Solving Method a5 ies - an - N Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear, Select the LP Simplex engire ae - =o = to for linear Sulver Probl r ine for
Trang 1UEH UNIVERSITY COLLEGE OF BUSINESS SCHOOL OF INTERNATIONAL BUSINESS - MARKETING
Trang 2UEH UNIVERSITY COLLEGE OF BUSINESS SCHOOL OF INTERNATIONAL BUSINESS - MARKETING
Trinh Huynh Quang Canh
22C1BUS50313704
Trân Mỹ Linh
K46 IBCO3 31201027174
Ho Chi Minh City, 12/2022
Trang 4Too long to read on your phone? Save to read later on your
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Trang 5I Linear programming 1 Question a
O Variable: Xj;: the number of units produced daily at plant i of product j
i=l, 2, 3, 4, 5 (plant)
j= 1, 2, 3 (product) O Objective
Total cost MIN = 29X1A + 43X1B + 48X1C + 28X2A + 42X2B + 35X2C + 32X3A + 46X3B + 30X3C + 29X4A + 41X4B + 31X5A 4 45X5B
O Constrain o Supply
Plant 1: XIA + XIB + XIC <= 400 Plant 2: X2A + X2B + X2C <= 600 Plant 3: X3A + X3B + X3C <= 400 Plant 4: X4A + X4B + X4C <= 600 & X4C =0 Plant 5: XSA + X5B + X5C <= 1000 & XSC =0
o Demand
Product 1: XIA + X2A + X3A + X4A + X5A = 600
Product 2: X1B + X2B + X3B + X4B + X5B = 1000
Product 3: X1C + X2C + X3C + X4C + X5C = 800 O Result
The minimum total cost is $85,800
Trang 6Solver Parameters x
Set Objective: scsze đè
— ie Me eas Ẵ To: O Max (đ Min {valueOt 9
Get & Transform Data Queries & Connections By Changing Variable Cells:
Picurel ~ Ê Subject to the Constraints in 7 = R l = ơ bh ' 7 toa = SDS22:$°Đ22 ^ || Add 1E es $f$19= 0 H = 2 $G$ 154$6$19 =~ $181551$19 | Shange
4 ‘Unit production cost
a = mm | Make Urconstrained Variables Noa-Negative
14 Product sees n Simplex LP vị hae
15 1 2 3 Total Capacity 16 1 400 < 400 1 2 600 ô 600 Solving Method
a5 ies - an - N Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear, Select the LP Simplex engire ae - =o = to for linear Sulver Probl r ine for Solver problems th
a Total 600 1000 300
(Gi OM for Windows - [Linear Programming Results}
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That minum total cost will be achieved if: - Plant 1 have to produce 400 units of Product 2
6
Trang 7- Plant 2 have to produce 200 units of Product 1 and 400 units of Product 3 - Plant 3 have to product 400 units of Product 3
- Plant 4 have to produce 600 units of Product 2 - Plant 5 have to produce 400 units of Product 1
2 Question b O Variable Xj: the number of units produced daily at plant i of product j
i=l, 2, 3, 4, 5 (plant)
j= 1, 2, 3 (product) O Objective
Total cost MIN = 29X1A + 43X1B + 48X1C + 28X2A + 42X2B + 35X2C + 32X3A + 46X3B + 30X3C + 29X4A + 41X4B + 31X5A 4 45X5B
550 units Plant 4: X4A + X4B + X4C <= 600 & X4C = 0 Plant 5: XSA + X5B + XSC <= 1000 & X5C =0
o Demand
Product 1: X1LA + X2A + X3A 4+ X4A 4+ X5A=1
Product 2: XIB + X2B + X3B + X4B + X5B = 1
Trang 8Product 3: XIC + X2C + X3C + X4C + X5C = 1 O Result
The minimum total cost is $61,820
0 5 31 45 1000 | Make Unconstrained Variables Non-Negative
13 Ee Require 950 320 ‘sso Select a Solving is Simpler LP a v Options a
Method: 1
Production cost of full required of exch product Tr 1 2 3 Solving Method
1 1 27550 15760 - 26400 ki : 3% s seas | aad] Sean, Select the GRG Nonlinear engne for Salver Problems that are smooth nonlinear Select the LP Simplex engine
20 Pisnt 3 30400 14720 16500 for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth, a 4 27550 | 13120 °
- Plant 2 have to produce Product 3 - Plant 4 have to produce Product 2 - Plant 5 have to produce Product 1
3 Question c O Variable:
Trang 9Xj;: the number of units produced daily at plant i of product j
i=l, 2, 3, 4, 5 (plant)
j= 1, 2, 3 (product) O Objective
Total cost MIN = 29X1A + 43X1B + 48X1C + 28X2A + 42X2B + 35X2C + 32X3A + 46X3B + 30X3C + 29X4A + 41X4B + 31X5A 4 45X5B
QO Constrain o Supply
Plant 1: XIA + XIB + XIC =400 Plant 2: X2A + X2B + X2C = 600 Plant 3: X3A + X3B + X3C = 400 Plant 4: X4A + X4B + X4C = 600 & X4C =0 Plant 5: XSA + X5B + X5C = 1000 & X5C =0
o Demand
Product 1: 1200 >= KIA + X2A + X3A + X4A + X5A <= 1400 Product 2: 650 >= X1B + X2B + X3B + X4B + X5B <= 800 Product 3: 850 >= X1C + X2C + X3C + X4C + XSC <= 1000
O Result
The minimum total cost is $100,550
