需求不确定性下概率销售与快速响应模式对比

doi:10.16381/j.cnki.issn1003-207x.2024.1677

Abstract

Abstract:

With the rapid development of the digital economy and consumers' growing pursuit of personalization， consumer demand has become more uncertain. To help retailers make inventory management and pricing strategies better， three ways to address this challenge are analyzed， that is， probabilistic selling， quick response， and a hybrid mode combining the two. The probabilistic selling mode refers to the retailer combining normally sold products into probabilistic products and offering consumers the opportunity to obtain one of them at a lower price. The quick response mode involves timely replenishment of out-of-stock products after the retailer observes the actual market demand. The two-stage sales model is constructed and the impact of different selling modes on retailers' decisions （e.g.， order quantity and pricing） and profits is explored in traditional and strategic consumer markets， respectively. Firstly， the performance of the three modes in different market environments is compared. Secondly， the effects of strategic consumers on the retailer's optimal strategies are analyzed. The research shows that the probabilistic selling and hybrid mode generate more profits for retailers than the quick response mode in most cases. The hybrid mode outperforms when the quick response cost is low and the ordering cost is high； otherwise， the probabilistic selling mode is more advantageous. Moreover， the relative advantage of the probabilistic selling mode increases as market demand uncertainty rises under the high quick response cost.

Key words: probability selling, quick response, strategic consumers, uncertain demand, hotelling model

CLC Number:

F274

Mingyang Zhang,Lan Deng,Juliang Zhang, et al. Comparison of Probabilistic Sales and Quick Response under Demand Uncertainty[J]. Chinese Journal of Management Science, 2026, 34(8): 195-209.

Figures/Tables 13

符号	变量说明
$c j$	产品j的正常订货单位成本， $c 1 = c 2 ≡ c$
$q j$	产品j的订货量， $q 1 = q 2 ≡ q$
$p j$	第一阶段的销售价格， $p 1 = p 2 ≡ p$
$x i$	消费者i在Hotelling线上的位置
$v j i$	消费者i对产品j的估值
$d j$	产品j的需求
$N$	潜在消费者总人数
$p p r o$	第二阶段概率产品的价格
$p P S , p Q R , p P S + Q R *$	零售商的最优定价
$q P S , q Q R , q P S + Q R *$	零售商的最优订货量
$π P S , π Q R , π P S + Q R *$	零售商的最优利润

符号	参数定义
$ξ p r o b$	考虑策略型消费者时，消费者对第二阶段获得产品的可能性的预期， $0 ≤ ξ p r o b ≤ 1$
$γ$	考虑策略型消费者时，策略型消费者心仪产品所占比例
$q P S s t r a , q P S + Q R s t r a $	考虑策略型消费者时，零售商在两种模式下的最优订货量
$p P S s t r a , p P S + Q R s t r a $	考虑策略型消费者时，零售商在两种模式下的最优定价
$π P S s t r a , π P S + Q R s t r a $	考虑策略型消费者时，零售商在两种模式下的最优利润

$c$	$π P S n o s t r a * - π Q R n o s t r a *$				$q P S n o s t r a * - q Q R n o s t r a *$				$p P S n o s t r a * - p Q R n o s t r a *$
$c$	$σ = 20$	$σ = 30$	$σ = 40$	$σ = 50$	$σ = 20$	$σ = 30$	$σ = 40$	$σ = 50$	$σ = 20$	$σ = 30$	$σ = 40$	$σ = 50$
0.05	12.272	12.226	12.426	13.279	4.2432	5.2839	6.5117	8.5512	0.2162	0.2121	0.2122	0.2227
0.1	11.772	11.642	11.703	12.278	6.9563	8.1265	9.3881	10.852	0.1855	0.1785	0.1754	0.1817
0.15	11.067	10.871	10.823	11.189	9.1747	10.198	11.29	12.491	0.1559	0.1467	0.1413	0.1446
0.2	10.189	9.967	9.8514	10.065	11.03	11.71	12.47	13.36	0.1271	0.116	0.1088	0.1102
0.25	9.1665	8.97	8.8373	8.9503	12.557	12.73	13.059	13.626	0.0989	0.0862	0.0781	0.0786
0.3	8.0253	7.9186	7.8205	7.8784	13.738	13.254	13.151	13.446	0.071	0.0573	0.0498	0.0504
0.35	6.7973	6.8546	6.8332	6.8701	14.485	13.248	12.83	12.929	0.0435	0.03	0.0245	0.0258
0.4	5.5295	5.8235	5.9012	5.9395	14.581	12.697	12.17	12.154	0.0163	0.0055	0.0028	0.0046
0.45	4.3063	4.8701	5.0445	5.0952	13.448	11.647	11.237	11.189	-0.0098	-0.0144	-0.0152	-0.0132
0.5	3.2867	4.0313	4.2765	4.3399	10.462	10.233	10.122	10.117	-0.0275	-0.0288	-0.0296	-0.0281

