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臺大管理論叢
第
27
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3. A Closed-Loop Supply Chain Model
The problem in this study involves a virgin material supplier and an EDRM supplier,
which collects end-of-life product and provides recovered materials under the subsidy of the
government, as shown in Figure 1. A group of manufacturers take materials from both
suppliers, pay environmental tax to the government, and sell the final products to the market.
The problem is postulated as maximizing the profits of all parties, including the profits of the
manufacturers and suppliers, and the social welfare in the entire closed-loop supply chain
and the environment.
Figure 1 Players and Key-Variables in a Supply Chain Network
virgin
material
Supplier x
EDRM recycler y
governmetn
consumption
(
1-σ
)
q
Wx
Wy
σq
q
φ
ε
η
manufacturers
We assume the market perform adopt Cournot competition and the inverse demand
function satisfies
p
= 1-∑
q
i
. Manufacturers produce total demand
q
i
, where
q
i
represents the demand of manufacturer
i
and
n
denotes the number of the competitive
manufacturers involved in the system.
Each manufacturer design its products with a predetermined ingredient and a design
specification fulfilling eco-design principles. The ingredient comprises 1-
σ
virgin materials
and
σ
EDRMs and the eco-design associates to the level of effluent
ξ
. The ingredient and
effluent can either be determined by law or by accommodating to an existing verified
processing ingredient. For example, (Molding) (Lead-free Solider) We set the variables
σ
and
ξ
as exogenous to the optimization framework so that further strategic analysis can be
applied to the variables. These two exogenous decisions are crucial for promoting voluntary