需求和成本扰动下闭环供应链的应急决策及协调研究

doi:10.6040/j.issn.1671-9352.0.2019.290

摘要/Abstract

摘要：

针对突发事件干扰需求和成本扰动的情况,构建了零售商回收、制造商回收和第三方回收等类别闭环供应链的应急决策模型。研究表明:在3类回收系统和集中式决策系统中,相比较正常运营环境下的均衡决策,当需求和成本的综合扰动程度不大时,产品销售量和废旧品回收率等均具鲁棒性,但应随市场需求扰动方向调整产品的批发价和销售价;当需求和成本的综合扰动程度较大时,应随市场需求扰动方向同时调整产品的批发价、销售价、销售量和废旧品的回收率;当需求减少和成本增加的综合扰动程度很大时, 3类回收系统和集中式决策系统会被破坏;在需求和成本扰动的各类情况下,制造商选择MRCRM系统运营可获得较大利润;当需求减少和成本增加的综合扰动程度超过一定阈值时,因集中式决策系统会承担较多的额外处理成本,使得利润减少较多,故其利润会小于MRCRM系统的总利润,在其他扰动情况下,可通过应急收益费用共享契约协调解决MRCRM系统中存在的“双重边际效应”问题,提高系统的运营效率,并使各成员均获得帕累托改进的利润。

关键词: 闭环供应链, 需求, 成本, 渠道决策, 收益费用共享契约

Abstract:

Considering demand and cost are disrupted by emergency events, there are three CLSC emergency models, i.e. retailer collecting, manufacturer collecting and third-party collecting. In the three decentralized collecting systems and centralized decision system, compared with equilibrium decisions in normal environment, when the disruptions of demand and cost are not large, sales quantity of products and collecting rate of used products have some robustness, but the wholesale price and selling price of products should be adjusted along the same direction with demand disruption; when the disruptions of demand and cost are large, the wholesale price, selling price, sales quantity of products and collecting rate of used products should be adjusted along the same direction with demand disruption; when the degree of demand decreasing and cost increasing are large, the three decentralized collecting systems and centralized decision system are all destroyed. In each case of demand and cost disruptions, manufacturer can obtain more profits by MRCRM system; when the degree of demand decreasing and cost increasing exceeds a certain threshold, the profits of centralized decision system decrease resulted from assuming more extra disposing costs, which results in its profits are less than MRCRM system. Furthermore, in other disruption cases, emergency revenue and expense sharing contract can solve "double marginalization" problems in MRCRM system, which improves system's operation efficiency and makes each member get Pareto improved profits.

Key words: closed-loop supply chain, demand, cost, channel choice, revenue and expense sharing contract

中图分类号:

F272

孙丹丹,李珂,谢礼斌,牟宗玉. 需求和成本扰动下闭环供应链的应急决策及协调研究[J]. 《山东大学学报(理学版)》, 2020, 55(7): 88-102, 110.

Dan-dan SUN,Ke LI,Li-bin XIE,Zong-yu MU. Channel decisions and coordination of closed-loop supply chain under demand and cost disruptions[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(7): 88-102, 110.

图/表 7

图1

图2

表1

表2

表3

3类回收系统和集中式决策系统的应急决策和利润"

