OPERATIONAL RESEARCH (OR)
INDIVIDUAL ASSIGNMENT- Take a problem from your own organization and apply the concepts taught in the class
NAME: RAJESH KUMAR VERMA SMS ID: 110387 SID NO: RB12044 BATCH: PGCBM-21 FACULTY: DR. SUPRIYA KUMAR DE STUDY CENTER: DAKC, NAVI MUMBAI
RAJESH KUMAR VERMA
PGCBM-21
SMS ID: 110387
PAGE: 1 6/16/2012
Table of Contents
1. PROJECT PROBLEM: ............................................................................................................................................................3 2. PROJECT SOLUTION ............................................................................................................................................................3
RAJESH KUMAR VERMA
PGCBM-21
SMS ID: 110387
PAGE: 2 6/16/2012
1.
PROJECT PROBLEM:
A “ZTE Corporation” has targeted the potential market in India and decided to sale the most demanding products to telecom companies in Indian market. The company has considered for the production of four potential products i.e. HSD, TAB- GSM, TAB- CDMA and Smart Phone. All products can be majorly obtained by just 4 resources: electronic Component, non-electronic component, battery and assembly time. The composition of the four products in terms of these four inputs is shown in the table given below along with unit selling price of the products:
Table- 1: Data for ZTE Corporation
Resource Electronic Component Nonelectronic Component Battery assembly Time (hours) Selling Price (Per Unit) HSD TAB-GSM TAB-CDMA Smart Phone 3 4 4 3 2 2 4 3 1 1 1 1 1 1 3 2 $70 $80 $150 $110 Supply 4700 4500 3000 2500
Electronic component can be obtained at $7 per unit; Non electronic component can obtain at $5 per unit, battery component can be obtained by$5 per unit and assembly time cost $10 per hour.
2.
PROJECT SOLUTION
Each resource is available in the limited quantities as shown in the above in Table-1.
2.1 COST CALCULAATION
Table-2: Cost calculation for products
COST CALCULATION Electronic Component Non Elecronic component Battery Assembly Time Total cost HSD TAB-GSM TAB-CDMA Smart $ 21.00 $ 28.00 $ 28.00 $ $ 10.00 $ 10.00 $ 20.00 $ $ 5.00 $ 5.00 $ 5.00 $ $ 10.00 $ 10.00 $ 30.00 $ $ 46.00 $ 53.00 $ 83.00 $ Phone 21.00 15.00 5.00 20.00 61.00
RAJESH KUMAR VERMA
PGCBM-21
SMS ID: 110387
PAGE: 3 6/16/2012
Cost has been calculated by multiplying with unit of components, e.g. cost calculation for each HSD is $46 (3x $7+2x$5+1x$5+1x$10) and other products so on…
2.2 PROFIT CALCULATION
Table-3: Profit calculation for products
HSD Solution Value Selling Price Cost Price Profit TAB-GSM 0 380 $ 70.00 $ 80.00 $ 46.00 $ 53.00 $ 24.00 $ 27.00 TAB-CDMA Smart Phone Total 0 1060 $ 150.00 $ 110.00 $ 147,000.00 $ 83.00 $ 61.00 $ 84,800.00 $ 67.00 $ 49.00 $ 62,200.00
Profit has been calculated by subtracting the total cost for making a product from its unit selling price. The profit contribution of each HSD is $24(selling price is $70 less the total cost of 3x $7+2x$5+1x$5+1x$10) and other product calculated as same… As per above calculation profit has been calculated for each HSD is $24,each TAB-GSM is $27, each TAB-CDMA is $67 and for each Smart phone is $49. We can assume here H, TG, TC and SP denotes for HSD, TAB-GSM, TAB-CDMA and Smart phone respectively. Now we can formulate the LP model for this problem as under: Maximize profit= $24H+$27TG+$67TC+$49SP
2.3 Constraints for the problem will be:
Electronic component Non-electronic component Battery Assembly Time (in hours) Non-negativity = = = = = 3H+4TG+4TC+3SP < 4700 2H+2TG+4TC+3SP < 4500 1H+1TG+1TC+1SP < 3000 1H+1TG+3TC+2SP < 2500 H, TG, TC, SP > 0
RAJESH KUMAR VERMA
PGCBM-21
SMS ID: 110387
PAGE: 4 6/16/2012
Now we can solve this ZTE Corporation problem through solver, the excel sheet is explained that ZTE corporation should make 380 TAB-GSM, 1060 Smart phone and no HSD cards or TAB –CDMA for a total profit of $62,200.