Trang 10Trần Mỹ Linh IBCO3 - Excel Pagelayout Formulas Data
Set Objective: ses27
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7| 1 23 43 4 | Reset All
8 = 28 42 3»
s| Plant 3 3z 45 30 | Load/Save 10 4 23 4 (| Make Unconstiained Variables Non-Negative
11] 5 31 45 EEE
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13 Units produced daily Method: | Sos
14) Product
te 2 3 Tetal Capacity Solving Method
i : “= = * Select the GAG Nonlinear engine for Solver Problems that are srrooth nonlinear Select the LP Simplex engine
18] Plant 3 20 - an for linear Solver Problems and select the Evolutionary engine for Solver problems thatare son-srneoth,
19 4 600 = 600 20| 5 1000 = 1000
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O Conclusion That minum total cost will be achieved if:
- Plant 1 have to produce 350 units of Product 1 and 50 units of Product 2
10
Trang 11- Plant 2 have to produce 50 units of Product 1 and 550 units of Product 3 - Plant 3 have to product 400 units of Product 3
- Plant 4 have to produce 600 units of Product 2 - Plant 5 have to produce 1000 units of Product 1
I Inventory 1 Question a We have:
D = 250 x 12 = 3000 units/year Price = $1.25/unit
h= 12% x 1.25 = $0.15/unit Salary = $18.75/hour K= —— = $6.25/unit L=0 day
WD = 360 days
By using EOQ model, Joseph’s problem can be solved:
O Excel: Set the formula as follow:
o Reorder point/Daily demand rate = = xL o Optimal quantity = ya
KxD
Q
hxQ 2
o Annual set up cost =
o Annual holding cost = o Total variable cost = Annual set up cost + Annual holding cost — After completely filling the formular, we have the result on Excel as picture below:
11
Trang 12
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6 D = 3000 unils pér year Re-order point 0
7 Price ($) = 1.25 per unit 8 h(s) = 0.15 per unit Annual Set up cost ($) 37.5
9 Salmy(S) = | 1875 perhour Annual holding cost ($)
10 K@) = 6.35 per order Total variable cost ae
11 L = 0 day 12 WD = 360 days
o Reorder point/Daily demand rate = = xL
o Annual set up cost = =
AxQ
o Annual holding cost = 2 o Total variable cost = Annual set up cost + Annual holding cost Open Solver and set :
o The “Total variable cost” minimum as the objective
o Variable is Q
o Selecting the solving method is “GRG nonlinear”
Salver Parameters x Set Oticcvc: $5510 +
To: Cmax @® Nin Ê) valueOt:
By Changing Variable Celis:
‘SM$1S +
Subjee to the Constaints;
Aid Chinge Delete Bezet All
KÉ Má Unconstrained Variables Non-Negative Select 1 Solving GRG Nonlinear v Options,
Mathod: Sulving Method! Seleu the GRG Noriinwat engine for Sols: Proliers that are amcoth nonlinear, Select the LP Simple engine for linear SoWver Problems, and Select the Evolutionary engine for Solver problems thet are ron-smuath,
Trang 13When completely filling the formular, set the solver and put “Solve” button, the solver can not get the result Therefore, we should fill the number which is >= 3 in Q and then solve the “Solver” again — After fill the number which is >= 3 in Q and then solve the “Solver” again, we have the result on Excel
Solver as picture below:
Price (S$) = 1.28 pst unit
h@ = 0.15 per uait Annual Set up cost ($)_ 37.5 Salary (S) = 187% per hour Ansuual holding cost ($) 37.8 K@ = 6.25 pet onder Total variable cost 3
1 - 9 day
O QM: Set EOQ model in Inventory section in the QM and choose “Compute reorder point” Fill the the required data in the table:
t QM for Windows - [Data Table]
File Edit View Module Format Tools
Arial ~ 82+ BT Reorder point
© No reorder point © Compute reorder point
Parameter Value
Demand rate(D) Setup/Ordering cost(S) Holding cost(H) Unit cost
Days per year(optional)
Daily demand rate(d) Lead time (in days) Safety stock
Trang 14
— After filling, we have the result on QM as picture below:
Gi OM for Windows - D:\ERP\2A.inv - [Inventory Results] e& File Edit View Module Format Tools Window Help
Cah &
Arial x
E H8 10% + G] Rak f2) Ml Edit Date
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Instructio 0 1 Thete are
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Question 24 Solution
Parameter Demand rate(D)
Setup/Ordering cost(S)
Holding cost(H) Unit cost Days per year (D/d)
Daily demand rate
Lead time (in days)
Annual Hoiding