$c$	$π P S n o s t r a * - π Q R n o s t r a *$
$c$	$σ = 20$	$σ = 30$	$σ = 40$	$σ = 50$
0.05	6.3879	7.36	7.7513	7.9023
0.1	6.3245	7.1574	7.4252	7.8508
0.15	6.0446	6.7102	7.1421	7.5343
0.2	5.4752	6.0284	6.6264	6.8965
0.25	4.6157	5.3565	5.8106	6.0079
0.3	3.7867	4.4137	4.7657	5.1724
0.35	2.9788	3.4464	3.7766	4.0581
0.4	2.2325	2.5889	2.8398	2.9924
0.45	1.583	1.8051	1.9457	2.0656
0.5	1.0208	1.1706	1.3012	1.4229

	$c$	$π P S s t r a * - π P S + Q R s t r a *$				$q P S s t r a * - q P S + Q R s t r a *$				$p P S s t r a * - p P S + Q R s t r a *$
	$c$	$σ = 20$	$σ = 30$	$σ = 40$	$σ = 50$	$σ = 20$	$σ = 30$	$σ = 40$	$σ = 50$	$σ = 20$	$σ = 30$	$σ = 40$	$σ = 50$
$c + c Q p$	0.05	4E-06	0.0059	0.0954	0.399	3E-06	0.0074	0.1505	0.8362	4E-08	6E-05	0.0009	0.0039
	0.1	2E-06	0.0027	0.0421	0.1725	1E-06	0.0023	0.0461	0.2361	3E-08	5E-05	0.0008	0.0034
	0.15	5E-13	5E-07	0.0001	0.0024	7E-12	5E-07	5E-05	0.003	3E-08	5E-05	0.0008	0.0032
$c + c Q p$	0.2	-2E-06	-0.002	-0.035	-0.135	-8E-07	-0.002	-0.043	-0.223	3E-08	4E-05	0.0007	0.0025
	0.25	-3E-06	-0.004	-0.045	-0.171	-3E-06	-0.007	-0.127	-0.486	-2E-09	-2E-05	-0.004	-0.004
	0.3	-3E-06	0.001	0.1077	-0.012	-3E-05	-0.033	-0.251	-0.79	-5E-07	-0.004	-0.007	-0.005
	0.35	1E-05	0.2417	0.4004	0.2943	-5E-04	0.0713	-0.48	-1.085	-8E-06	-0.009	-0.005	-0.004
	0.4	0.0396	0.6053	0.8016	0.7118	0.7098	-0.092	-0.605	-1.221	-0.025	-0.005	-0.002	-6E-04
	0.45	0.5522	1.0739	1.2767	1.1888	0.8131	-0.026	-0.43	-0.999	-0.007	-2E-04	0.0026	0.0045
	0.5	1.1264	1.6035	1.7518	1.6422	1.6273	0.7088	0.4238	-0.101	-6E-04	0.0061	0.0086	0.0106

