Dynamic pricing and sales effort in dual-channel retailing for seasonal products

Wanting Hu; Jingjing Ding; Pengzhen Yin; Liang Liang

doi:10.3934/jimo.2022005

Article Contents

2023, Volume 19, Issue 2: 1528-1549. Doi: 10.3934/jimo.2022005

This issue Previous Article Optimality and duality for

$ E $

-differentiable multiobjective programming problems involving

$ E $

-type Ⅰ functions Next Article Investment strategy for renewable energy and electricity service quality under different power structures

Dynamic pricing and sales effort in dual-channel retailing for seasonal products

School of Management, Hefei University of Technology, Hefei, 230009, China

^*Corresponding author: Pengzhen Yin
^*Corresponding author: Pengzhen Yin

Received: April 30, 2021

Revised: August 31, 2021

Early access: February 2022

Published: February 2023

Abstract Full Text(HTML) Figure(4) / Table(4) Related Papers Cited by

Abstract

This paper studies the joint strategies of dynamic pricing and sales effort involving a seller and a third-party e-commerce platform (TPECP). The seller sells seasonal products through both offline and online channels, and the latter is opened on the TPECP. Considering a dual-channel setting, this paper fills a gap in the studies of joint strategies of dynamic pricing and sales effort. This paper formulates dynamic decision models and investigates them under both centralized and decentralized decision-making cases. Furthermore, a revenue-cost sharing contract is proposed to coordinate the two parties' decisions in the decentralized case, and it is validated theoretically and numerically. The key findings are as follows: For a given selling slot, the optimal online price decreases and the optimal sales effort level increases in the centralized case as the inventory level increases and remains below a threshold; however, when the inventory level exceeds the threshold, both the optimal online price and sales effort level remain fixed as the the inventory level increases in both cases. In addition, for a given inventory level below the threshold, the optimal online price decreases and the optimal sales effort level increases over time in both cases; however, when the inventory level exceeds the threshold, over time, the optimal online price increases and the optimal sales effort level decreases in the centralized case, and both the optimal online price and sales effort level increase in the decentralized case. Finally, a numerical experiment and some management implications are provided.

Keywords:

Dynamic pricing,
sales effort,
coordination mechanism,
centralized and decentralized decision making,
dual-channel retailing.

Mathematics Subject Classification: Primary: 90B50, 91B24; Secondary: 90C39, 90B06.

Citation:

Full Text(HTML)

Figure 1. The schematic structure of the cooperation process between the seller and the TPECP

Download: Full-size image PowerPoint slide

Figure 2. Impact of selling slot on optimal strategies

Download: Full-size image PowerPoint slide

Figure 3. Impact of channel factors on optimal strategies

Download: Full-size image PowerPoint slide

Figure 4. The comparison of the total expected profits over whole selling season between two cases

Download: Full-size image PowerPoint slide

Table 1. Summary of the highly-related literature

Authors	Dual channels	Pricing strategy	Sales effort / advertising	Others
Li et al.[19]; Liu et al.[25]	$ \checkmark $	Static pricing		Risk aversion
Radhi & Zhang [28];	$ \checkmark $	Static pricing		Channel coordination
Zhang et al.[36]
Gallego & Van Ryzin [11];		Dynamic pricing		Stochastic demand
Kaya [15]; Li et al. [24]
Wu et al.[33]; Dye & Yang [10]; Duan & Liu[9]		Dynamic pricing		Reference price effect
Gurnani et al.[13]		Static pricing	$ \checkmark $	Competition
Li [20]; Ke and Liu [16]	$ \checkmark $		$ \checkmark $	Competition
Li et al.[23]	$ \checkmark $		$ \checkmark $	Online to offline
Chenavaz et al.[6]		Dynamic pricing	$ \checkmark $	Product quality
This paper	$ \checkmark $	Dynamic pricing	$ \checkmark $	revenue-cost sharing contract