2.4 Excel Solution BY SOLVER
Table:4 Excel Layout and for Solver Entries of ZTE Corporation
ZTE Corpora tion HSD Solution Value Selling Price Cost Price Profit Constra ints Electronic Component Non Elecronic component Battery Assembly Tim e TAB-GSMTAB-CDMA mart Phone S Total 0 380 0 1060 $ 70.00 $ 80.00 $ 150.00 $ 110.00 $ 147,000.00 $ 46.00 $ 53.00 $ 83.00 $ 61.00 $ 84,800.00 $ 24.00 $ 27.00 $ 67.00 $ 49.00 $ 62,200.00 3 2 1 1 4 2 1 1 4 4 1 3 3 3 1 2 4700 <= 3940 <= 1440 <= 2500 <= Cost 4700 $ 4500 $ 3000 $ 2500 $ 7.00 5.00 5.00 10.00
On the above excel sheet, we can apply Answer report: Here “Answer report” indicates that Non-electronic component and Battery have potential supply of 4500 and 3000 respectively. Only 3940 unit of non electronic and 1440 units of battery are used. It means that additional non electronic components and battery are of no value to ZTE Corporation in terms of contribution to profit, it prove that shadow price is zero. The shadow price is valid for unlimited increase in supply for non electronics component and battery. ZTE Corporation has as many as 560 numbers of non electronic components and 1440 unit of batteries, which has no impact on profit.
RAJESH KUMAR VERMA
PGCBM-21
SMS ID: 110387
PAGE: 5 6/16/2012
SREENSHORT- 1 (Answer Report)
Microsoft Excel 11.0 Answer Report Worksheet: [project OR excel sheet.xls]Sheet2 Report Created: 08-06-2012 01:32:29
Target Cell (Max) Cell $F$8 Profit Total
Name
Original Value $ 62,200.00
Final Value $ 62,200.00
Optimal profit
Adjustable Cells Cell Name $B$5 Solution Value HSD $C$5 Solution Value TAB-GSM $D$5 Solution Value TAB-CDMA $E$5 Solution Value Smart Phone
Original Value 0 380 0 1060
Final Value 0 380 0 1060
Constraints Cell Name $F$10 Electronic Component Total $F$11 Non Elecronic component Total $F$12 Battery Total $F$13 Assembly Time Total
Cell Value 4700 3940 1440 2500
Formula $F$10<=$H$10 $F$11<=$H$11 $F$12<=$H$12 $F$13<=$H$13
Status Binding Not Binding Not Binding Binding
Slack 0 560 1560 0
560 unit and 1560 unit of non-electronic and Battery component respectively unused
ZTE Corporation “Sensitivity Report”:
RAJESH KUMAR VERMA PGCBM-21 SMS ID: 110387 PAGE: 6 6/16/2012
The changes to OFC value has solved in below mentioned range and below sensitivity report indicates that allowable decrease is infinity since the product is not attractive even at current OFC value. Allowable increase is also infinity since there are already 560 units of non-electronic component and 1440 unit of batteries are in stock and on the same time since non electronic components and batteries are non binding shadow price will be zero. SREENSHORT- 2 (Sensitivity Report)
M icrosoft Ex ce l 11.0 Se nsitivity Re port W orkshe e t: [proje ct OR e x ce l she e t.x ls]S he e t2 Re port Cre a te d: 08-06-2012 01:32:51
A djustable Cells Ce ll $B$5 $C$5 $D$5 $E$5 Fina l Re duce d Obje ctive Allow a ble Allow a ble Na m e Va lue Cost Coe fficie nt Incre a se De cre a se V alue HS D 0 -2.000000001 24 2.000000001 1E + 30 V alue TA B -GSM 380 0 27 30.00000002 2.5 V alue TA B -CDM A 0 -6.000000008 67 6.000000008 1E + 30 V alue S m art Phone 1060 0 49 5 3.750000005
S olution S olution S olution S olution
Cons traints Fina l Ce ll Na m e Va lue $F$10 E lectronic Com ponent Total 4700 $F$11 Non E lecronic c om ponent Total3 940 $F$12 B attery Total 1440 $F$13 A ssem bly Tim e Total 2500 S ha dow Price 1 0 0 23 Constra int Allow a ble Allow a ble R.H. S ide Incre a se De cre a se 4700 2800 950 4500 1E + 30 560 3000 1E + 30 1560 2500 466.6666667 1325
Now we can see the impact of profit if we could increase the supply of electronic component by 500 units and increase the total number of electronic component for 4700+500= 5200 units. We will check the allowable increase column of electronic component in “Sensitivity Report” and verify that the current shadow price is valid or not. As per the report the allowable increase column shows a value of 2800, it means the shadow price is valid. After this we will check the shadow price of electronic component which could be $1 per unit, it means up to additional 2800 unit ZTE Corporation will allow to increase its profit by $1.The impact of 500 unit will increase in profit by $500. The net profit will be $62200+$500= $62700. ==============
RAJESH KUMAR VERMA
PGCBM-21
SMS ID: 110387
PAGE: 7 6/16/2012
doc_108492581.doc
INDIVIDUAL ASSIGNMENT- Take a problem from your own organization and apply the concepts taught in the class
NAME: RAJESH KUMAR VERMA SMS ID: 110387 SID NO: RB12044 BATCH: PGCBM-21 FACULTY: DR. SUPRIYA KUMAR DE STUDY CENTER: DAKC, NAVI MUMBAI
RAJESH KUMAR VERMA
PGCBM-21
SMS ID: 110387
PAGE: 1 6/16/2012
Table of Contents
1. PROJECT PROBLEM: ............................................................................................................................................................3 2. PROJECT SOLUTION ............................................................................................................................................................3
RAJESH KUMAR VERMA
PGCBM-21
SMS ID: 110387
PAGE: 2 6/16/2012
1.