	扰动范围		(-(ϕ-βc_m)-βλ₁, -βλ₁]	(-βλ₁, βλ₂)	$ \left[ {\beta {\lambda _2}, \frac{{4{C_{\rm{L}}}\left[ {\phi - \beta {c_{\rm{m}}} + \beta \left( {\delta - A} \right)} \right]\left( {\delta - A} \right)}}{{\left( {\delta - A} \right)}} + \beta {\lambda _2}} \right] $
价格	MRCRM		$ {p^{{{\rm{R}}^*}}} + \frac{{\Delta \phi }}{\beta } - \frac{{{C_{\rm{L}}}\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}}{{\beta \left[ {4{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $	$ {p^{{{\rm{R}}^*}}} + \frac{{\Delta \phi }}{\beta } $	$ {p^{{{\rm{R}}^*}}} + \frac{{\Delta \phi }}{\beta } - \frac{{{C_{\rm{L}}}\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _2}} \right)}}{{\beta \left[ {4{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $
	MRCM		$ {p^{{{\rm{M}}^*}}} + \frac{{\Delta \phi }}{\beta } - \frac{{2{C_{\rm{L}}}\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}}{{\beta \left[ {8{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $	$ {p^{{{\rm{M}}^*}}} + \frac{{\Delta \phi }}{\beta } $	$ {p^{{{\rm{M}}^*}}} + \frac{{\Delta \phi }}{\beta } - \frac{{2{C_{\rm{L}}}\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _2}} \right)}}{{\beta \left[ {8{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $
	MRCTM		$ {p^{{{\rm{T}}^*}}} + \frac{{\Delta \phi }}{\beta } - \frac{{4{C_{\rm{L}}}\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}}{{\beta \left[ {16{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $	$ {p^{{{\rm{T}}^*}}} + \frac{{\Delta \phi }}{\beta } $	$ {p^{{{\rm{T}}^*}}} + \frac{{\Delta \phi }}{\beta } - \frac{{4{C_{\rm{L}}}\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _2}} \right)}}{{\beta \left[ {16{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $
	集中式		$ {p^{{{\rm{c}}^*}}} + \frac{{\Delta \phi }}{\beta } - \frac{{2{C_{\rm{L}}}\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}}{{\beta \left[ {4{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $	$ {p^{{{\rm{c}}^*}}} + \frac{{\Delta \phi }}{\beta } $	$ {p^{{{\rm{c}}^*}}} + \frac{{\Delta \phi }}{\beta } - \frac{{2{C_{\rm{L}}}\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _2}} \right)}}{{\beta \left[ {8{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $
产量	MRCRM		$ {q^{{{\rm{R}}^*}}} + \frac{{{C_{\rm{L}}}\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}}{{4{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}}} $	q^{R^*}	$ {q^{{{\rm{R}}^*}}} + \frac{{{C_{\rm{L}}}\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _2}} \right)}}{{4{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}}} $
	MRCM		$ {q^{{{\rm{M}}^*}}} + \frac{{2{C_{\rm{L}}}\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}}{{8{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}}} $	q^{M^*}	$ {q^{{{\rm{M}}^*}}} + \frac{{2{C_{\rm{L}}}\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _2}} \right)}}{{8{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}}} $
	MRCTM		$ {q^{{{\rm{T}}^*}}} + \frac{{4{C_{\rm{L}}}\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}}{{16{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}}} $	q^{T^*}	$ {q^{{{\rm{T}}^*}}} + \frac{{4{C_{\rm{L}}}\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _2}} \right)}}{{16{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}}} $
	集中式		$ {q^{{{\rm{c}}^*}}} + \frac{{2{C_{\rm{L}}}\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}}{{4{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}}} $	q^{c^*}	$ {q^{{{\rm{c}}^*}}} + \frac{{2{C_{\rm{L}}}\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _2}} \right)}}{{4{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}}} $
回收率	MRCRM		$ {\tau ^{{{\rm{R}}^*}}} + \frac{{\left( {\delta - A} \right)\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}}{{2\left[ {4{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $	τ^{R^*}	$ {\tau ^{{{\rm{R}}^*}}} + \frac{{\left( {\delta - A} \right)\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _2}} \right)}}{{2\left[ {4{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $
	MRCM		$ {\tau ^{{{\rm{M}}^*}}} + \frac{{\left( {\delta - A} \right)\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}}{{8{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}}} $	τ^{M^*}	$ {\tau ^{{{\rm{M}}^*}}} + \frac{{\left( {\delta - A} \right)\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _2}} \right)}}{{8{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}}} $
	MRCTM		$ {\tau ^{{{\rm{T}}^*}}} + \frac{{\left( {\delta - A} \right)\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}}{{16{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}}} $	τ^{T^*}	$ {\tau ^{{{\rm{T}}^*}}} + \frac{{\left( {\delta - A} \right)\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _2}} \right)}}{{16{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}}} $