| Show Table

DownLoad: CSV

Table 2. Definitions of notations

Parameters
$ T $	The length of the whole selling season
$ N $	Initial total inventory
$ \beta $	The ratio of sales effort cost that borne by the seller
$ \phi $	The ratio of online store revenue that taken away by the TPECP
$ h $	The unit stock-holding cost per unit selling slot for the seller
$ \theta $	The customers channel preference coefficient for the online store
$ a $	The potential total demand rate for the product in dual-channel
$ b_1 $	The elasticity coefficient of online demand for online price
$ b_2 $	The elasticity coefficient of offline demand for offline price
$ k $	The elasticity coefficient of online demand for the sales effort exerted by the TPECP
$ c_1 $	The elasticity coefficient of online demand for offline price
$ c_2 $	The elasticity coefficient of offline demand for online price
$ p_2 $	The price of product that sold in the brick-and-mortar store, i.e., offline price
State variables
$ t $	The state variable of selling slot
$ n $	The state variable of inventory level
Other variables
$ \lambda _{1t}^{n} $	The demand rate of online product (or the probability of customer buying online product)
$ \lambda _{2t}^{n} $	The demand rate of offline product (or the probability of customer buying offline product)
Decision variables
$ p_{1t}^{n} $	The price of product that sold in the online store, i.e., online price, which decided by the seller
$ e_{t}^{n} $	Sales effort level, which exerted and decided by the TPECP, the sales effort cost is $ {{{(e_{t}^{n})}^{2}}}/{2}\; $

| Show Table

DownLoad: CSV

Table 3. The default values assigned to parameters

Parameter	Value	Parameter	Value	Parameter	Value	Parameter	Value
$ p_2 $	30	$ b_2 $	0.016	k	0.015	h	0.06
$ \theta $	0.5	$ c_1 $	0.006	$ \beta $	0.3	N	30
$ a $	1.2	$ c_2 $	0.008	$ \phi $	0.2	T	40
$ b_1 $	0.02

| Show Table

DownLoad: CSV

Table 4. The numerical results given t = 30 in the centralized case

n	$ U_{30}^{n} $	$ U_{30}^{n+1}-U_{30}^{n} $	$ p_{1}^{{}}{{_{30}}^{n\text{*}U}} $	$ e{{_{30}}}^{n\text{*}U} $	n	$ U_{30}^{n} $	$ U_{30}^{n+1}-U_{30}^{n} $	$ p_{1}^{{}}{{_{30}}^{n\text{*}U}} $	$ e{{_{30}}}^{n\text{*}U} $
1	30.758	30.466	34.727	0.061	16	175.276	–0.660	25.449	0.392
2	61.224	29.584	34.603	0.065	17	174.616	–0.660	25.449	0.392
3	90.808	27.400	34.211	0.079	18	173.956	–0.660	25.449	0.392
4	118.208	23.413	33.308	0.111	19	173.296	–0.660	25.449	0.392
5	141.621	17.836	31.809	0.165	20	172.636	–0.660	25.449	0.392
6	159.458	11.607	29.916	0.232	21	171.976	–0.660	25.449	0.392
7	171.065	5.991	28.033	0.299	22	171.316	–0.660	25.449	0.392
8	177.056	2.041	26.579	0.351	23	170.656	–0.660	25.449	0.392
9	179.097	0.050	25.771	0.380	24	169.996	–0.660	25.449	0.392
10	179.147	–0.572	25.492	0.390	25	169.336	–0.660	25.449	0.392
11	178.576	–0.660	25.449	0.392	26	168.676	–0.660	25.449	0.392
12	177.916	–0.660	25.449	0.392	27	168.016	–0.660	25.449	0.392
13	177.256	–0.660	25.449	0.392	28	167.356	–0.660	25.449	0.392
14	176.596	–0.660	25.449	0.392	29	166.696	–0.660	25.449	0.392
15	175.936	–0.660	25.449	0.392	30	166.036	/	25.449	0.392