PROJECT PROBLEM:
A “ZTE Corporation” has targeted the potential market in India and decided to sale the most demanding products to telecom companies in Indian market. The company has considered for the production of four potential products i.e. HSD, TAB- GSM, TAB- CDMA and Smart Phone. All products can be majorly obtained by just 4 resources: electronic Component, non-electronic component, battery and assembly time. The composition of the four products in terms of these four inputs is shown in the table given below along with unit selling price of the products:
Table- 1: Data for ZTE Corporation
Resource Electronic Component Nonelectronic Component Battery assembly Time (hours) Selling Price (Per Unit) HSD TAB-GSM TAB-CDMA Smart Phone 3 4 4 3 2 2 4 3 1 1 1 1 1 1 3 2 $70 $80 $150 $110 Supply 4700 4500 3000 2500
Electronic component can be obtained at $7 per unit; Non electronic component can obtain at $5 per unit, battery component can be obtained by$5 per unit and assembly time cost $10 per hour.
2.
PROJECT SOLUTION
Each resource is available in the limited quantities as shown in the above in Table-1.
2.1 COST CALCULAATION
Table-2: Cost calculation for products
COST CALCULATION Electronic Component Non Elecronic component Battery Assembly Time Total cost HSD TAB-GSM TAB-CDMA Smart $ 21.00 $ 28.00 $ 28.00 $ $ 10.00 $ 10.00 $ 20.00 $ $ 5.00 $ 5.00 $ 5.00 $ $ 10.00 $ 10.00 $ 30.00 $ $ 46.00 $ 53.00 $ 83.00 $ Phone 21.00 15.00 5.00 20.00 61.00
RAJESH KUMAR VERMA
PGCBM-21
SMS ID: 110387
PAGE: 3 6/16/2012
Cost has been calculated by multiplying with unit of components, e.g. cost calculation for each HSD is $46 (3x $7+2x$5+1x$5+1x$10) and other products so on…
2.2 PROFIT CALCULATION
Table-3: Profit calculation for products
HSD Solution Value Selling Price Cost Price Profit TAB-GSM 0 380 $ 70.00 $ 80.00 $ 46.00 $ 53.00 $ 24.00 $ 27.00 TAB-CDMA Smart Phone Total 0 1060 $ 150.00 $ 110.00 $ 147,000.00 $ 83.00 $ 61.00 $ 84,800.00 $ 67.00 $ 49.00 $ 62,200.00
Profit has been calculated by subtracting the total cost for making a product from its unit selling price. The profit contribution of each HSD is $24(selling price is $70 less the total cost of 3x $7+2x$5+1x$5+1x$10) and other product calculated as same… As per above calculation profit has been calculated for each HSD is $24,each TAB-GSM is $27, each TAB-CDMA is $67 and for each Smart phone is $49. We can assume here H, TG, TC and SP denotes for HSD, TAB-GSM, TAB-CDMA and Smart phone respectively. Now we can formulate the LP model for this problem as under: Maximize profit= $24H+$27TG+$67TC+$49SP
2.3 Constraints for the problem will be:
Electronic component Non-electronic component Battery Assembly Time (in hours) Non-negativity = = = = = 3H+4TG+4TC+3SP < 4700 2H+2TG+4TC+3SP < 4500 1H+1TG+1TC+1SP < 3000 1H+1TG+3TC+2SP < 2500 H, TG, TC, SP > 0
RAJESH KUMAR VERMA
PGCBM-21
SMS ID: 110387
PAGE: 4 6/16/2012
Now we can solve this ZTE Corporation problem through solver, the excel sheet is explained that ZTE corporation should make 380 TAB-GSM, 1060 Smart phone and no HSD cards or TAB –CDMA for a total profit of $62,200.
