This document summarizes a presentation on the replacement problem in operations research. The replacement problem aims to determine the optimal time to replace equipment by minimizing total replacement costs over time. Total costs consider running costs like maintenance, depreciation costs as the value decreases over time, and scrap value from selling old equipment. Two replacement models are described: one for equipment that declines in value and efficiency over time, and one for equipment that fails completely. Individual and group replacement policies are also outlined. The document provides an example problem calculating total costs each year to determine when a machine should be replaced.

1. Operations Research
Replacement Problem
Presented By-
Binaya Kumar Behera : 2012106055
Arman Pattanaik : 2012106052
Guided By-
Dr. Sudhansu Sekhar Routray

2. Content-
Replacement Problem
Introduction
Definition, Objective, Models, Policy
Depreciation Cost
Running Cost
Scrap Value
Total Cost

3. Introduction
• In Industries, all machinery, electronics equipment's are
put continuous use.
• Decreases the efficiency and increases the maintenance
cost of the equipment.
• Sudden breakdown or complete failure of that equipment.

4. Definition
• Replacement means the action or process of replacing
someone or something.
Objective
• Determine the optimal time at which the equipment is to be
replaced with a new one.

5. Replacement Models
Replacement That Decline With Time
• Ignoring the money value
Equipment is okay but outdated due to new developments.
• Considering the money value
Equipment maintenance cost is high, efficiency less.
Replacement That Fail Completely
• Sudden failure or breakdown of equipment, no indication.

6. Replacement Policy
Individual Replacement Policy
• Under this policy, an equipment is replaced immediately
after its failure.
Group Replacement Policy
• Under this policy, if one equipment is failed, then we have to
replace whole total equipment.

7. Scrap Value
• It refers to the amount of money we get for something when
it's old, damaged, or no longer useful.
• We are selling in a small amount of money because it's not
in good condition or people don't want it as much anymore.
Depreciation Cost
• It refers to the gradual decrease in value of something
over time.
• It is important because it helps businesses and
individuals to understand how much an asset's value has
decreased over a certain period.
• Depreciation Cost = Initial Cost - Scrap Value

8. Running Cost
• It refers to the expenses or money we need to
continuously spend over time to keep something
operational or maintain it
• Ex - fuel, maintenance, repairs, and other ongoing
expenses associated with different equipment.
Total Cost
• It includes all the expenses, both direct and indirect,
associated with a particular activity, project, or item.
• It's the sum of all the costs involved in making or obtaining
something.
• Total Cost = Cum. Running Cost + Depreciation Cost

9. • A factory is considering the replacement of machine,
whose cost price Rs. 12,200 and the scrap value is
Rs 200. From experience, the running cost are found :
Year 1 2 3 4 5 6 7 8
Running Cost 200 500 800 1200 1800 2500 3200 4000
When should the machine will be replaced?

10. Year 1 2 3 4 5 6 7 8
Running Cost 200 500 800 1200 1800 2500 3200 4000
Year Scrap Value Depreciation Cost Running Cost Cum. Running Cost Total Cost Average Cost
1 200 12000 200 200 12200 12200
2 200 12000 500 700 12700 6350
3 200 12000 800 1500 13500 4500
4 200 12000 1200 2700 14700 3675
5 200 12000 1800 4500 16500 3300
6 200 12000 2500 7000 19000 3167
7 200 12000 3200 10200 22200 3171
8 200 12000 4000 14200 26200 3275
• Solution-

11. • A factory is considering the replacement of machine,
whose cost price Rs. 12,200. From experience, the
running cost and scrap value are given below :
Year 1 2 3 4 5 6 7 8
Running Cost 200 500 800 1200 1800 2500 3200 4000
Scrap Value 8000 7000 6000 5000 4500 3000 1200 500
When should the machine will be replaced?

12. Year Scrap Value Depreciation Cost Running Cost Cum. Running Cost Total Cost Average Cost
1 8000 4200 200 200 4400 4400
2 7000 5200 500 700 5900 2950
3 6000 6200 800 1500 7700 2566
4 5000 7200 1200 2700 9900 2475
5 4500 7700 1800 4500 12200 2440
6 3000 9200 2500 7000 16200 2700
7 1200 11000 3200 10200 21200 3028
8 500 11700 4000 14200 25900 3237
• Solution-
Year 1 2 3 4 5 6 7 8
Running Cost 200 500 800 1200 1800 2500 3200 4000
Scrap Value 8000 7000 6000 5000 4500 3000 1200 500

13. Replacement Problem
Importance
Necessity
Objective
Models
Policy
Solving techniques for it.
Conclusion

14. Resources-
Text Book –
Operations Research
Kanti Swarup, P.K Gupta, Man Mohan
S Chand & Sons Publication
Web Links -
https://youtube.com/playlist?list=PLsh2FvSr3n7dpUbg1BxYcuSCM2J4LNIl6

15. THANK YOU !!!