| Show Table

DownLoad: CSV

Related Papers

Cited by

References

[1]	G. R. Bitran and S. V. Mondschein, Periodic pricing of seasonal products in retailing, Management Science, 43 (1997), 64-79. doi: 10.1287/mnsc.43.1.64.
[2]	D. Boer, V. Arnoud and B. Zwart, Dynamic pricing and learning with finite inventories, Oper. Res., 63 (2015), 965-979. doi: 10.1287/opre.2015.1397.
[3]	G. P. Cachon, Supply chain coordination with contracts, Handbooks in Operations Research and Management Science, 11 (2003), 227-339.
[4]	J. X. Chen, L. Liang, D. Yao and S. Sun, Price and quality decisions in dual-channel supply chains, European J. Oper. Res., 259 (2017), 935-948. doi: 10.1016/j.ejor.2016.11.016.
[5]	X. Chen, C. Liu and S. Li, The role of supply chain finance in improving the competitive advantage of online retailing enterprises, Electronic Commerce Research and Applications, 33 (2019), 100821.
[6]	R. Y. Chenavaz, G. Feichtinger, R. F. Hartl and P. M. Kort, Modeling the impact of product quality on dynamic pricing and advertising policies, European J. Oper. Res., 284 (2020), 990-1001. doi: 10.1016/j.ejor.2020.01.035.
[7]	B. Dan, G. Xu and C. Liu, Pricing policies in a dual-channel supply chain with retail services, International Journal of Economics, 139 (2012), 312-320.
[8]	Z. S. Dong, W. Chen, Q. Zhao and J. Li, Optimal pricing and inventory strategies for introducing a new product based on demand substitution effects, J. Ind. Manag. Optim., 16 (2020), 725-739, doi: 10.3934/jimo.2018175.
[9]	Y. Duan and J. Liu, Optimal dynamic pricing for perishable foods with quality and quantity deteriorating simultaneously under reference price effects, International Journal of Systems Science Operations & Logistics, 6 (2019), 346-355. doi: 10.1080/23302674.2018.1465618.
[10]	C. Y. Dye and C. T. Yang, Optimal dynamic pricing and preservation technology investment for deteriorating products with reference price effects, Omega, 62 (2016), 52-67.
[11]	G. Gallego and G. V. Ryzin, Optimal dynamic pricing of inventories with stochastic demand over finite horizons, Management Science, 40 (1994), 999-1020. doi: 10.5555/2827835.2827840.
[12]	X. González, Chain heterogeneity and price-setting behavior: Evidence from e-grocery retailers, Electronic Commerce Research and Applications, 26 (2017), 62-72.
[13]	H. G. Gurnani and Y. Xu, Resale price maintenance contracts with retailer sales effort: Effect of flexibility and competition, Naval Res. Logist., 53 (2006), 448-463. doi: 10.1002/nav.20152.
[14]	W. Huang and J. M. Swaminathan, Introduction of a second channel: Implications for pricing and profits, European Journal of Operational Research, 194 (2009), 258-279.
[15]	O. Kaya, Dynamic pricing of durable products with heterogeneous customers and demand interactions over time, Computers and Industrial Engineering, 65 (2013), 679-688.
[16]	H. Ke and J. Liu, Dual-channel supply chain competition with channel preference and sales effort under uncertain environment, Journal of Ambient Intelligence & Humanized Computing, 8 (2017), 781-795. doi: 10.1007/s12652-017-0502-8.
[17]	W. M. Kincaid and D. A. Darling, An inventory pricing problem, J. Math. Anal. Appl., 7 (1963), 183-208. doi: 10.1016/0022-247X(63)90047-7.
[18]	T. C. Lee and M. Hersh, A model for dynamic airline seat inventory control with multiple seat bookings, Transportation Science, 27 (1993), 252-265. doi: 10.1287/trsc.27.3.252.
[19]	B. Li, P. W. Hou, P. Chen and Q. H. Li, Pricing strategy and coordination in a dual channel supply chain with a risk-averse retailer, International Journal of Production Economics, 178 (2016), 154-168.
[20]	P. Li, Sale effort competition in dual-channel supply chain based on a Weakest online manufacturer, International Conference on Artificial Intelligence, Management Science and Electronic Commerce, (2011), 1491–1494, .