$c$	$π P S s t r a * - π P S + Q R s t r a *$				$q P S s t r a * - q P S + Q R s t r a *$				$p P S s t r a * - p P S + Q R s t r a *$
$c$	$σ = 20$	$σ = 30$	$σ = 40$	$σ = 50$	$σ = 20$	$σ = 30$	$σ = 40$	$σ = 50$	$σ = 20$	$σ = 30$	$σ = 40$	$σ = 50$
0.05	2E-05	0.0297	0.4732	1.9297	2E-05	0.0368	0.7327	3.7338	3E-08	6E-05	0.0009	0.0039
0.1	2E-05	0.0242	1.6254	2.1094	9E-06	0.0207	17.017	24.66	9E-08	5E-05	0.0789	0.0812
0.15	1E-05	0.9574	0.1645	0.1706	7E-06	10.533	16.532	22.796	3E-08	0.0708	0.0675	0.0668
0.2	1E-05	0.0018	-1.065	-1.399	6E-06	9.7336	14.932	20.338	1E-07	0.0599	0.0518	0.0464
0.25	8E-06	0.0122	-2.061	-2.553	9E-06	0.0218	13.241	18.174	1E-07	0.0003	0.0262	0.019
0.3	5E-06	-1.585	-2.674	-3.266	5E-05	7.2329	11.906	16.214	9E-07	0.0247	0.0056	0.002
0.35	-1E-05	-1.947	-3.006	-3.658	0.0005	6.5573	10.507	14.268	8E-06	0.0003	-0.007	-0.011
0.4	-0.038	-2.094	-3.132	-3.788	0.728	5.6325	9.1364	12.364	-0.025	-0.009	-0.017	-0.022
0.45	-1.041	-2.11	-3.089	-3.69	2.0753	4.7864	7.8619	10.524	-0.006	-0.016	-0.026	-0.03
0.5	-1.048	-2.052	-2.901	-3.399	1.8557	4.269	6.7588	8.76	-0.012	-0.024	-0.034	-0.037

