The sustainable supply chain management model and
model formation
he authors developed a mixed integer, nonlinear optimization
model to provide decision makers of enterprises a guideline for
SSCM, with consideration of the operational costs, as well as the
social costs of CO2 emissions.
4.1. Parameter notations and definitions
Before the model is formulated, the basic parameter notations and
definitions are introduced. In this study, the authors use the following
indices: j ˛ J, a set of candidate suppliers; k ˛ K, a set of potential
plants; l ˛ L, a set of possible distribution centers; m ˛ M, a set of
materials needed for production, and, i ˛ I, a set of products. The
problem parameters and decision variables are defined as follows:
4.1.1. Parameters
MCmjk unit cost of material m ordered from supplier j to plant k
SCmj capacity limit of material m of supplier j
CPk capacity limit of plant k
PCik unit production cost of product i in plant k
TCikl unit transportation cost of product i shipped from plant k to
DC l
LCik, UCik lower, and upper production capacity limits of product
i in plant k
CO2ik unit CO2 emission of product i produced in plant k
CO2r CO2 emission of unit weight, unit distance using transportation
mode r
Wm unit weight of material m
Wi unit weight of product i
4.1.2. Decision variables
Gmjk total units of material m purchased from supplier j to plant
k
Hikl total units of product i transported from plant k to DC l
TDmr material m transportation distance of mode r
TDir product i transportation distance of mode r
SCRCO2 social cost rate of CO2 emission
4.2. The objective function
The total costs of the objective function include the operational
costs and social costs of CO2 emissions. The operational costs of the
supply chain include purchasing costs, production costs, and
transportation costs. The social costs of carbon emissions of the
supply chain include the carbon emissions caused by the process of
products production and transportation of products. Therefore, the
objective function to be minimized is given by:
The first term in the objective function is the total purchasing
cost of materials from all suppliers (including transportation costs
of materials). The second term is the total production costs in all
plants. The third term is the total transportation costs of all products.
The last term is the total social costs of CO2 emissions
(including emissions caused by products production, materials
transportation, and products transportation).
4.3. Constraints
For a supply chain management model, there are many generic
constraints to be considered, including balance constraints of materials
and products, the capacity limit constraint, and the
throughput limit constraints. These constraints are discussed
below
socail cost