[21]	Q. Li and Z. Liu, Supply chain coordination via a two-part tariff contract with price and sales effort dependent demand, Decision Science Letters, 4 (2015), 27-34.
[22]	S. Li, J. Zhang and W. Tang, Joint dynamic pricing and inventory control policy for a stochastic inventory system with perishable products, International Journal of Production Research, 53 (2014), 2937-2950. doi: 10.1080/00207543.2014.961206.
[23]	X. Li, Y. Li and W. Cao, Cooperative advertising models in O2O supply chains, International Journal of Production Economics, 215 (2019), 144-152.
[24]	X. Li, G. Sun and Y. Li, A Multi-period ordering and clearance pricing model considering the competition between new and out-of-season products, Ann. Oper. Res., 242 (2016), 207-221. doi: 10.1007/s10479-013-1498-x.
[25]	M. Liu, E. Cao and C. K. Salifou, Pricing strategies of a dual-channel supply chain with risk aversion, Transportation Research Part E: Logistics and Transportation Review, 90 (2016), 108-120.
[26]	S. Minsuk and A. Goker, Dynamic pricing of substitutable products with limited inventories under logit demand, IIE Transactions, 43 (2011), 323-331.
[27]	X. Pu, L. Gong and X. Han, Consumer free riding: Coordinating sales effort in a dual-channel supply chain, Electronic Commerce Research and Applications, 22 (2017), 1-12.
[28]	M. Radhi and G. Zhang, Pricing policies for a dual-channel retailer with cross-channel returns, Computers and Industrial Engineering, 119 (2018), 63-75.
[29]	T. Taylor, Supply chain coordination under channel rebates with sales effort effects, Management Science, 48 (2002), 992-1007. doi: 10.1287/mnsc.48.8.992.168.
[30]	Y. C. Tsao and G. J. Sheen, Dynamic pricing, promotion and replenishment policies for a deteriorating item under permissible delay in payments, Computers and Operations Research, 35 (2008), 3562-3580.
[31]	A. Tsay and N. Agrawal, Modeling conflict and coordination in multi-channel distribution systems: A review, Handbook of Quantitative Supply Chain Analysis, 74 (2004), 557-606. doi: 10.1007/978-1-4020-7953-5_13.
[32]	Y. Y. Wang, J. C. Wang and B. Shou, Pricing and effort investment for a newsvendor-type product, European J. Oper. Res., 229 (2013), 422-432. doi: 10.1016/j.ejor.2012.11.055.
[33]	S. Wu, Q. Liu and R. Q. Zhang, The reference effects on a retailer's dynamic pricing and inventory strategies with strategic consumers, Oper. Res., 63 (2015), 1320-1335. doi: 10.1287/opre.2015.1440.
[34]	Y. B. Xiao, F. Y. Chen and J. Chen, Optimal inventory and dynamic admission policies for a retailer of seasonal products with affiliate programs and drop-shipping, Naval Res. Logist., 56 (2009), 300-317. doi: 10.1002/nav.20346.
[35]	R. Yan and Z. Pei, Retail services and firm profit in a dual-channel market, Journal of Retailing and Consumer Services, 16 (2009), 306-314.
[36]	C. Zhang, Y. Wang and Y. Liu, Coordination contracts for a dual-channel supply chain under capital constraints, J. Ind. Manag. Optim., 17 (2021), 1485-1504. doi: 10.3934/jimo.2020031.
[37]	F. Zhang and C. Wang, Dynamic pricing strategy and coordination in a dual-channel supply chain considering service value, Appl. Math. Model., 54 (2018), 722-742. doi: 10.1016/j.apm.2017.10.006.
[38]	J. Zhang, S. Zhao, T. C. E. Cheng and G. Hua, Optimisation of online retailer pricing and carrier capacity expansion during low-price promotions with coordination of a decentralised supply chain, International Journal of Production Research, 57 (2019), 2809-2827. doi: 10.1080/00207543.2018.1516901.
[39]	S. X. Zhou and X. Chao, Dynamic pricing and inventory management with regular and expedited supplies, Production and Operations Management, 23 (2014), 65-80.