Research on Supply chain management (SCM) has gained remarkable attention among academics and practitioners^{ }
To reduce the environmental and economic impacts of supply chains in ^{4}, a singleitem comprehensive green supply chain planning optimization model is created. In ^{5}, a multiobjective, singleitem, singleperiod optimization model in the strategic supply network planning process that includes the environmental investment decision is suggested. In^{ }
This work is an extension of the work done in ^{4, 12}. It entails the supply chain network's configuration and influence of performance considering the stated objectives ^{13}. So, it was decided that the profit be maximized directly in this work.
The proposed supply chain consists of three stages of potential suppliers, and retailers in a factory as shown in
The following assumptions were considered:
Each product is composed of multiitems.
The model aims to maximize profit.
All products may have Initial/final inventory.
All facilities have limited capacity for each period.
The customers’ demands are deterministic and known.
P: Set of products,
I: Set of items,
S: Set of potential suppliers,
C: Set of potential retailers,
T: Set of periods,
FFCt: facility’s fixed cost at period t
DEM_{cpt}: demand of retailer c from product p in period t (unit/period)
REQip: Required amount of item i for product p(unit)
IIf_{p}: the initial inventory of product p (unit)
FIf_{p}: the final inventory of product p (unit)
P_{pct}: the unit price of product p at retailer c in period t ($)
W_{p}: the weight of product p (kg)
MH_{p}: manufacturing hours for product p (hour)
D_{sf}: the linear distance between supplier s and the facility (km)
D_{fc}: the linear distance between the facility and retailer c (km)
CAP_{sit}: the capacity of supplier s for item i in period t (kg)
CAPHf_{t}: manufacturing capacity of the facility in period t (hour)
CAPMf_{t}: raw material storing capacity of the facility in period t (kg)
CAPFSf_{t}: the finished good storing capacity of the facility in period t (kg)
MATCsit: material cost per unit of item i supplied by supplier s in period t ($/kg)
MC_{ft}: manufacturing cost per hour for the facility in period t($/hour)
MH_{p}: manufacturing hours for product p (hour)
NUCCf: nonutilized manufacturing capacity cost per hour of the facility ($/hour)
SCPU_{p}: backordering cost per unit per period ($/unit/period)
HC: holding cost per unit weight per period at the facility store ($/kg/period)
B_{si}: the batch size of item i transported from supplier s to the factory(unit)
Bf_{p}: batch size transported from the facility for product p to retailer (unit)
TC_{mt}: transportation cost for the transportation mode per kilometer in period t ($/km)
QSF_{sit}: number of batches of item i transported from suppliers to the facility in period t
QFC_{cpt}: number of batches of product p transported from the facility to retailer c in period t
IFF_{pt}: number of batches transported from the facility to its store for product p in period t
IFC_{cpt}: number of batches transported from store of the facility to retailer c for product p in period t
Rf_{pt}: facility store a residual inventory of product p in period t
The profit is calculated by subtracting the total cost from the total revenue. The total revenue is calculated using Equation 1.
The total cost is the summation of the following costs.
Fixed Cost
Material costs
Manufacturing costs
NonUtilized capacity cost (for the facility)
Backordering cost (for retailers)
Transportation costs
Inventory holding costs
To ensure flow balance and capacity limits, this model considered two types of constraints.
Constraint (913) ensures that materials and goods flow in a balanced manner.
Constraint (1416) ensures that all facilities work within their limited capacities.
Constraint (17) guarantees that the facility store's remaining inventory does not surpass its storing capacity at any given time.
The Overall Service Level (OSL) is determined using Equation 18 as the ratio between the total weights of products sent to all retailers during the planning horizon and the weight of products requested during the same planning horizon.
The efficacy of the model has been verified through the following comprehensive example.
To verify the model, the following random example is solved, and the results are analyzed. The assumed demands are shown in
Period 
1 
2 
3 
4 
5 
6 

Retailer 1 
Product 1 
2,200 
2,700 
3,200 
3,700 
4,200 
4,700 
Product 2 
500 
650 
800 
950 
1,100 
1,250 

