Engines stock control

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study to decide the number of engines in stocks based on cost and service level using statistical tools

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Engines stock control

  1. 1. Engines Stock Control Cost vs Service Level By : Mohammed Salem MIDDLE EAST AIRLINE ENGINEERING & MAINTENANCE 2005 11 th Annual Conference Aviation Industry Conferences 15-16 March 2005 The Intercontinental Hotel Abu Dhabi, UAE
  2. 2. Objective <ul><li>To Find The Optimum Number Of Engines In Stock by </li></ul><ul><ul><li>Minimize Total Cost. </li></ul></ul><ul><ul><li>Achieving The Desired Service Level. </li></ul></ul>
  3. 3. Introduction <ul><li>The aim of material planning policy is to justify the optimum number of spare parts. </li></ul><ul><li>The availability of spare parts acts as supporting role to keep equipments and system operating effectively maintaining a maximum output. </li></ul><ul><li>Depending on the situation and the relative costs, the proper policy may be selected. </li></ul>
  4. 4. Introduction <ul><li>Number of spare should be optimum </li></ul><ul><li>What are the guide line to indicating when number of spare is likely to be economical ? </li></ul><ul><li>What is U Curve Technique, what costs should be involved ? And how fleet size effects the out comes result? </li></ul><ul><li>What service level is appropriated for a specified number of spare parts ? And how we reflect real data to get a fair result ? </li></ul><ul><li>What is Monto Carlo Simulation, how to develop it ? </li></ul>
  5. 5. Philosophy - ESC <ul><li>Airlines Engine Stock Philosophy is to balance between these two terms Cost and Service Level. </li></ul><ul><li>A decision making problem for number of engines in stock for an Airline is determine by using a proper mathematical model, based on the setting objectives I.e cost or service level the desired approach is selected, basically there are two techniques that use in this situation </li></ul><ul><ul><li>U curve technique ( Minimize cost ) </li></ul></ul><ul><ul><li>Monto Carlo Simulation (desired service level) </li></ul></ul>
  6. 6. Techniques <ul><li>U Curve Technique </li></ul><ul><li>Based on Costs </li></ul><ul><li>Holding Cost </li></ul><ul><li>OAG Cost </li></ul><ul><li>Breakdown Cost </li></ul><ul><li>Poisson Sampling </li></ul><ul><li>Repair Cycle is Constant </li></ul><ul><li>Monto Carlo Simulation </li></ul><ul><li>Based on Service level. </li></ul><ul><li>Operating Time and Repair Time. </li></ul><ul><li>Computer Program Model. </li></ul><ul><li>Repair Time is Random Variable. </li></ul>
  7. 7. Techniques <ul><li>U Curve Technique </li></ul><ul><ul><li>A Cost of Spare Engines </li></ul></ul><ul><ul><li>B Cost of Aircraft On Ground </li></ul></ul><ul><ul><li>C Total </li></ul></ul><ul><ul><li>Cost </li></ul></ul>A Cost of Spare Engines B Cost of Aircraft On Ground C Total Cost NUMBER OF SPARE ENGINES COST IN US$
  8. 8. Techniques <ul><li>U Curve Technique </li></ul><ul><ul><li>A Cost of Spare Engines </li></ul></ul><ul><ul><li>These costs including </li></ul></ul><ul><ul><li>Ownership and </li></ul></ul><ul><ul><li>Holding Cost. </li></ul></ul><ul><ul><li>B Cost of Aircraft On Ground </li></ul></ul><ul><ul><li>These cost reflect the cost of losing opportunities, in terms of losing revenue due to unavailability of engine. </li></ul></ul><ul><ul><li>C Total Cost </li></ul></ul><ul><ul><li> Optimum result is the balance outcome of pre-mentioned above costs ( Minimum) </li></ul></ul>