	集中式		$ {\tau ^{{{\rm{c}}^*}}} + \frac{{\left( {\delta - A} \right)\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}}{{4{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}}} $	τ^{c^*}	$ {\tau ^{{{\rm{c}}^*}}} + \frac{{\left( {\delta - A} \right)\left( {\Delta \phi - \beta \Delta c + \beta {\lambda _2}} \right)}}{{4{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}}} $
利润	MRCRM	M	$ \frac{{{C_{\rm{L}}}\left[ {{{\left( {\phi - \beta {c_{\rm{m}}} + \Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}^2} - 2\beta {\lambda _1}\left( {\phi - \beta {c_{\rm{m}}}} \right)} \right]}}{{2\beta \left[ {4{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $	$ \frac{{{C_{\rm{L}}}\left( {\phi - \beta {c_{\rm{m}}}} \right)\left[ {\phi - \beta {c_{\rm{m}}} + 2\left( {\Delta \phi - \beta \Delta c} \right)} \right]}}{{2\beta \left[ {4{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $	$ \frac{{{C_{\rm{L}}}\left[ {{{\left( {\phi - \beta {c_{\rm{m}}} + \Delta \phi - \beta \Delta c + \beta {\lambda _2}} \right)}^2} - 2\beta {\lambda _2}\left( {\phi - \beta {c_{\rm{m}}}} \right)} \right]}}{{2\beta \left[ {4{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $
		R	$ \frac{{{C_{\rm{L}}}{{\left( {\phi - \beta {c_{\rm{m}}} + \Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}^2}}}{{4\beta \left[ {4{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $	$ \frac{{{C_{\rm{L}}}{{\left( {\phi - \beta {c_{\rm{m}}}} \right)}^2}}}{{4\beta \left[ {4{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $	$ \frac{{{C_{\rm{L}}}{{\left( {\phi - \beta {c_{\rm{m}}} + \Delta \phi - \beta \Delta c + \beta {\lambda _2}} \right)}^2}}}{{4\beta \left[ {4{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $
		S	$ \frac{{{C_{\rm{L}}}\left[ {3{{\left( {\phi - \beta {c_{\rm{m}}} + \Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}^2} - 4\beta {\lambda _1}\left( {\phi - \beta {c_{\rm{m}}}} \right)} \right]}}{{4\beta \left[ {4{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $	$ \frac{{{C_{\rm{L}}}\left( {\phi - \beta {c_{\rm{m}}}} \right)\left[ {3\left( {\phi - \beta {c_{\rm{m}}}} \right) + 4\left( {\Delta \phi - \beta \Delta c} \right)} \right]}}{{4\beta \left[ {4{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $	$ \frac{{{C_{\rm{L}}}\left[ {3{{\left( {\phi - \beta {c_{\rm{m}}} + \Delta \phi - \beta \Delta c + \beta {\lambda _2}} \right)}^2} - 4\beta {\lambda _2}\left( {\phi - \beta {c_{\rm{m}}}} \right)} \right]}}{{4\beta \left[ {4{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $
	MRCM	M	$ \frac{{{C_{\rm{L}}}\left[ {{{\left( {\phi - \beta {c_{\rm{m}}} + \Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}^2} - 2\beta {\lambda _1}\left( {\phi - \beta {c_{\rm{m}}}} \right)} \right]}}{{\beta \left[ {8{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $	$ \frac{{{C_{\rm{L}}}\left( {\phi - \beta {c_{\rm{m}}}} \right)\left[ {\phi - \beta {c_{\rm{m}}} + 2\left( {\Delta \phi - \beta \Delta c} \right)} \right]}}{{\beta \left[ {8{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $	$ \frac{{{C_{\rm{L}}}\left[ {{{\left( {\phi - \beta {c_{\rm{m}}} + \Delta \phi - \beta \Delta c + \beta {\lambda _2}} \right)}^2} - 2\beta {\lambda _2}\left( {\phi - \beta {c_{\rm{m}}}} \right)} \right]}}{{\beta \left[ {8{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $
		R	$ \frac{{4C_{\rm{L}}^2{{\left( {\phi - \beta {c_{\rm{m}}} + \Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}^2}}}{{\beta {{\left[ {8{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}^2}}} $	$ \frac{{4C_{\rm{L}}^2{{\left( {\phi - \beta {c_{\rm{m}}}} \right)}^2}}}{{\beta {{\left[ {8{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}^2}}} $	$ \frac{{4C_{\rm{L}}^2{{\left( {\phi - \beta {c_{\rm{m}}} + \Delta \phi - \beta \Delta c - \beta {\lambda _2}} \right)}^2}}}{{\beta {{\left[ {8{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}^2}}} $
		S	$ {C_{\rm{L}}}\left\{ \begin{array}{l} \frac{{{{\left( {\phi - \beta {c_{\rm{m}}} + \Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}^2}\left[ {12{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}}{{\beta {{\left[ {8{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}^2}}}\\ \;\;\;\;\;\;\;\frac{{2{\lambda _1}\left( {\phi - \beta {c_{\rm{m}}}} \right)}}{{8{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}}} \end{array} \right\} $	$ {C_{\rm{L}}}\left( {\phi - \beta {c_{\rm{m}}}} \right)\left\{ \begin{array}{l} \frac{{\left( {\phi - \beta {c_{\rm{m}}}} \right)\left[ {12{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}}{{\beta {{\left[ {8{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}^2}}}\\ \;\;\;\;\; + \frac{{2\left( {\Delta \phi - \beta \Delta c} \right)}}{{\beta \left[ {8{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} \end{array} \right\} $	$ {C_{\rm{L}}}\left\{ \begin{array}{l} \frac{{{{\left( {\phi - \beta {c_{\rm{m}}} + \Delta \phi - \beta \Delta c + \beta {\lambda _2}} \right)}^2}\left[ {12{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}}{{\beta {{\left[ {8{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}^2}}}\\ \;\;\;\; + \frac{{2{\lambda _1}\left( {\phi - \beta {c_{\rm{m}}}} \right)}}{{8{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}}} \end{array} \right\} $