Retailer 2 
Product 1 
2,100 
2,350 
2,600 
2,850 
3,100 
3,350 
Product 2 
600 
700 
800 
900 
1,000 
1,100 
No. Input parameter Value Unit No. Input parameter Value Unit 1 S and C 2  14 MCft 2 $/hr 2 P 2  15 MHp 1, 2 hrs 3 IIfp 10, 10 Unit 16 MCft 10 $/hr 4 FIfp 20, 10 Unit 17 NUCCf 1 $/hr 5 Ppct 110, 220 $/Unit 18 SCPUp 5 $/period 6 W1,2 6, 12 Kg 19 HC 0.75 $/kg. period 7 MH1,2 1, 2 Hrs 20 Bsi 10, 5 Unit 8 CAPsit 18,000 Kg 21 Bfp 1, 1 Unit 9 CAPHft 10,000 Hrs 22 TCt 0.05 $ 10 CAPMft 50,000 Kg 23 FC 50,000 $ 11 CAPFSft 10,000 Kg 24 Bf 1 unit 12 MATCit 0.9, 1, 2.7, 2.8 $/kg 25 Dsf 55.8, 40.4 Km 13 REQip 4, 8, 2, 1 Kg./unit 26 Dfc 14.8, 22.4 Km
The model is solved using Evolver software on an Intel® Core™ i77700 CPU @3.60 GHz 4 Core(s) 8 logical processors (8 GB of RAM).
For more discussion, the demand of each retailer from each product has been studied individually. From
Balancing of the supplied material and the received products during all periods have been presented in

Period 
T1 
T2 
T3 
T4 
T5 
T6 
Supplied Item 1 
Qsit11 
788 
1,300 
1,533 
1,533 
1,533 
1,533 
Qsit21 
1,800 
1,800 
1,800 
1,800 
1,800 
1,800 

Nsit11 
7,880 
13,000 
15,333 
15,333 
15,333 
15,333 

Nsit21 
18,000 
18,000 
18,000 
18,000 
18,000 
18,000 

I1 in II 
120 






SUM 
26,000 
31,000 
33,333 
33,333 
33,333 
33,333 

190,333 

Received Item 1 
I1 in P1 
17,120 
20,200 
23,200 
26,200 
29,200 
32,280 
I1 in P2 
8,720 
10,800 
10,133 
7,133 
4,133 
1,053 

I1 in FI 
 
 
 
 
 
160 

SUM 
25,840 
31,000 
33,333 
33,333 
33,333 
33,493 

190,333 

Supplied Item 2 
Qsit12 
 
 
 
 
 
 
Qsit22 
2,588 
3,100 
3,333 
3,333 
3,333 
3,333 

Nsit12 
 
 
 
 
 
 

Nsit22 
12,940 
15,500 
16,667 
16,667 
16,667 
16,667 

I2 in II 
60 






SUM 
13,000 
15,500 
16,667 
16,667 
16,667 
16,667 

95,167 

Received Item 2 
I2 in P1 
8,560 
10,100 
11,600 
13,100 
14,600 
16,140 
I2 in P2 
4,360 
5,400 
5,067 
3,567 
2,067 
527 

I2 in FI 





80 

SUM 
12,920 
15,500 
16,667 
16,667 
16,667 
16,747 

95,167 
In this section, the effect parameter change has on system behavior has been studied. The following parameters are shown in
No. 
Input parameter 
Value 
Unit 
No. 
Input parameter 
Value 
Unit 
1 
Ppct 
100, 100 
$/Unit 
8 
REQip 
1, 10, 1, 10 
Kg./unit 
2 
CAPsit 
20,000 
Hrs 
9 
SCPUp 
5, 10 
$/period 
3 
CAPHft 
20,000 
Kg 
10 
HC 
2, 4 
$/kg. period 
4 
CAPMft 
20,000 
Hrs 
11 
Bsi 
10 
Unit 
5 
CAPFSft 
10,000 
Kg 
12 
Ts, Tf 
0.005, 0.001 
$ 
6 
MATCit 
1, 2 
$/kg 
13 
FC 
50,000 
$ 
7 
Dsf, Dfc 
50 
Km 




The effect of demand on the total revenue, cost, profit, and OSL have been studied by assuming equal demands for all products and customers in all periods. The results of this study have been presented in
The developed multiitem, multiproduct, and multiperiod mathematical model has successfully optimized the supply, production, distribution, and inventory planning for a multiechelon supply chain of two suppliers, one factory, and two retailers to maximize the profit.
The efficiency of this model has been verified by solving and analyzing the results of a comprehensive example. Also, the effect of demand on the total revenue, cost, profit, and OSL have been studied and analyzed.
The model is limited to nonperishable products and materials.
For larger problems, it is recommended that software like GAMS or Xpress be used instead of Evolver.
Tackle the robust demand problems
Optimize more than one objective like maximizing the overall service level and minimizing the total cost.
Considering the time value of money and the interest rate by optimizing the NPV.
Study the same problem under disruptions and modularity.