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以綠色導向政策探討低經濟價值再生材料之回收供應鏈
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improvement of product greenness. They are often strategic for the business and may not
apply to the maximum rationality in optimization. For example, the decision of EDRM
mixture
σ
is often driven by the procurement cost while the environmentally friendly product
design
ξ
is determined by the level of acceptance in the consumer market. On the other hand,
the ingredient mixture and product composition are costly in realizing frequent change. They
can take as given for the purpose of analysis in this paper.
To urge manufacturers to move toward GSCM, government agencies plan to apply
economic instruments – a pollution tax (denoted by
ϕ
for producing one unit of a
manufactured product) and a subsidy (denoted by ε for recycling one unit of an end-of-life
product) – to manufacturers in charge of manufacturing and end-of-life product recycling.
This study employs a variable rate tax, which depends on product eco-design or the level of
effluent
ξ
. Governments collect less tax if the product emits less effluent. In this study, the
amount of tax is linear to the effluent, that is,
ϕ
i
ξ
i
.
The game in the analysis is Stackelberg. The government acts as the first leader and the
two suppliers are the second leaders, and the manufacturers follow the actions. By above set
of game, the relationship among each player can then be readily induced. We begin modeling
the closed-loop supply chain by manufacturers’ profits:
π
mi
=
pq
i
– (
σ
xi
+
σ
yi
)
q
i
–
q
i
–
ϕ
i
ξ
i
q
i
, where
w
x
and
w
y
are the wholesale prices for manufacturer
i
for procuring a unit of
virgin and recycled materials, respectively, and
is the marginal cost of producing a unit
of products. The virgin-material supplier can determine its wholesale price
w
xi
to each
manufacturer and seek to maximize profit
π
x
=
σ
xi
q
i
–
c
x
σ
xi
q
i
, where
c
x
denotes the
marginal cost for generating a unit of virgin materials. The EDRM material supplier also
determines its wholesale price
to each manufacturer and seeks to maximize profit
π
y
=
q
i
–
c
h
h
i
–
c
u
(1-
η
)
h
i
+
, where
c
h
and
c
u
are the marginal costs of
collecting and final disposal of the waste.
We temporarily use a notation here and this one will be substituted by a new symbol
w
later for a simplification of notations. In response to the legislative requirements for the
input amount of EDRMs to produce a unit of product as well as the recycled-material supply
process, the system converts waste into usable materials, at which
σy
i
q
i
=
ηh
i
at a fixed
conversion rate η. Assuming a long-term flow balance condition in the closed-loop supply
chain, the
h
i
part in the profit of EDRM supplier can be replaced by
σy
i
q
i
/
η
.
The government’s optimal decisions with respect to the environmental taxes (
ϕ
) and
subsidies ( ) for managing recycled-material supply chain members are developed as the
Stackelberg first leader. Drawing from the concept of social welfare (SW) maximization