  9. 9. Techniques <ul><li>U Curve Technique </li></ul><ul><ul><li>Theoretical Model </li></ul></ul><ul><ul><li>Depending on the Sampling Method. </li></ul></ul><ul><ul><li>Time of analysis is Fixed </li></ul></ul><ul><ul><li>Number of Failure is random variable. </li></ul></ul><ul><ul><li>Thus select Poisson Distribution. </li></ul></ul>
  10. 10. Techniques <ul><li>U Curve Technique </li></ul><ul><ul><li>Theoretical Model </li></ul></ul><ul><ul><li>Poisson Distribution </li></ul></ul><ul><ul><li>The probability </li></ul></ul><ul><ul><li>function of Poisson </li></ul></ul>
  11. 11. Techniques <ul><li>U Curve Technique </li></ul><ul><ul><li>Theoretical Model </li></ul></ul><ul><ul><li>Poisson Sampling </li></ul></ul>
  12. 12. Techniques <ul><li>U Curve Technique </li></ul><ul><ul><li>Theoretical Model </li></ul></ul><ul><ul><li>Poisson Sampling </li></ul></ul>
  13. 13. Techniques <ul><li>U Curve Technique </li></ul><ul><ul><li>Theoretical Model </li></ul></ul><ul><ul><li>Estimation the Parameters of Poisson Distribution </li></ul></ul>
  14. 14. Techniques <ul><li>U Curve Technique </li></ul><ul><ul><li>Theoretical Model </li></ul></ul><ul><ul><li>Estimation the Parameters of Poisson Distribution </li></ul></ul>
  15. 15. Techniques <ul><li>Monto Carlo Simulation </li></ul><ul><ul><li>To Simulate is to copy the behavior of a system under study </li></ul></ul><ul><li>Developing Modeling </li></ul><ul><li>System For Airlines </li></ul><ul><li>based service level. </li></ul><ul><ul><li>Main Factors </li></ul></ul><ul><ul><li>Demand Distribution </li></ul></ul><ul><ul><li>Repair Distribution </li></ul></ul>time Stock Level
  16. 16. Techniques <ul><li>Monto Carlo Simulation </li></ul><ul><ul><li>Developing Modeling System For Airlines based On </li></ul></ul><ul><ul><li>Service Level . </li></ul></ul>Simulation Model Engine Fleet Repair Distribution AIRLINE SYSTEM Engine Fleet Demand Distribution Desired Service level Optimum Engines Number
  17. 17. Techniques <ul><li>Flow Chart </li></ul><ul><li>described the main program steps </li></ul>AIRLINE SYSTEM <ul><li>Simulation </li></ul><ul><li>Model </li></ul>Airline Operating System Same A/C Fleet - Engines Stock Level at T 1 = ( Current Level – 1 ) Stock Level at T 1 +T R = ( Current Level + 1 ) Calculate Cumulative Distribution Generate Random Numbers Calculate Corresponding Values of operating times Engines Failure Distribution Engines Repair Distribution Calculate Cumulative Distribution Generate Random Numbers Calculate Corresponding Values of repair times At Tentative values of stock level Run Computer program for 1000 trails Calculate Null Stock Cases And Service Level
  18. 18. Techniques <ul><li>Figures shows the steps, how to generate and use random numbers in reflecting operating / demand distribution </li></ul><ul><li>Simulation Model – Operating Distribution </li></ul>OPERATING DISTRIBUTION Generation of Random Number (x) 100 x t 100 CUMULATIVE DISTRIBUTION SELECTING OPERATING DAYS OPERATING DAYS OPERATING DAYS OPERATING DAYS FREQUENCIES FREQUENCIES
  19. 19. Techniques <ul><li>Figures shows the steps, how to generate and use random numbers in reflecting repair distribution </li></ul><ul><li>Simulation Model – Repair Distribution </li></ul>REPAIR DISTRIBUTION Generation of Random Number (x) 100 x t 100 CUMULATIVE DISTRIBUTION SELECTING REPAIR DAYS REPAIR DAYS REPAIR DAYS REPAIR DAYS FREQUENCIES FREQUENCIES
  20. 20. Techniques <ul><li>Engines Stock Level – Operating Times – Repair Times </li></ul><ul><li>Simulation Model </li></ul>ENGINES STOCK LEVEL DAYS (TIME ) OPERATING PERIODS REPAIR PERIODS