2.4 Excel Solution BY SOLVER
Table:4 Excel Layout and for Solver Entries of ZTE Corporation
ZTE Corpora tion HSD Solution Value Selling Price Cost Price Profit Constra ints Electronic Component Non Elecronic component Battery Assembly Tim e TAB-GSMTAB-CDMA mart Phone S Total 0 380 0 1060 $ 70.00 $ 80.00 $ 150.00 $ 110.00 $ 147,000.00 $ 46.00 $ 53.00 $ 83.00 $ 61.00 $ 84,800.00 $ 24.00 $ 27.00 $ 67.00 $ 49.00 $ 62,200.00 3 2 1 1 4 2 1 1 4 4 1 3 3 3 1 2 4700 <= 3940 <= 1440 <= 2500 <= Cost 4700 $ 4500 $ 3000 $ 2500 $ 7.00 5.00 5.00 10.00
On the above excel sheet, we can apply Answer report: Here “Answer report” indicates that Non-electronic component and Battery have potential supply of 4500 and 3000 respectively. Only 3940 unit of non electronic and 1440 units of battery are used. It means that additional non electronic components and battery are of no value to ZTE Corporation in terms of contribution to profit, it prove that shadow price is zero. The shadow price is valid for unlimited increase in supply for non electronics component and battery. ZTE Corporation has as many as 560 numbers of non electronic components and 1440 unit of batteries, which has no impact on profit.
RAJESH KUMAR VERMA
PGCBM-21
SMS ID: 110387
PAGE: 5 6/16/2012
SREENSHORT- 1 (Answer Report)
Microsoft Excel 11.0 Answer Report Worksheet: [project OR excel sheet.xls]Sheet2 Report Created: 08-06-2012 01:32:29
Target Cell (Max) Cell $F$8 Profit Total
Name
Original Value $ 62,200.00
Final Value $ 62,200.00
Optimal profit
Adjustable Cells Cell Name $B$5 Solution Value HSD $C$5 Solution Value TAB-GSM $D$5 Solution Value TAB-CDMA $E$5 Solution Value Smart Phone
Original Value 0 380 0 1060
Final Value 0 380 0 1060
Constraints Cell Name $F$10 Electronic Component Total $F$11 Non Elecronic component Total $F$12 Battery Total $F$13 Assembly Time Total
Cell Value 4700 3940 1440 2500
Formula $F$10<=$H$10 $F$11<=$H$11 $F$12<=$H$12 $F$13<=$H$13
Status Binding Not Binding Not Binding Binding
Slack 0 560 1560 0
560 unit and 1560 unit of non-electronic and Battery component respectively unused
ZTE Corporation “Sensitivity Report”:
RAJESH KUMAR VERMA PGCBM-21 SMS ID: 110387 PAGE: 6 6/16/2012
The changes to OFC value has solved in below mentioned range and below sensitivity report indicates that allowable decrease is infinity since the product is not attractive even at current OFC value. Allowable increase is also infinity since there are already 560 units of non-electronic component and 1440 unit of batteries are in stock and on the same time since non electronic components and batteries are non binding shadow price will be zero. SREENSHORT- 2 (Sensitivity Report)
M icrosoft Ex ce l 11.0 Se nsitivity Re port W orkshe e t: [proje ct OR e x ce l she e t.x ls]S he e t2 Re port Cre a te d: 08-06-2012 01:32:51
A djustable Cells Ce ll $B$5 $C$5 $D$5 $E$5 Fina l Re duce d Obje ctive Allow a ble Allow a ble Na m e Va lue Cost Coe fficie nt Incre a se De cre a se V alue HS D 0 -2.000000001 24 2.000000001 1E + 30 V alue TA B -GSM 380 0 27 30.00000002 2.5 V alue TA B -CDM A 0 -6.000000008 67 6.000000008 1E + 30 V alue S m art Phone 1060 0 49 5 3.750000005
S olution S olution S olution S olution
Cons traints Fina l Ce ll Na m e Va lue $F$10 E lectronic Com ponent Total 4700 $F$11 Non E lecronic c om ponent Total3 940 $F$12 B attery Total 1440 $F$13 A ssem bly Tim e Total 2500 S ha dow Price 1 0 0 23 Constra int Allow a ble Allow a ble R.H. S ide Incre a se De cre a se 4700 2800 950 4500 1E + 30 560 3000 1E + 30 1560 2500 466.6666667 1325
Now we can see the impact of profit if we could increase the supply of electronic component by 500 units and increase the total number of electronic component for 4700+500= 5200 units. We will check the allowable increase column of electronic component in “Sensitivity Report” and verify that the current shadow price is valid or not. As per the report the allowable increase column shows a value of 2800, it means the shadow price is valid. After this we will check the shadow price of electronic component which could be $1 per unit, it means up to additional 2800 unit ZTE Corporation will allow to increase its profit by $1.The impact of 500 unit will increase in profit by $500. The net profit will be $62200+$500= $62700. ==============
RAJESH KUMAR VERMA
PGCBM-21
SMS ID: 110387
PAGE: 7 6/16/2012
doc_108492581.doc