Operations ResearchAAA Company’s Project

Instructor: Gurgen KhachatryanStudents: Antranik Babikian Asdghig Ashekain Avedis Koshkerian

CONTENTSINTRODUCTIONProblem 1: Traveling SalesmanProblem 2: Marketing Problem (NLP)

Problem 3: Equipment Replacement

Conclusion

INTRODUCTIONAAA Importing and Distribution Company (imaginary).

AAA’s warehouse is on Proshyan Street.

AAA Distribute to SAS & Yerevan City Supermarkets .

Problem 1: Traveling SalesmanThe truck will distribute the products

to SAS and Yerevan City supermarket chains,

3 trips/3 days a week. Our total weekly demand is 80 units. The truck capacity is 27 Units.

Warehouse

sas mashdots

sas tumanyan

sas gomidas

sas baghramian

sas isahakian

sas kievian

Yc rubinyants

YC Dikran medz

YC Ohanov

YC davtashen

YC gai 16

YCavan

YCkomidas

YCsebastya

YC Dalma

YC Pak Shuka

YC Erebuni

YC Shenkavit

Demand

Warehouse 0 1.8 2.5 4.7 2 3.1 2.6 7.3 2.7 7.8 5.4 8.5 9.1 5.7 7.3 3.2 1.4 6.8 6.4 

sas mashdots 1.8 0 0.8 6.3 2.9 2.4 4.1 7.9 1.5 7.9 6.6 9.610.

1 5.9 6.4 2.4 0.4 5.2 5.5 4

sas tumanyan 2.5 0.8 0 5.3 2.5 1.7 4 7.4 1.7 8.7 6.4 7.2 7.7 4.5 7.1 3.1 1.2 5.8 6.3 6

sas gomidas 4.7 6.3 5.3 0 2.9 5.3 3.5 3.4 7.6 8.3 4 6.3 6.9 1.3 6.7 6.1 5.5 11 9.7 3sas baghramian 2 2.9 2.5 2.9 0 3.7 1.4 6.3 4.8 7.8 3.9 8.6 9.1 3.6 6.3 4.9 2.8 8.7 7.5 3

sas isahakian 3.1 2.4 1.7 5.3 3.7 0 4.3 6.2 1.9 8.4 6.2 6.1 6.6 3.9 6.9 4.1 2.2 6.1 6.7 5

sas kievian 2.6 4.1 4 3.5 1.4 4.3 0 6.6 5.4 4.7 4.3 9.710.

2 4.4 3.2 2.6 3.7 9.2 7.1 6

Yc rubinyants 7.3 7.9 7.4 3.4 6.3 6.2 6.6 0 8.811.

6 7.4 3.2 3.7 2.6 9.4 8.7 7.313.

312.

5 5YC Dikran medz 2.7 1.5 1.7 7.6 4.8 1.9 5.4 8.8 0 8.4 7 8.2 8.5 6.1 6.9 2.9 1.4 4 4.8 4

YC Ohanov 7.8 7.9 8.7 8.3 7.8 8.4 4.711.

6 8.4 0 7.716.

216.

4 9.1 1.9 5.5 7.5 9.8 5.1 6

YC davtashen 5.4 6.6 6.4 4 3.9 6.2 4.3 7.4 7 7.7 0 1112.

5 4.6 5.7 6 6.312.

5 9.8 3

YC gai 16 8.5 9.6 7.2 6.3 8.6 6.1 9.7 3.2 8.216.

2 11 0 3.1 514.

610.

6 8.2 9.912.

1 5

YCavan 9.110.

1 7.7 6.9 9.1 6.610.

2 3.7 8.516.

412.

5 3.1 0 6.515.

611.

2 8.7 1312.

9 3

YCkomidas 5.7 5.9 4.5 1.3 3.6 3.9 4.4 2.6 6.1 9.1 4.6 5 6.5 0 7.6 7 5.511.

710.

4 5

YCsebastya 7.3 6.4 7.1 6.7 6.3 6.9 3.2 9.4 6.9 1.9 5.714.

615.

6 7.6 0 4 6 9.3 4.6 4

YC Dalma 3.2 2.4 3.1 6.1 4.9 4.1 2.6 8.7 2.9 5.5 610.

611.

2 7 4 0 2.4 6.8 5.4 6

YC Pak Shuka 1.4 0.4 1.2 5.5 2.8 2.2 3.7 7.3 1.4 7.5 6.3 8.2 8.7 5.5 6 2.4 0 5.7 5.5 5

YC Erebuni 6.8 5.2 5.8 11 8.7 6.1 9.213.

3 4 9.812.

5 9.9 1311.

7 9.3 6.8 5.7 0 4.7 3

YC Shenkavit 6.4 5.5 6.3 9.7 7.5 6.7 7.112.

5 4.8 5.1 9.812.

112.

910.

