1. AAA Company’s Project Instructor: Gurgen Khachatryan Students: Antranik Babikian Asdghig Ashekain Avedis Koshkerian

2. CONTENTS INTRODUCTION Problem 1: Traveling Salesman Problem 2: Marketing Problem (NLP) Problem 3: Equipment Replacement Conclusion

3. INTRODUCTION AAA Importing and Distribution Company (imaginary). AAA’s warehouse is on Proshyan Street. AAA Distribute to SAS & Yerevan City Supermarkets.

4. Problem 1: Traveling Salesman The 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.

5. 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 01.82.54.723.12.67.32.77.85.48.59.15.77.33.21.46.86.4 sas mashdots 1.800.86.32.92.44.17.91.57.96.69.610.15.96.42.40.45.25.54 sas tumanyan 2.50.805.32.51.747.41.78.76.47.27.74.57.13.11.25.86.36 sas gomidas 4.76.35.302.95.33.53.47.68.346.36.91.36.76.15.5119.73 sas baghramian 22.92.52.903.71.46.34.87.83.98.69.13.66.34.92.88.77.53 sas isahakian 3.12.41.75.33.704.36.21.98.46.26.16.63.96.94.12.26.16.75 sas kievian 2.64.143.51.44.306.65.44.74.39.710.24.43.22.63.79.27.16 Yc rubinyants 7.37.97.43.46.36.26.608.811.67.43.23.72.69.48.77.313.312.55 YC Dikran medz 2.71.51.77.64.81.95.48.808.478.28.56.16.92.91.444.84 YC Ohanov 7.87.98.78.37.88.44.711.68.407.716.216.49.11.95.57.59.85.16 YC davtashen 5.46.66.443.96.24.37.477.701112.54.65.766.312.59.83 YC gai 16 8.59.67.26.38.66.19.73.28.216.21103.1514.610.68.29.912.15 YCavan 9.110.17.76.99.16.610.23.78.516.412.53.106.515.611.28.71312.93 YCkomidas 5.75.94.51.33.63.94.42.66.19.14.656.507.675.511.710.45 YCsebastya 7.36.47.16.76.36.93.29.46.91.95.714.615.67.60469.34.64 YC Dalma 3.22.43.16.14.94.12.68.72.95.5610.611.27402.46.85.46 YC Pak Shuka 1.40.41.25.52.82.23.77.31.47.56.38.28.75.562.405.75.55 YC Erebuni 6.85.25.8118.76.19.213.349.812.59.91311.79.36.85.704.73 YC Shenkavit 6.45.56.39.77.56.77.112.54.85.19.812.112.910.44.65.45.54.704

6. Problem 1: Traveling Salesman Demand sas mashdots4 sas tumanyan6 sas gomidas3 sas baghramian3 sas isahakian5 sas kievian6 Yc rubinyants5 YC Dikran medz4 YC Ohanov6 YC davtashen3 YC gai 165 YCavan3 YCkomidas5 YCsebastya4 YC Dalma6 YC Pak Shuka5 YC Erebuni3 YC Shenkavit4

7. Problem 1: Traveling Salesman Formulation

8. Problem 1: Traveling Salesman

10. Optimal solution Total trips = 69.2 KM Excel file:

11. Problem 1: Traveling Salesman Day One FromToDistance Warehousesas Komidas4.7 sas KomidasYCkomidas1.3 YCkomidasYc rubinyants2.6 Yc rubinyantsYCavan3.7 YCavanYC gai 163.1 YC gai 16sas isahakian6.1 sas isahakianWarehouse3.1

12. Day : one

13. Problem 1: Traveling Salesman day two fromtodistance Warehousesas kievian2.6 sas kievianYC Ohanov4.7 YC OhanovYCsebastya1.9 YCsebastyaYC davtashen5.7 YC davtashensas baghramian3.9 sas baghramianYC Pak Shuka2.8 YC Pak ShukaWarehouse1.4

14. Day : two

15. Problem 1: Traveling Salesman day three fromtodistance Warehousesas mashdots1.8 sas mashdotssas tumanyan0.8 sas tumanyanYC Dikran medz1.7 YC Dikran medzYC Erebuni4 YC Shenkavit4.7 YC ShenkavitYC Dalma5.4 YC DalmaWarehouse3.2

16. Day : three

17. Problem 2: Marketing Problem (NLP) On Average one minute TV advertisement costs 30000 AMD, one minute Radio advertisement costs 20000 one 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 ads 4 daily Radio ads They advice to not use more than 3 Billboard

18. The figure bellow explains the relationship between sales increase and the number of commercials.

19. Problem Formulating

20. Solution daily whole campaign unit costcost sales increase TV39012,500.00 1,125,000.00 56139 Radio51506,666.67 1,000,000.00 32143 Billboard3905,000.00 450,000.00 12030 total2,575,000.00 100311

21. 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).

22. PROBLEM 3: EQUIPMENT REPLACEMENT YearCMSalvageprice 16000 6000080000 212000180004500080000 36000240003000080000 412000360001500080000 5600042000500080000

23. Solution g (6)=0 Ctx: net cost at time t and operating cost till time x. C 01 =C 12 =C 23 =C 34 =C 45 =C 56 =80000+6000- 60000=26000 C 02 =C 13 =C 24 =C 35 =C 46 =80000+18000-45000=53000 C 03 =C 14 =C 25 =C 36 =80000+24000-30000=74000 C 04 =C 15 =C 26 =80000+48000-15000=113000 C 05 =C 16 =80000+56000-5000=131000 g (5)= C 56 + g (6)= 26000 g(4)=min C 45 + g (5) =52000* C 46 + g (6) =53000 g(3)=min C 34 + g(4) = 74000* C 35 + g(5) = 79000 C 36 +g (6)= 74000* g(2)=min C 23 + g(3) =100000* C 24 + g(4) =105000 C 25 + g(5) =148000 C 26 + g(6) =101000 g(1)= min C 12 + g(2) =127000 C 13 + g(3) =127000 C 14 + g(4) =126000 C 15 + g(5) =127000 C 16 + g(6) =117000* g(0)=min C 01 + g(1) =143000* C 02 + g(2) =153000 C 03 + g(3) =148000 C 04 + g(4) =153000 C 05 + g(5) =143000*

24. Solution The printers needs to be changed in the 5 th 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.

25. CONCLUSION As 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.