  21. 21. Case Study <ul><li>Input Data </li></ul><ul><li>Implementation of U curve technique. </li></ul><ul><li>Implementation of Monto Carlo Simulation. </li></ul><ul><li>Results Comparison. </li></ul><ul><li>Effects of Fleet Size on Engines Stock Level. </li></ul>
  22. 22. Case Study <ul><li>Input Data </li></ul>
  23. 23. Case Study <ul><li>Implementation of U curve technique. </li></ul>
  24. 24. Case Study <ul><li>Implementation of U curve technique. </li></ul>
  25. 25. Case Study <ul><li>Implementation of U curve technique. </li></ul>
  26. 26. Case Study <ul><li>Implementation of Monto Carlo Simulation </li></ul><ul><li>Ref to INPUT Data : We Have 13 reading Operating time </li></ul><ul><li>and 13 reading Repairing time. </li></ul>
  27. 27. Case Study <ul><li>Implementation of Monto Carlo Simulation </li></ul><ul><li>The Flow chart demonstrate the simulation process, </li></ul><ul><li>and that achieved by the following steps </li></ul><ul><li>1- Fitting operating distribution to Weibull Distribution, </li></ul><ul><li>2- Develop the cumulative probability distribution. </li></ul><ul><li>3- Generate Random Numbers </li></ul><ul><li>4- Reflect these R. No. to get the corresponding values of operating time. </li></ul><ul><li>5- Repeat this process for Repairing Time. </li></ul>Airline Operating System Same A/C Fleet - Engines Stock Level at T 1 = ( Current Level – 1 ) Stock Level at T 1 +T R = ( Current Level + 1 ) Calculate Cumulative Distribution Generate Random Numbers Calculate Corresponding Values of operating times Engines Failure Distribution Engines Repair Distribution Calculate Cumulative Distribution Generate Random Numbers Calculate Corresponding Values of repair times At Tentative values of stock level Run Computer program for 1000 trails Calculate Null Stock Cases And Service Level
  28. 28. Case Study <ul><li>Implementation of Monto Carlo Simulation </li></ul><ul><li>Random Numbers Generation </li></ul>
  29. 29. Case Study <ul><li>Implementation of Monto Carlo Simulation </li></ul><ul><li>Service Level = 100 % at Stock Level = 2 Engines </li></ul>
  30. 30. Case Study <ul><li>Monto Carlo Simulation ( Effects of Repair Distribution) At Stock Level = 1 Engine Service Level = 72 % </li></ul>
  31. 31. Case Study <ul><li>Results Comparison ( All Most Close ) </li></ul><ul><li>U curve technique </li></ul><ul><li>Based on Costs </li></ul><ul><li>Factors Can be Adjusted, and each one be examined especially Fleet Size. </li></ul><ul><li>Repair Cycle is Constant </li></ul><ul><li>Monto Carlo Simulation </li></ul><ul><li>Based on Service level. </li></ul><ul><li>Reflect Actual Airline Situation </li></ul><ul><li>Computer Program Model. </li></ul><ul><li>Repair Time is Random Variable. </li></ul>
  32. 32. Case Study <ul><li>Effects of Fleet Size on Engines Stock Level </li></ul>By changing values of Fleet Size in U curve Technique The corresponding level of Spare Engines Stock level will be determined.
  33. 33. Summary <ul><li>In this paper two approaches are examined </li></ul><ul><li>U Curve Technique and Monto Carlo Simulation, Both are useful in terms of cost and service level </li></ul><ul><li>It depends on a company policy and incurred related cost to implemented each approach. </li></ul><ul><li>Simulation techniques reflects more reality to a practical situations </li></ul><ul><li>While U curve technique offering more flexibility to adapts its parameters </li></ul>
  34. 34. Thank You <ul><li>Contact : </li></ul><ul><li>Mohammed Salem Awad </li></ul><ul><li>Consultant </li></ul><ul><li>Tel : 00967734777518 </li></ul><ul><li>Email: </li></ul><ul><li>smartdecison2002@yahoo.com </li></ul>

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