Multi-Objective Green Supply Chain Optimization

編輯群

編輯者	學號
林昭廷	Q36101341
簡煒軒	Q36104234

Table of Contents

• Background and Motivation
• Green Supply Chain Model
• Methodology
• Analysis Result
• Summary
• Reference

1. Background and Motivation

1.1 Background:

Green Supply Chain refers to the management between the facility operation, transportation and environmental effects of all facilities in a supply chain, i.e. the environment protection constraint is brought into facility location and allocation. Its purpose is to add environment protection consciousness into production and transportation, in order to improve the competitive edge of the supply chain regarding environmental effects.

1.2 Motivation:

The aim of most supply chain optimization problems is to minimize the total cost of the supply chain. However, since environmental protection is of concern to the public, a green supply chain,because of its minimum effect on nature, has been seriously considered as a solution to this concern.

1.3 Problem Definition:

We want to minimize the total cost of the supply chain and minimize the air pollution discharged from the supply chain to reduce the impact on the environment.

2.Green Supply Chain Model

2.1 Supply Chain Model(SCM):

There are some important roles in a supply chian:

1.Manufacturers
2.Warehouses
3.Distribution centers
4.Customers

And these four roles will have the following five activities:

1.Manufacturer purchase raw materials
2.Assemble products in Manufacturers
3.Transport products from Manufacturers to Warehouses
4.Transport products from Warehouses to Distribution centers
5.Transport products from Distribution centers to customers

We assume 3 Manufacturers,4 Warehouses,5 Distribution centers,16 Customers,below figure is an assumption example which shows the structure of a supply chain:

2.2 Sets:

Set	Description
C	customers
D	distribution centers
W	warehouses
M	manufacturers
TM	transportation options for manufacturers
TW	transportation options for warehouses
TD	transportation options for distribution centers
I	suppliers producing raw material, type i
J	suppliers producing raw material, type j

2.3 Notation:

• Environmental impact function:

PN	The amount of nitrogen oxide produced in supply chain (liter)
PC	The amount of carbon monoxide produced in supply chain (liter)
PO	The amount of volatile organic produced in supply chain (liter)

• Cost function:

RC	Total cost of purchasing raw materials from suppliers
FC	Fixed costs of opened facilities
VC	Variable costs of opened facilities
TC	Transportation costs
HC	Holding inventory costs in warehouses and distribution centers
BC	Backorder cost

2.4 Parameter:

Parameter	Description
demc	demand of customer c with mean μc and standard deviation σc
demf	demand of facility f ∈ {m,w, d}
crim	unit raw material cost from supplier of type i to manufacturer m
crjm	unit raw material cost from supplier of type j to manufacturer m
ctmmw	unit transportation cost from manufacturer m to warehouse w with transportation option tm
ctwwd	unit transportation cost from warehouse w to distribution centers d with transportation option tw
ctddc	unit transportation cost from distribution center d tocustomer c with transportation option td
disff′	distance between facility f ∈ {m,w, d} and facility f ′ ∈ {w, d, c}
fcf	fixed cost of opening facility f ∈ {m,w, d}
ltm	lead time of facility f ∈ {m,w}
vcf	unit variable cost per unit for facility f ∈ {m,w, d}
invf	expected inventory at facility f ∈ {w, d}
nrri	number of units of raw material of type i required to produce one unit of the product
nrrj	number of units of raw material of type j required to produce one unit of the product
p	penalty cost per unit of customer demand if it is not fulfilled
caf	the capacity of facility f ∈ {m,w, d}
caf′	capacity of transportation option f ′ ∈ {tm, tw, td}
GfN	rate of released nitrogen oxide to produce/handle one unit of product in facility f ∈ {m,w, d}
GfC	rate of released carbon monoxide to produce/handle one unit of product in facility f ∈ {m,w, d}
GfO	rate of released organic to produce/handle one unit of product in facility f ∈ {m,w, d}
Gf′N	rate of released nitrogen oxide per one unit of distance for transportation option f ′ ∈ {tm, tw, td}
Gf′C	rate of released carbon monoxide per one unit of distance for transportation option f ′ ∈ {tm, tw, td}
Gf′O	rate of released volatile organic per one unit of distance for transportation option f ′ ∈ {tm, tw, td}

2.5 Decision Variables:

Decision Variables	Description
xm	1 if manufacturer m is opened / 0 otherwise
xw	1 if warehouse w is opened / 0 otherwise
xd	1 if distribution house d is opened / 0 otherwise
xtmmw	quantity of products shipped from manufacturer m to warehouse w by transportation option tm
xtwwd	quantity of products shipped from warehouse w to distribution center d by transportation option tw
xtddc	quantity of products shipped from distribution center d tocustomer c by transportation option td
xim	quantity of raw material transported to manufacturer m from supplier that produce raw material type i
xjm	quantity of raw material transported to manufacturer m from supplier that produce raw material type j

2.6 Objective function:

• Objective function 1 --> Minimize cost:

• Objective function 2 --> Minimize pollution:

2.7 Constraints:

(12)–(14) determine the demand of each facility:

(15) and (16) also calculate the inventory level that each warehouse and distribution center must hold:

(17)–(18) also show that the standard deviation of demand for warehouses and distribution centers is defined as the weighted average of the standard deviation of demands assigned to them:

(19)–(21) ensure that we cannot assign a demand to a facility that is higher than its capacity:

(22)–(24) assure that if a facility does not supply any facility at its lower level, it will be closed and its binary variable is equal to zero:

(25) and (26) guarantee that the total raw material shipped from suppliers to a manufacturer can not be greater than the manufacturer demand, according to the required raw material for one product unit:

(27)–(28) ensure that the amount of product transported from a manufacturer and a warehouse must be equal to warehouse and distribution center demand respectively:

(29) distribution centers are allowed to not serve the percentage or total demand of a customer:

(30)–(32) are capacity constraints on transportation means, which prohibit assigning more than their capacity to the transportation means:

3. Methodology

3.1 The ϵ-constrained method

We minimize two objectives by setting one objectives to the constraint.

3.2 Pyomo

Although the majority of our equations are linear, this is a nonlinear problem , subtitute (17)(18) into (15)(16). We call a module from Python,called "Pyomo".
There is a solver Ipopt can caculate continuous nonlinear problems.

4.Analysis Result

4.1 Analyze the different nubmber of manufacturer and distribution center

Both the number of manufacturer and distribution center increase,the cost and pollution are also increased in SCM.
However,the distribution center has many routes, when the number of distribution centers increases, the cost and pollution increase is larger than that of the manufacturer.

4.2 Analyze the different nubmber of customers

The following pictures show that transportation cost account for large proportion in SCM.
If the customer number grow ,more products could not deliverd to customer in time so that the backorder cost increase.

5.Summary

Manufacturers, warehouse and distribution centers increase, cost and pollution will rise. Each facility has a different rate of increase in cost and pollution. The company has to consider what their target is. However,in reality, the cost and pollution functions may not be linear. This is the part that our model cannot explain.

6.Reference

• Multi-objective green supply chain optimization with a new hybrid memetic algorithm using the Taguchi method ,R. Jamshidi, S.M.T. Fatemi Ghomi,B. Karimi

• Pyomo

• Operations-Research-Applications github, Dr. Chia-Yen Lee

• Handout of Operations Research Applications, ORA_08_MODA_2021_ncku, Dr. Chia-Yen Lee