Imagine a situation where a business negotiates contracts for the maintenance of widgets it sells.


  • Customer buys 20 widgets.
  • Customer negotiates contract for widgets to be serviced/replaced.
  • Business makes money by servicing or replacing widgets at a cost lower than the contract payment.
    • (Contract Payment - Actual Maintenance Cost > 0 ... profit!)


  • Each contract is for multiple widgets.
  • Each widget can only be in use for a specified period of time before repair. However, these repair periods can be stretched for a percentage of time with minimal risk to the widget.
  • Each widget has a limited number of repair cycles before it needs to be replaced.
  • Buying widgets is always more expensive than repairing widgets.
  • Widget inspections must accompany every potential repair.
  • Multiple inspection event types exist (Level 1, Level 2). Level 2 is MUCH more expensive.
    • Level 1 can occur for a small number of widgets rather cheaply.
    • Level 2 must occur for all widgets
  • A repair event is cheaper if it occurs when multiple widgets can be inspected and repaired at once.

What would be appropriate algorithms to forecast the best possible schedule for inspecting/replacing/repairing widgets on a contract over time to maximize profit?

They key goal is to stagger inspection events to have the fewest inspection events and fewest new widget purchases over the life of a contract.

Example - Widget 1 can be in use for 100 hours before repair. Widget 2 can be in use for 110 hours before repair. Stagger Widget 1 forward 10 hours to inspect both at the same time instead of doing an inspection/repair at 100 and 110 hours.

I am doing research on branch and bound ... A* and minimum spanning tree algorithms, but I am not sure which approach was more appropriate for the problem.

Please note that this seems similar to What type of analysis is appropriate for assessing the performance time-series forecasts?

  • $\begingroup$ I was told this was more easily tackled using simulations, but with limited data science experience, I am wondering if anybody has any resources where I can learn more about different types of simulation techniques for this kind of forecasting. $\endgroup$
    – ds1984
    Mar 29, 2016 at 19:47


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