Research Article

Multiobjective Optimization of Sustainable WCO for Biodiesel Supply Chain Network Design

Table 1

Notation.

Set
ISet of kitchen waste supply point i
JSet of potential pretreatment facility locations j
KSet of potential biodiesel refinery site k
OSet of biodiesel demand location o
LSet of biodiesel refinery size level l
TThe set of t in time
Parameter
Distance from kitchen waste supply point i to pretreatment facility j
Distance from pretreatment facility j to biodiesel refinery k
Distance from biodiesel refinery k to biodiesel demand point o
Supply of restaurant kitchen waste i at time t
Demand of biodiesel demand point o at time t
Kitchen waste processing capacity of the pretreatment facility j
Waste oil processing capacity of a biodiesel refinery of size l
Storage capacity of the pretreatment facility j
Storage capacity of waste cooking oil from a biodiesel refinery of size l
Storage capacity of biodiesel from a biodiesel refinery of size l
Pretreatment facility handles the cost of unit kitchen waste
Cost of process of waste cooking oil per unit at a biodiesel refinery
Transportation cost of per unit kitchen waste
Transportation cost of per unit waste cooking oil
Distance transport cost of per unit biodiesel
Storage cost of per unit kitchen waste
Storage cost of per unit waste cooking oil
Storage cost of per unit biodiesel
Fixed construction cost of the pretreatment facility at j
Fixed construction cost of a biodiesel refinery of size l at site k
Carbon emission of unit kitchen waste collection
Carbon emission of unit kitchen waste pretreatment
Carbon emission of unit waste cooking oil processing
Carbon emissions per kilometer transported by trucks
Transformation factor of kitchen waste to waste cooking oil
Conversion factors of waste cooking oil to biodiesel
Decision variables
Quantity of kitchen waste supply point transported to pretreatment facility j at time t
Quantity of pretreatment facility j delivered to biodiesel refinery k at time t
Quantity of biodiesel refinery k transported to biodiesel demand point o at time t
It is 1 when position j is used to build the pretreatment plant; otherwise, it is 0
It is 1 when location k is used to build a refinery of size l; otherwise, it is 0
Quantity of kitchen waste processed by the pretreatment plant j at time t
Quantity of waste oil treated by refinery k at time t
Quantity of kitchen waste stored in the pretreatment facility j at time t
Quantity of waste oil stored in biodiesel refinery k at time t
Quantity of biodiesel stored in biodiesel refinery k at time t