Modeling and Assumptions

Model Symbols and Definitions

Table 1, Table 2 and Table 3 show and defines the symbols, parameters and decision variables of our model.

Table 1. Meaning of the symbols and settings in Numerical Example.

Symbol Meaning of the Symbols Settings in Numerical Example
m Manufacturer 4
s Supplier 1
w DC warehouse 1
r Retailer 1
c Packaging materials
g Merchants
TM Utilize the model of returning vehicle in the supply chain 1: Recycling packaging materials
2: Transport goods to upstream suppliers
n The planning period 120
a Number of suppliers, a = 1, …a 4
b The types of merchandise offered by the supplier, b = 1, …b 5
S Start ordering time of merchants


Table 2. Meaning of the Parameters.

Parameter Meaning of the Parameters:
PSM Unit cost to the supplier for purchasing products from the manufacturer
PWS Unit cost to the DC warehouse for purchasing products from the supplier
PRW Unit cost to the retailer for purchasing products from the DC warehouse
PWM Unit cost to the DC warehouse for purchasing products from the manufacturer
PWC Unit cost to the DC warehouse for purchasing packaging materials
TMS Unit cost from the manufacturer to the supplier
TSW Unit cost from the supplier to the DC warehouse
TWR Unit cost from the DC warehouse to the retailer
TRM Unit cost from the retailer to the manufacturer
TMW Unit cost to ship from the manufacturer to the DC warehouse
FG Unit cost to the producing merchant
FC Unit cost of producing packaging materials
IW Unit cost of inventory for the DC warehouse
IM Unit cost of inventory for the manufacturer
QG The ordering quantity of goods
MIPG The maximum inventory in the production of goods
MADG The maximum annual demand for goods
OCG Order cycle time
LTG Lead time of purchasing goods
SSDG Safety stock with demand fluctuations for goods
SSLTG Safety stock with lead time fluctuations of purchasing goods
OHG On hand inventory
OOG On-order inventory
EMS Unit carbon emissions as a result of transportation from the manufacturer to the supplier
ESW Unit carbon emissions as a result of transportation from the supplier to the DC warehouse
EWR Unit carbon emissions as a result of transportation from the DC warehouse to the retailer
ERM Unit carbon emissions as a result of transportation from the DC warehouse to the retailer
EMW Unit carbon emissions as a result of transportation from the manufacturer to the DC warehouse
ECP Unit carbon emissions as a result of producing packaging materials at the manufacturing plant

Table 3. Meaning of the Strategic-Decision Variable.

Strategic-Decision Variable Meaning of the Strategic-Decision Variable
X(a, b), T M, n To determine whether or not to ship product B from manufacturer A, on the nth day of the TM case.