References 50

[1]	Fay S， Xie J. Probabilistic goods： A creative way of selling products and services［J］. Marketing Science， 2008， 27（4）： 674-690.
[2]	Zhang Y， Zhang J. Strategic customer behavior with disappointment aversion customers and two alleviation policies［J］. International Journal of Production Economics， 2017， 191： 170-177.
[3]	Li Q， Ma J. Research on price Stackelberg game model with probabilistic selling based on complex system theory［J］. Communications in Nonlinear Science and Numerical Simulation， 2016， 30（1-3）： 387-400.
[4]	毛可，傅科，徐佳焱. 无理由退货政策下的概率销售策略［J］. 系统工程理论与实践， 2020， 40（4）： 964-977.
	Mao K， Fu K， Xu J Y. Probabilistic selling with money back guarantees［J］. Systems Engineering —Theory Practice， 2020， 40（4）： 964-977.
[5]	杨光，刘新旺，秦晋栋. 基于消费者损失效用的概率销售策略研究［J］.中国管理科学，2020，28（7）： 146-155.
	Yang G， Liu X W， Qin J D. Probabilistic selling policy based on consumers’ loss utility［J］. Chinese Journal of Management Science， 2020， 28（7）： 146-155.
[6]	舒斯亮，柳键. 不同权力结构下供应链概率销售策略比较研究［J］. 中国管理科学， 2022， 30（9）： 152-161.
	Shu S L， Liu J. A comparative study on probabilistic selling strategy of supply chain under different power structures［J］. Chinese Journal of Management Science， 2022， 30（9）： 152-161.
[7]	Fay S， Gheibi S. The effect of probabilistic selling on channel dynamics in supply chains［J］. Manufacturing Service Operations Management，2023，26（2）： 632-645.
[8]	戴睿，吴明霞. 考虑消费者信息更新的概率销售策略［J］. 运筹与管理， 2024， 33（3）： 133-139.
	Dai R， Wu M X. Probabilistic selling strategy considering Consumers’Information update［J］. Operations Research and Management Science， 2024， 33（3）： 133-139.
[9]	Yin Z， Huang T. Probabilistic selling with customization？ A theoretical analysis［J］. Production and Operations Management， 2025， 34（9）： 2891-2909.
[10]	沈瑞蓉，徐燕翼. 考虑消费者公平偏好行为的概率销售定价策略研究［J］. 工业工程与管理， 2022， 27（2）： 118-127.
	Shen R R， Xu Y Y. Research on pricing strategy of probabilistic selling based on Consumers’Fair preference［J］. Industrial Engineering and Management， 2022， 27（2）： 118-127.
[11]	Huang T， Yu Y. Sell probabilistic goods？ A behavioral explanation for opaque selling［J］. Marketing Science， 2014， 33（5）： 743-759.
[12]	Huang Y S， Wu T Y， Fang C C， et al. Decisions on probabilistic selling for consumers with different risk attitudes［J］. Decision Analysis， 2021， 18（2）： 121-138.
[13]	付红，高江明，李凯，等. 考虑消费者重复购买行为的盲盒设计与库存联合决策［J］. 系统管理学报， 2025， 34（6）： 1497-1508.
	Fu H， Gao J M， Li K， et al. Joint decision-making on blind box design and inventory considering consumer’s repurchase behavior［J］. Journal of Systems Management， 2025， 34（6）： 1497-1508.
[14]	Fay S， Xie J. Timing of product allocation： Using probabilistic selling to enhance inventory management［J］. Management Science， 2015， 61（2）： 474-484.
[15]	Zheng Q， Pan X A， Carrillo J E. Probabilistic selling for vertically differentiated products with salient thinkers［J］. Marketing Science， 2019， 38（3）： 442-460.
[16]	Cachon G P， Swinney R. Purchasing， pricing， and quick response in the presence of strategic consumers［J］. Management Science， 2009， 55（3）： 497-511.
[17]	Cachon G P， Swinney R. The value of fast fashion： Quick response， enhanced design， and strategic consumer behavior［J］. Management Science， 2011， 57（4）： 778-795.
[18]	Fisher M， Raman A. Reducing the cost of demand uncertainty through accurate response to early sales［J］. Operations Research， 1996， 44（1）： 87-99.
[19]	Eppen G D， Iyer A V. Improved fashion buying with Bayesian updates［J］. Operations Research， 1997， 45（6）： 805-819.
[20]	Petruzzi N C， Dada M. Information and inventory recourse for a two-market， price-setting retailer［J］. Manufacturing Service Operations Management， 2001， 3（3）： 242-263.
[21]	Lin Y T， Parlaktürk A. Quick response under competition［J］. Production and Operations Management， 2012， 21（3）： 518-533.
[22]	Choi T M. Inventory service target in quick response fashion retail supply chains［J］. Service Science， 2016， 8（4）： 406-419.
[23]	Deshpande V， Pendem P K. Logistics performance， ratings， and its impact on customer purchasing behavior and sales in E-commerce platforms［J］. Manufacturing Service Operations Management， 2023， 25（3）： 827-845.
[24]	Xu J， Duan Y. Pricing， ordering， and quick response for online sellers in the presence of consumer disappointment aversion［J］. Transportation Research Part E： Logistics and Transportation Review， 2020， 137： 101925.
[25]	Long X， Nasiry J. Sustainability in the fast fashion industry［J］. Manufacturing Service Operations Management， 2022， 24（3）： 1276-1293.
[26]	王辉，易思源，杨海丽. 供应链中的快速反应和行为学研究：综述与展望［J］. 管理评论， 2023， 35（4）： 303-310.
	Wang H， Yi S Y， Yang H L. Quick response and behavioral research in supply chains： Review and outlook［J］. Management Review， 2023， 35（4）： 303-310.