4 4.6 5.4 5.5 4.7 0 4

Problem 1: Traveling SalesmanDemandsas mashdots 4sas tumanyan 6sas gomidas 3sas baghramian 3sas isahakian 5sas kievian 6Yc rubinyants 5YC Dikran medz 4YC Ohanov 6YC davtashen 3YC gai 16 5YCavan 3YCkomidas 5YCsebastya 4YC Dalma 6YC Pak Shuka 5YC Erebuni 3YC Shenkavit 4

Problem 1: Traveling SalesmanFormulation

Problem 1: Traveling SalesmanTruck capacity constraints

Sub-tours elimination

Problem 1: Traveling SalesmanVariables non-negativity and binary

variables constraints

Problem 1: Traveling SalesmanOptimal solution

Total trips = 69.2 KMExcel file:

Problem 1: Traveling SalesmanDay One

From To Distance

Warehouse sas Komidas 4.7

sas Komidas YCkomidas 1.3

YCkomidas Yc rubinyants 2.6

Yc rubinyants YCavan 3.7

YCavan YC gai 16 3.1

YC gai 16 sas isahakian 6.1

sas isahakian Warehouse 3.1

Day : one

Problem 1: Traveling Salesmanday two

from to distance

Warehouse sas kievian 2.6

sas kievian YC Ohanov 4.7

YC Ohanov YCsebastya 1.9

YCsebastya YC davtashen 5.7

YC davtashen sas baghramian 3.9

sas baghramian YC Pak Shuka 2.8

YC Pak Shuka Warehouse 1.4

Day : two

Problem 1: Traveling Salesmanday three

from to distance

Warehouse sas mashdots 1.8

sas mashdots sas tumanyan 0.8

sas tumanyan YC Dikran medz 1.7

YC Dikran medz YC Erebuni 4

YC Erebuni YC Shenkavit 4.7

YC Shenkavit YC Dalma 5.4

YC Dalma Warehouse 3.2

Day : three

Problem 2: Marketing Problem (NLP)On Average

one minute TV advertisement costs 30000 AMD,one minute Radio advertisement costs 20000one road sign for one day costs 5000 AMD.

The Company’s wants to sale 100000 units’ after the campaign

Marketing professionals advices to make at least :2 daily TV ads4 daily Radio ads

They advice to not use more than 3 Billboard

The figure bellow explains the relationship between sales

increase and the number of commercials.

Problem FormulatingObjective function

Min Constraints

t≥ 2r ≥ 4b < 3T=30*tB=30*sR=30*r 70000(1- 35000(1- 15000(1-

T,R,B,t,r,b >0 , T,R,B,t,r,b integer

Solution

daily whole campaig

n

unit cost cost sales increase

TV 3 90 12,500.00 ֏ 1,125,000.00 ֏

56139

Radio 5 150 6,666.67 ֏ 1,000,000.00 ֏

32143

Billboard

3 90 5,000.00 ֏ 450,000.00 ֏

12030

total 2,575,000.00 ֏

100311

PROBLEM 3: EQUIPMENT REPLACEMENT

The company wants to know when it has to change its printers. Their initial cost are 80000 AMD each, the company’s estimated life is 6 years, the printers useful life is 5 years. The table below shows the annual costs and the salvage values at the end of each 5 years. (annual costs for printers are ink cost and rolls changing cost).

PROBLEM 3: EQUIPMENT REPLACEMENT

Year C MSalva

ge price1 6000 6000 60000 80000

2 12000 18000 45000 80000

3 6000 24000 30000 80000

4 12000 36000 15000 80000

5 6000 42000 5000 80000

Solution g (6)=0

Ctx: net cost at time t and operating cost till time x.

C01=C12=C23=C34=C45=C56=80000+6000-60000=26000C02=C13=C24=C35=C46=80000+18000-45000=53000C03=C14=C25=C36=80000+24000-30000=74000C04=C15=C26=80000+48000-15000=113000C05=C16=80000+56000-5000=131000

g (5)= C56 + g (6)= 26000

g(4)=min C45 + g (5) =52000* C46 + g (6) =53000 

g(3)=min C34 + g(4) = 74000* C35 + g(5) = 79000 C36 +g (6)= 74000*

g(2)=min C23 + g(3) =100000*

C24 + g(4) =105000

C25+ g(5) =148000

C26+ g(6) =101000

g(1)= min C12+ g(2) =127000 C13+ g(3) =127000 C14+ g(4) =126000 C15+ g(5) =127000

C16+ g(6) =117000*

g(0)=min C01+ g(1) =143000* C02+ g(2) =153000 C03+ g(3) =148000 C04+ g(4) =153000 C05+ g(5) =143000*

SolutionThe printers needs to be changed in the 5th

year, or it should be used for one year and be changed to be used for the next five years, in other words printers should be used till the end of its useful life.

CONCLUSIONAs a conclusion we can see that we have reached to optimal solutions for each of our company’s problems.

In the traveling salesman problem our optimal trips were 3 weekly, fulfilling the demand of 80 units, with the minimum distance and costs possible, which was 69.2 km.

For our advertising problem the optimal solution was to buy 90 TV, 150 Radio commercials, and 90 road signs (3 everyday) for the campaign with the minimum cost of 2,575,000.00 AMD.

Regarding to the equipment replacement problem, we have found that our printers should be used till the end of its useful life.