Un# costs (PD) Total Cost 75
Reorder point
The optimal inventory policy under these conditions are that Joseph should place an order of 500 units each time and 6 times per year @ so that he can reach the minimum total variable cost at $75 and still has enough inventory
2 Question b We have:
L=5 days
By using EOQ model, Joseph’s problem can be solved:
O Excel:
14
Trang 15Set the formula as follow: o Reorder point/Daily demand rate = = xL
o Optimal quantity = ya
o Annual set up cost = =
AxQ
o Annual holding cost = ) o Total variable cost = Annual set up cost + Annual holding cost — After completely filling the formular, we have the result on Excel as picture below:
Trần Mỹ Linh IBC03 - Excel
Home Insert Page Layout Formulas Review M
§ h(S) = 0.15 per unit Annual Set up cost ($) 37.Š
9 Salary(S) = 1875 perhow Annual holding cost (S$) 37.5
10 K@® = 6.25 per order Total variable cost 75 "1 L = 5 day
12
13 Decision
14 Q=
QO Excel Solver: Set the formula as follow except the optimal quantity (Q):
o Reorder point/Daily demand rate = — xL
360 KxD
o Annual set up cost = 0
AxQ o Annual holding cost = 5
15
Trang 16o Total variable cost = Annual set up cost + Annual holding cost Open Solver and set :
o The “Total variable cost” minimum as the objective
By Changing Variable Cells:
Select 4 Solving GRG Nonlinear Options Method:
Solver as picture below:
16
Trang 17Say) = 1875 per how Anmual bolting cost (S) 3 a K® L = + 6358 $ prorder cay Total varisble cost |i)” oon f
om
imation (tae nome sa nse
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& QM for Windows - [Data Table] | File Edit View Module ‘Format | Tools
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|| Arial v 821v | B
Reorder point- © No teorder point @ Compute reorder point
Parameter Value Demand rate(D) 3000
Setup/Ordering cost(S) 6.25
Holding cost(H) AS Unit cost 0 Days per year(optional) 360
Daily demand rate(d) | 0
Lead time (in days) q
Trang 18& File Edit View Module Format Tools Window Help
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Instruction No reorder point 0 There ate more re (* Compute reorder point +l| >| using the WIND
Question 2B Solution Parameter Value Parameter Value i Demand rate(D) Optimal order) 500;
Setup/Ordering cost(S) Maximum | 500 Holding cost(H) Average 250 Unit cost Orders per| 6 Days per year (D/d) Annual Setup | 37.5
Daily demand rate Annual Holding | 37.5
Lead time (in days) Safety stock Unit costs (PD) | 0
Total Cost 75 Reorder point | 41.67 units
D = 250 x 12 = 3000 units/year Price = $1.25/unit
h= 12% x 1.25 = $0.15/unit Salary = $18.75/hour
o Optimal quantity (Q) = yan
18
Trang 19Tran My Linh Home Inset Pagelayout Formulas Review View Help SAU
Data » — From Table/Range All > Be
Get & Transform Data Queries & Connections Sort & F
S~¢ * I9 i fe | =E12*C1642/(2*C15)
6 D = 3000 units per year
7 Price ($) = 1.25 per unit Annual Set up cost ($) 36.28
8 | hs) = 0.15 per unit Annual holding cost ($) _ 33.97 9 | Salary (S) = 18.75 per hour Annual shortage cost @{ 232 10 | K@) = 6.25 per order Total variable cost ($) 72.57 11 | L = 5 day
12 p(s) = 22
13
14| Decision
mi
O Excel Solver: Set the formula as follow except the optimal quantity (Q):
o Optimal quantity (Q) = ya
timal hort: = ——_ o Optimal maximum shortage (S) mạng
KxD
o Annual set up cost =
19
Trang 20o The “Total variable cost” minimum as the objective
o Variable is Q and S
o Selecting the solving method is “GRG nonlinear
Solver Parameters Set Objective: $S$:0| +
Te _) Max @ Min ©) Value Of:
By Changing Variable Cells:
Subject to the Constraints
aud Change
Delete
Reset All
Load/Save
lv] Make Unconstrained Variables Non-Negative
Select a Solving GRG Nonlnear ¥ Options
Method: solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear Select the IP Simplex engine
for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth
When completely filling the formular, set the solver and put “Solve” button, the solver can not get the result Therefore, we should fill the number which is >= 3 in Q and S and then solve the “Solver” again
— After fill the number which is >= 3 in Q and S and then solve the “Solver” again, we have the result on Excel Solver as picture below:
20