[27]	Qiu R， Sun Y， Zhou H， et al. Dynamic pricing and quick response of a retailer in the presence of strategic consumers： A distributionally robust optimization approach［J］. European Journal of Operational Research， 2023， 307（3）： 1270-1298.
[28]	Wang H， Bai C， Lev B， et al. Quick response under strategic consumers with high-price and stockout regrets［J］. Computers Operations Research， 2024， 166： 106590.
[29]	Fay S， Xie J. The economics of buyer uncertainty： Advance selling vs. probabilistic selling［J］. Marketing Science， 2010， 29（6）： 1040-1057.
[30]	Jerath K， Netessine S， Veeraraghavan S K. Revenue management with strategic customers： Last-minute selling and opaque selling［J］. Management Science， 2010， 56（3）： 430-448.
[31]	Rice D H， Fay S A， Xie J. Probabilistic selling vs. markdown selling： Price discrimination and management of demand uncertainty in retailing［J］. International Journal of Research in Marketing， 2014， 31（2）： 147-155.
[32]	Zhang Y， Hua G， Wang S， et al. Managing demand uncertainty： Probabilistic selling versus inventory substitution［J］. International Journal of Production Economics， 2018， 196： 56-67.
[33]	Zhang J， Deng L， Liu H， et al. Which strategy is better for managing multi-product demand uncertainty： Inventory substitution or probabilistic selling？［J］. European Journal of Operational Research， 2022， 302（1）： 79-95.
[34]	Liu Q， Van Ryzin G J. Strategic capacity rationing to induce early purchases［J］. Management Science， 2008， 54（6）： 1115-1131.
[35]	Huang T， Van Mieghem J A. The promise of strategic customer behavior： On the value of click tracking［J］. Production and Operations Management， 2013， 22（3）： 489-502.
[36]	Chun S Y， Ovchinnikov A. Strategic consumers， revenue management， and the design of loyalty programs［J］. Management Science， 2019， 65（9）： 3969-3987.
[37]	Araman V F， Fayad B. Intertemporal price discrimination with time-varying valuations［J］. Operations Research， 2021， 69（1）： 245-265.
[38]	Du J， Zhang J， Hua G. Pricing and inventory management in the presence of strategic customers with risk preference and decreasing value［J］. International Journal of Production Economics， 2015， 164： 160-166.
[39]	Su X， Zhang F. On the value of commitment and availability guarantees when selling to strategic consumers［J］. Management Science， 2009， 55（5）： 713-726.
[40]	李贺，张玉林，仲伟俊. 考虑战略消费者行为风险的动态定价策略［J］. 管理科学学报， 2012， 15（10）： 11-25.
	Li H， Zhang Y L， Zhong W J. Dynamic pricing strategies in the presence of strategic consumer behavior risks［J］. Journal of Management Sciences in China， 2012， 15（10）： 11-25.
[41]	Chen Y， Shi C. Joint pricing and inventory management with strategic customers［J］. Operations Research， 2019， 67（6）： 1610-1627.
[42]	Lin Y T， Parlaktürk A K， Swaminathan J M. Are strategic customers bad for a supply chain？［J］. Manufacturing Service Operations Management， 2018， 20（3）： 481-497.
[43]	Wang J， Levin Y， Nediak M. Selling passes to strategic customers［J］. Operations Research， 2020， 68（4）： 1095-1115.
[44]	Chen Y， Trichakis N. Technical note—On revenue management with strategic customers choosing when and what to buy［J］. Operations Research， 2021， 69（1）： 175-187.
[45]	Singh N， Ramachandran K， Subramanian R. Intertemporal product management with strategic consumers： The value of defective product returns［J］. Manufacturing Service Operations Management， 2022， 24（2）： 1146-1164.
[46]	Chen H， Hu M， Wu J. Intertemporal price discrimination via randomized promotions［J］. Manufacturing Service Operations Management， 2023， 25（3）： 1176-1194.
[47]	蔺康康，刘新民，王垒. 考虑异质性策略消费者等待时间的产品定价换代策略研究［J］. 中国管理科学， 2024， 32（8）： 204-213.
	Lin K K， Liu X M， Wang L. Product pricing and rollover strategy based on the waiting time for heterogeneous strategic consumers［J］. Chinese Journal of Management Science， 2024， 32（8）： 204-213.
[48]	夏良杰，黄迎，冯锦茹，等. 面向策略型消费者的过度自信零售商产品定价与订货决策研究［J］. 中国管理科学， 2026， 34（3）： 297-308.
	Xia L J， Huang Y， Feng J R， et al. Pricing and ordering policies of overconfident retailers considering strategic consumers［J］. Chinese Journal of Management Science， 2026， 34（3）： 297-308.
[49]	李犇，高倩，郭晓龙，等. 考虑策略消费者线上凑单购买行为的免邮策略研究［J］. 中国管理科学， 2026， 34（5）： 1-10.
	Li B， Gao Q， Guo X L， et al. Contingent Free-Shipping Decisions when Considering the Merging Behavior of Strategic Consumers［J］. Chinese Journal of Management Science， 2026， 34（5）： 1-10.
[50]	Gneezy U， List J A， Wu G. The uncertainty effect： When a risky prospect is valued less than its worst possible outcome［J］. The Quarterly Journal of Economics， 2006， 121（4）： 1283-1309.

Comparison of Probabilistic Sales and Quick Response under Demand Uncertainty

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