 | ||||||
270 | 270 | 268.5185 | 268.5185 | 264.8633 | 264.8633 | ||||||
311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | |||
259.6189 | 169.7678 | 71.4952 | 261.4923 | 177.1413 | 83.8399 | 261.8907 | 181.7852 | 92.0999 | |||
270 | 270 | 270 | 268.5185 | 268.5185 | 268.5185 | 264.8633 | 264.8633 | 264.8633 | |||
311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | |||
248.2615 | 135.5270 | 27.4710 | 249.1956 | 140.7354 | 34.7699 | 248.7501 | 143.5081 | 39.4236 | |||
270 | 270 | 270 | 268.5185 | 268.5185 | 268.5185 | 264.8633 | 264.8633 | 264.8633 | |||
96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | |||
29.5585 | 24.7304 | 26.4622 | |||||||||
30 | 30 | 28.2369 | |||||||||
96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | |||
27.4769 | 17.5997 | 8.61672 | 27.3621 | 19.2783 | 10.8693 | 19.0687 | 11.674 | ||||
30 | 30 | 30 | 28.2369 | 28.2369 | 28.2369 | 25.4313 | 25.4313 | ||||
96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | |||
20.6633 | 6.42676 | 0.8171 | 20.8133 | 7.6716 | 1.2734 | 19.6287 | 7.9764 | 1.5628 | |||
30 | 30 | 30 | 28.2369 | 28.2369 | 28.2369 | 25.4313 | 25.4313 | 25.4313 | |||
Note: The expected profits are the classical inventory model, the proposed model and the model under price commitment strategy in turn. We mark by red and green color when the expected profit of our model is larger than that of under price commitment strategy model. |
465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | |||
298.9421 | 162.4174 | 304.5730 | 175.2384 | 309.4728 | 185.7115 | ||||||
403.3333 | 403.3333 | 402.8578 | 402.8578 | 401.5556 | 401.5556 | ||||||
465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | |||
394.9592 | 260.6531 | 94.1742 | 395.8801 | 264.8910 | 105.3170 | 396.6050 | 268.5129 | 113.9793 | |||
403.3333 | 403.3333 | 403.3333 | 402.8578 | 402.8578 | 402.8578 | 401.5556 | 401.5556 | 401.5556 | |||
465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | 465.3846 | |||
388.0647 | 235.1442 | 46.7179 | 388.5513 | 237.8978 | 54.9701 | 388.8571 | 240.1336 | 60.9781 | |||
403.3333 | 403.3333 | 403.3333 | 402.8578 | 402.8578 | 402.8578 | 401.5556 | 401.5556 | 401.5556 | |||
384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | |||
256.3412 | 154.3494 | 264.0884 | 169.3020 | 270.0823 | 180.6548 | ||||||
333.3333 | 333.3333 | 332.4099 | 332.4099 | 330 | 330 | ||||||
384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | |||
323.4039 | 212.4169 | 84.3076 | 324.9323 | 218.7253 | 96.7836 | 325.7676 | 223.4203 | 105.7881 | |||
333.3333 | 333.3333 | 333.3333 | 332.4099 | 332.4099 | 332.4099 | 330 | 330 | 330 | |||
384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | 384.6154 | |||
313.9245 | 180.8531 | 36.9033 | 314.7191 | 185.1787 | 45.1564 | 314.8643 | 188.0670 | 50.7402 | |||
333.3333 | 333.3333 | 333.3333 | 332.4099 | 332.4099 | 332.4099 | 330 | 330 | 330 | |||
311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | |||
214.7582 | 138.5999 | 223.2811 | 153.8583 | 228.8967 | 164.4633 | ||||||
270 | 270 | 268.5185 | 268.5185 | 264.8633 | 264.8633 | ||||||
311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | |||
259.6189 | 169.7678 | 71.4952 | 261.4923 | 177.1413 | 83.8399 | 261.8907 | 181.7852 | 92.0999 | |||
270 | 270 | 270 | 268.5185 | 268.5185 | 268.5185 | 264.8633 | 264.8633 | 264.8633 | |||
311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | 311.5384 | |||
248.2615 | 135.5270 | 27.4710 | 249.1956 | 140.7354 | 34.7699 | 248.7501 | 143.5081 | 39.4236 | |||
270 | 270 | 270 | 268.5185 | 268.5185 | 268.5185 | 264.8633 | 264.8633 | 264.8633 | |||
96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | |||
29.5585 | 24.7304 | 26.4622 | |||||||||
30 | 30 | 28.2369 | |||||||||
96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | |||
27.4769 | 17.5997 | 8.61672 | 27.3621 | 19.2783 | 10.8693 | 19.0687 | 11.674 | ||||
30 | 30 | 30 | 28.2369 | 28.2369 | 28.2369 | 25.4313 | 25.4313 | ||||
96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | 96.1538 | |||
20.6633 | 6.42676 | 0.8171 | 20.8133 | 7.6716 | 1.2734 | 19.6287 | 7.9764 | 1.5628 | |||
30 | 30 | 30 | 28.2369 | 28.2369 | 28.2369 | 25.4313 | 25.4313 | 25.4313 | |||
Note: The expected profits are the classical inventory model, the proposed model and the model under price commitment strategy in turn. We mark by red and green color when the expected profit of our model is larger than that of under price commitment strategy model. |
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