Maintenance Strategic and Capacity Planning

Abstract

The theme of this chapter is planning and techniques required for accomplishing it. Strategic and capacity planning are the main subjects of this chapter. The techniques covered include: quantitative and qualitative forecasting, deterministic and stochastic techniques for capacity planning. The capacity planning techniques presented are linear programming, queuing, and simulation. The applications of these techniques in maintenance are demonstrated.

Exercises

• 1. The forecasting of the maintenance load that is generated by a newly developed sophisticated equipment does not seem to be amenable to time series forecasting. Why? Suggest a procedure to predict the maintenance load for the next two years for this equipment.

• 2. In the absence of data, you may have to resort to qualitative forecasting. Explain how would you perform qualitative forecasting and how to validate it?

• 3. When is it possible to use a control chart to control the qualitative forecasting process? What type of control charts will you use? Explain how.

• 4. Prove that using the least squares method to estimate the slope, b, and the intercept, a, of the single variable linear fit, x(t) = a + bt results in estimates for b and a as follows:

  $$\begin{aligned} \hat{b} & = \frac{{n\sum_{t = 1}^{n} {tx(t) - \left( {\sum_{t = 1}^{n} t } \right)\left( {\sum_{t = 1}^{n} {x(t)} } \right)} }}{{n\sum_{t = 1}^{n} {t^{2} - \left( {\sum_{t = 1}^{n} t } \right)^{2} } }} \\ \hat{a} & = \overline{x} (t) - b\overline{t} \\ \end{aligned}$$

• 5. Use the least squares method to estimate the parameters of the quadratic model

  $$x(t) = a + bt + bt^{2}$$

• 6. Derive the simultaneous equations a and b for the model $x(t) = ab^{t}$ using the least squares method.

• 7. Given the following data:

  t	1	2	3	4	5	6
  x(t)	5	4	7	8	7	10

  Predict x(t) for periods 7 and 8 using five-period moving average and linear regression model. Which resulting prediction will you recommend for use in this case and why?

• 8. Show quantitatively that the estimate you obtain from the basic exponential smoothing equation is a function of all previous observations; however, the most recent ones are heavily weighted than the far-distant ones.

• 9. Use a linear model and exponential smoothing to predict the values of x(t) for periods 7, 8, and 10 for the data in Exercise 7.

• 10. Prove that if a set of data have a noise-free ramp with slope b, the first exponential smoothing will lag the true value by $\left( {\frac{\beta }{\alpha }} \right)b{\text{ where }}\beta = 1 - \alpha$

• 11. How would you determine α optimally in the exponential smoothing model?

• 12. Consider the following quarterly data for the maintenance load in man-hours for the last 5 years.

  Year	Quarter
  	I	II	III	IV
  1	215	120	150	100
  2	250	175	75	150
  3	300	250	75	165
  4	350	275	100	200
  5	400	300	125	225

  • (a) Determine an appropriate seasonal index for each quarter.

  • (b) Deseasonalize the data and fit it to an appropriate growth model.

  • (c) Predict the quarter values for the 6th and 7th years.

• 13. Discuss the advantages and disadvantages of the approaches given in this chapter for capacity planning.

• 14. Suppose you were asked to develop a capacity plan for a maintenance department. Which approach will you select from the approaches given in this chapter? and why?

• 15. For the data in Table 2.9, evaluate the cost of the plan given in the table if an in-house regular hour is 10$, overtime hour is 15$, and a contract man-hour costs 25. In addition, every backlog man-hour delayed from period t to t + 1 costs 5. Develop an alternative competitive plan in which you can have instead of 5 skilled employees have a mixture of skill and unskilled. The hour of unskilled worker is 8$.

• 16. Develop a linear programming model for the data given in Table 2.9. Assume that the trades in problem 15 are available.

• 17. Explain how would you use the machine servicing model for determining optimal mix of crafts and skills to meet the maintenance load.

• 18. What are the disadvantages of using linear programming for capacity planning.

• 19. Locate a factory near your area and study its operations and maintenance.

  • (a) Forecast their maintenance load.

  • (b) Use the structured tableau method to determine their maintenance capacity in terms of staff only.

  • (c) Use linear and integer programming to plan their maintenance capacity.

• 20. Apply stochastic simulation to plan the maintenance capacity for the factory in problem 19. Is there a difference between the approaches in problems 19 and 20. Why do you expect such a difference? Which is more appropriate for this case and why?