	MRCTM	M	$ \frac{{2{C_{\rm{L}}}\left[ {{{\left( {\phi - \beta {c_{\rm{m}}} + \Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}^2} - 2\beta {\lambda _1}\left( {\phi - \beta {c_{\rm{m}}}} \right)} \right]}}{{\beta \left[ {16{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $	$ \frac{{2{C_{\rm{L}}}\left( {\phi - \beta {c_{\rm{m}}}} \right)\left[ {\phi - \beta {c_{\rm{m}}} + 2\left( {\Delta \phi - \beta \Delta c} \right)} \right]}}{{\beta \left[ {16{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $	$ \frac{{2{C_{\rm{L}}}\left[ {{{\left( {\phi - \beta {c_{\rm{m}}} + \Delta \phi - \beta \Delta c + \beta {\lambda _2}} \right)}^2} - 2\beta {\lambda _2}\left( {\phi - \beta {c_{\rm{m}}}} \right)} \right]}}{{\beta \left[ {16{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $
		R	$ \frac{{16C_{\rm{L}}^2{{\left( {\phi - \beta {c_{\rm{m}}} + \Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}^2}}}{{\beta {{\left[ {16{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}^2}}} $	$ \frac{{16{C_{\rm{L}}}^2{{\left( {\phi - \beta {c_{\rm{m}}}} \right)}^2}}}{{\beta {{\left[ {16{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}^2}}} $	$ \frac{{16C_{\rm{L}}^2{{\left( {\phi - \beta {c_{\rm{m}}} + \Delta \phi - \beta \Delta c - \beta {\lambda _2}} \right)}^2}}}{{\beta {{\left[ {16{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}^2}}} $
		T	$ \frac{{{C_{\rm{L}}}{{\left( {\delta - A} \right)}^2}{{\left( {\phi - \beta {c_{\rm{m}}} + \Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}^2}}}{{{{\left[ {16{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}^2}}} $	$ \frac{{{C_{\rm{L}}}{{\left( {\delta - A} \right)}^2}{{\left( {\phi - \beta {c_{\rm{m}}}} \right)}^2}}}{{{{\left[ {16{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}^2}}} $	$ \frac{{{C_{\rm{L}}}{{\left( {\delta - A} \right)}^2}{{\left( {\phi - \beta {c_{\rm{m}}} + \Delta \phi - \beta \Delta c - \beta {\lambda _2}} \right)}^2}}}{{{{\left[ {16{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}^2}}} $
			$ \frac{{{C_{\rm{L}}}}}{{\beta \left[ {16{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $	$ \frac{{{C_{\rm{L}}}\left( {\phi - \beta {c_{\rm{m}}}} \right)}}{{\beta \left[ {16{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $	$ \frac{{{C_{\rm{L}}}}}{{\beta \left[ {16{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $
		S	$ \left\{ \begin{array}{l} \frac{{\left[ {48{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]{{\left( {\phi - \beta {c_{\rm{m}}} + \Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}^2}}}{{16{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}}}\\ \;\;\;\;\; - 4\beta {\lambda _1}\left( {\phi - \beta {c_{\rm{m}}}} \right) \end{array} \right\} $	$ \left\{ \begin{array}{l} \frac{{\left[ {48{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]\left( {\phi - \beta {c_{\rm{m}}}} \right)}}{{16{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}}}\\ \;\;\;\;\; + 4\left( {\Delta \phi - \beta \Delta c} \right) \end{array} \right\} $	$ \left\{ \begin{array}{l} \frac{{\left[ {48{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}} \right]{{\left( {\phi - \beta {c_{\rm{m}}} + \Delta \phi - \beta \Delta c + \beta {\lambda _2}} \right)}^2}}}{{16{C_{\rm{L}}} - \beta {{\left( {\delta - A} \right)}^2}}}\\ \;\;\;\;\; + 4\beta {\lambda _2}\left( {\phi - \beta {c_{\rm{m}}}} \right) \end{array} \right\} $
	集中式		$ \frac{{{C_L}\left[ {{{\left( {\phi - \beta {c_m} + \Delta \phi - \beta \Delta c + \beta {\lambda _1}} \right)}^2} - 2\beta {\lambda _1}\left( {\phi - \beta {c_m}} \right)} \right]}}{{\beta \left[ {4{C_L} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $	$ \frac{{{C_L}\left( {\phi - \beta {c_m}} \right)\left[ {\phi - \beta {c_m} + 2\left( {\Delta \phi - \beta \Delta c} \right)} \right]}}{{\beta \left[ {4{C_L} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $	$ \frac{{{C_L}\left[ {{{\left( {\phi - \beta {c_m} + \Delta \phi - \beta \Delta c + \beta {\lambda _2}} \right)}^2} - 2\beta {\lambda _2}\left( {\phi - \beta {c_m}} \right)} \right]}}{{\beta \left[ {4{C_L} - \beta {{\left( {\delta - A} \right)}^2}} \right]}} $

表3

表4

3类回收渠道系统和集中式决策系统的应急均衡决策结果"

Δϕ-βΔc	回收模式	分散式决策									集中式决策
		零售商				制造商			第三方	分散式总利润	集中式决策
		${\bar p}$	${\bar q}$	τ	Π_r	${\bar w}$	${\bar b}$	Π_m	Π_t	Π^d	${\bar p}$^c	${\bar q}$^c	τ^c	Π^c
-20	MRCRM	6.748	5.036	0.072	5.036	5.000	1	1.259	—	6.295	6.496	10.072	0.144	2.518
	MRCM	6.749	5.018	0.072	5.036	4.896	—	1.254	—	6.290
	MRCTM	6.750	5.009	0.036	5.018	4.996	0.90	1.252	0.01	6.279
-7	MRCRM	7.639	8.309	0.119	13.710	5.900	1	18.608	—	32.318	6.078	16.619	0.237	37.216
	MRCM	7.644	8.280	0.118	13.710	5.691	—	18.541	—	32.251
	MRCTM	7.647	8.265	0.059	13.661	5.696	0.90	18.508	0.02	32.194
-5	MRCRM	7.837	8.813	0.126	15.423	6.194	1	22.032	—	37.455	6.075	17.626	0.252	44.065
	MRCM	7.844	8.781	0.125	15.422	6.087	—	21.953	—	37.376
	MRCTM	7.847	8.766	0.063	15.367	6.094	0.90	21.914	0.03	37.309
-2	MRCRM	8.037	8.813	0.126	15.423	6.300	1	27.320	—	42.743	6.275	17.626	0.252	54.640
	MRCM	8.044	8.781	0.125	15.422	6.287	—	27.222	—	42.645
	MRCTM	8.047	8.766	0.063	15.367	6.294	0.90	27.174	0.03	42.568
0	MRCRM	8.237	8.813	0.126	15.423	6.500	1	30.845	—	46.268	6.475	17.626	0.252	61.691
	MRCM	8.244	8.781	0.125	15.422	6.487	—	30.735	—	46.157
	MRCTM	8.247	8.766	0.063	15.367	6.494	0.90	30.680	0.03	46.075
2	MRCRM	8.437	8.813	0.126	15.423	6.700	1	34.371	—	49.793	6.675	17.626	0.252	68.741
	MRCM	8.444	8.781	0.125	15.422	6.687	—	34.247	—	49.670
	MRCTM	8.447	8.766	0.063	15, 367	6.694	0.90	34.186	0.03	49.581
5	MRCRM	8.837	8.813	0.126	15.423	7.100	1	39.658	—	55.081	7.075	17.626	0.252	79.317
	MRCM	8.844	8.781	0.125	15.422	7.087	—	39.516	—	54.939
	MRCTM	8.847	8.766	0.063	15, 367	7.094	0.90	39.445	0.03	54.840
20	MRCRM	9.727	12.590	0.180	31.475	8.000	1	71.763	—	103.240	6.453	25.180	0.360	143.520
	MRCM	9.738	12.545	0.179	31.474	7.982	—	71.505	—	102.980
	MRCTM	9.744	12.522	0.089	31.362	7.991	0.90	71.377	0.03	102.770
100	MRCRM	15.670	32.734	0.468	212.770	14.000	1	434.350	—	647.120	4.338	65.468	0.935	868.710
	MRCM	15.710	32.616	0.466	212.760	13.950	—	432.790		645.560
	MRCTM	15.730	32.558	0.233	212.980	13.980	0.90	432.020	0.04	644.410

表4

表5

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符号	意义	符号	意义
c_m	使用原材料生产新产品单位生产成本	β	市场上产品价格敏感系数
c_r	使用废旧品生产再造品单位生产成本	q	产品的销售量(零售商的决策变量)
w	制造商给零售商产品单位批发价	A	回收商回收废旧品单位回收价
b	制造商从回收方处回收废旧品单位回收价(制造商的决策变量)	τ	废旧品回收率, 0≤τ≤1
p	零售商处产品单位销售价(零售商的决策变量)	C_L	回收努力成本系数
ϕ	产品的最大市场需求规模	δ	δ=c_m-c_r

	扰动区间	系统总利润	制造商利润
Δϕ>0, Δc＜0	$ 0 \le \Delta \phi - \beta \Delta c ＜ \frac{{4{C_{\rm{L}}}\left[ {\phi - \beta {c_{\rm{m}}} - \beta \left( {\delta - A} \right)} \right]\left( {\delta - A} \right)}}{{\left( {\delta - A} \right)}} + \beta {\lambda _2} $	$ {\mathit{\overline \Pi} ^{\rm{c}}} > \mathit{\overline \Pi} _{\rm{m}}^{\rm{R}} + \mathit{\overline \Pi} _{\rm{r}}^{\rm{R}} $	$ \mathit{\overline \Pi} _{\rm{m}}^{\rm{R}} > \mathit{\overline \Pi} _{\rm{m}}^{\rm{M}} > \mathit{\overline \Pi} _{\rm{m}}^{\rm{T}}$
Δϕ＜0, Δc>0	$ \sqrt {6\beta {\lambda _1}\left( {\phi - \beta {c_{\rm{m}}}} \right)} - \left( {\phi - \beta {c_{\rm{m}}}} \right) - \beta {\lambda _1} ＜ \Delta \phi - \beta \Delta c \le 0 $	$ {\mathit{\overline \Pi} ^{\rm{c}}} > \mathit{\overline \Pi} _{\rm{m}}^{\rm{R}} + \mathit{\overline \Pi} _{\rm{r}}^{\rm{R}} $
Δϕ＜0, Δc>0	$ - \left( {\phi - \beta {c_{\rm{m}}}} \right) - \beta {\lambda _1} \le \Delta \phi - \beta \Delta c ＜ \sqrt {6\beta {\lambda _1}\left( {\phi - \beta {c_{\rm{m}}}} \right)} - \left( {\phi - \beta {c_{\rm{m}}}} \right) - \beta {\lambda _1} $	$ {\mathit{\overline \Pi} ^{\rm{c}}} \le \mathit{\overline \Pi} _{\rm{m}}^{\rm{R}} + \mathit{\overline \Pi} _{\rm{r}}^{\rm{R}} $

Δϕ-βΔc	θ范围	θ取值	w(θ)	b(θ)	$ \mathit{\overline \Pi} _{\rm{r}}^{\rm{d}} $	$ \mathit{\overline \Pi} _{\rm{m}}^{\rm{d}} $	$ \mathit{\overline \Pi} _{\rm{m}}^{\rm{d}} + \mathit{\overline \Pi} _{\rm{r}}^{\rm{d}} $
-7	(0.15, 0.5)	0.435	2.437	0.435	16.198	21.018	37.216
-5	(0.19, 0.5)	0.443	2.483	0.443	19.538	24.527	44.065
-2	(0.22, 0.5)	0.474	2.465	0.474	25.901	28.739	54.640
0	(0.25, 0.5)	0.282	1.409	0.282	17.381	44.310	61.691
2	(0.28, 0.5)	0.480	2.302	0.480	32.960	35.781	68.741
5	(0.35, 0.5)	0.369	1.698	0.369	29.272	50.045	79.317
20	(0.22, 0.5)	0.247	0.987	0.247	35.405	108.121	143.525
100	(0.25, 0.5)	0.491	0.982	0.491	426.572	442.133	868.705

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