Algorithm [SISM]

CPM 1½ � ¼ d þ tPM, BPM k½ � ¼ B½ � <sup>1</sup>kk þ tQ½ � <sup>1</sup>kk , k ¼ 1, 2, …, g,

> α � �tPM � tq s \$ %

Eq. (14) declares an objective function to minimize total costs consisting of inventory costs, setup cost, preventive maintenance cost, corrective maintenance cost, and rework cost. Eq. (15) states the balance of the material in the shop, where the number of parts in all batches must be equal to the number of parts that will be scheduled. Eqs. (16) and (17) state the beginning time of each batch on the first run and the next runs, respectively. All batches are scheduled tight to a common due date d sequentially. Eqs. (18) and (19) state the length of first run and the next runs, respectively. Eq. (20) states the estimation of nonconforming parts for each run. Eqs. (21) and (22) state the estimation of total nonconforming parts and total rework cost for nonconforming parts, respectively. Eqs. (23) and (24) state the possible number of CM action with cumulative Weibull ROCOF and the expected cost of CM action, respectively. Eq. (25) represents a set of constraints for the beginning and the next of the PM times, with the assumption that first PM in schedule or the last PM in processing (backward approach) after all batches has been completed at a common due date d to ensure the machine in as good as new condition for the next order. Eq. (26) states the possible number of batches in a planning horizon. Eq. (27) states the possible number of production runs in a planning horizon. Equation (28) states a binary constraint that each batch will have: X½ � ik<sup>k</sup> ¼ 1 for non-empty batches and X½ � ik<sup>k</sup> ¼ 0 for empty batches. Eq. (29) states non-negativity of batch size. Eq. (30) states batch size less or equal with all parts that will be scheduled. Eq. (31) states the

The algorithm developed begins with problem solving without involving restoration cost (CM) and rework cost for nonconforming parts or without the constraints of Eqs. (20)–(24). It begins with one batch in one production run with one

nonconforming parts by Eq. (20) and the number of restoration (CM) by Eq. (23). Next, compute estimated rework cost by Eq. (22) and estimated restoration cost by Eq. (24), and then compute total cost. This step is done for two batches until an increased total cost is found. Write the best total cost for one production run and one PM. This process is carried out for two production runs with two PMs until the best total cost is found for two production runs with two PMs. Continue the process

PM. After having obtained a production schedule, estimate the number of

<sup>N</sup> <sup>¼</sup> <sup>d</sup> � <sup>d</sup>

1, ifQ½ � ikk 6¼ 0, 0, ifQ½ � ikk ¼ 0

X½ � ikk ¼

Industrial Engineering

(

existence of the number of batches in each run.

3.5 Algorithm

38

CPM k½ � ¼ BPM k½ � þ tPM, k ¼ 1, 2, …, g (25)

, ik ¼ 1, 2, …, Nk, k ¼ 1, 2, …, g

Nk ≥1, k ¼ 1, 2, …, g (31)

Q½ � ikk ≥ 0, ik ¼ 1, 2, …, Nk, k ¼ 1, 2, …, g (29)

Q½ � ikk ≤X½ � ikk q, ik ¼ 1, 2, …, Nk, k ¼ 1, 2, …, g (30)

g ¼ d e tq=α (27)

(26)

(28)

Step-1. Set the length of the first failure time interval after PM as α. Go to Step -2. Step-2. A problem is said as feasible if and only if the total time of process with one setup doesn't exceed the due date of delivering d, otherwise the problem is unfeasible for a model or if s + tq ≤ d then the problem is feasible; continue to Step-3. If s + tq> d, the problem is unfeasible, stop.

Step-3. Compute g by Eq. (27), and set Nk = Nb c, being computed by Eq. (26), k = 1, 2,…, g. Go to Step-4.

Step-4. For R = 1, 2, …, g. Go to Step-5.

Step-5. Set R = 1. Go to Step-6.

Step-6. Set g = R. Go to Step-7.

Step-7. Substitute the values of g, Nk, p, q, t, s, d, tPM into the model and set Set X½ � ikk = 1 for ik=1 and k=1 dan set X½ � ikk = 0 for other ik and k. Go to Step-8.

Step-8. Solve SISM Model without the constraint of Eqs. (20)-(24). Compute estimated rework cost by Eq. (22) and estimated restoration cost by Eq. (24), and compute a total cost to find TC, write TC½ � <sup>111</sup> = TC. Go to Step-9.

Step-9. Set k=1. Go to Step-10.

Step-10. Set ik = 2. Go to Step-11.

$$\underset{\underbrace{\text{\textbf{Step-11. Set}}}\_{\textbf{\ldots}} \mathbf{11. Set} \, X\_{\left[\underset{\textbf{j}\neq k}{\textbf{I}}\right]} = \mathbf{1} \text{ for } j\_{\mathbf{i}} \mathbf{1}, \mathbf{2}, \dots, i\_k \text{ and } l = \mathbf{1}, \mathbf{2}, \dots, k, \text{ and } \\ X\_{\left[\underset{\textbf{j}\neq k}{\textbf{j}}\right]} = \mathbf{0} \text{ otherwise.} $$

Go to Step-12.

Step-12. Solve SISM Model without the constraint of Eqs. (20)-(24). Compute estimated rework cost by Eq. (22) and estimated restoration cost by Eq. (24), and compute a total cost to find TC, write TC½ � ikk = TC. Go to Step-13.

Step-13. Observe whether TC½ � ikk <sup>&</sup>lt;TC ð Þ <sup>i</sup>�<sup>1</sup> <sup>k</sup> ½ �<sup>k</sup> ,





and writeall of TC[k]\* -related decision

variables, go to Step-15.

Step-14. Write TC[k]\*= TC½ � ikk and writeall of TC\*-related decisionvariables, go to Step-15.

Step-15. Observe whether k = g,



Step-16. Set k = k + 1, go to Step-17.

Step-17. Set ik= 2, go to Step-18.

Step-18. Set X <sup>j</sup> <sup>l</sup> ½ �<sup>l</sup> = 1 for <sup>j</sup> l = 1,2, …, ik and l = 1,2,…,k+1, and set X <sup>j</sup> <sup>l</sup> ½ �<sup>l</sup> = 0 for other <sup>j</sup> l , l. Go to Step-19.

Step-19. Solve SISM Model without the constraint of Eqs. (20)-(24). Compute estimated rework cost by Eq. (22) and estimated restoration cost by Eq. (24), and compute a total cost to find TC, write TC[i(k+1)] = TC. Go to Step-20. Step-20. Observe whether TC <sup>i</sup>½ � ð Þ <sup>k</sup>þ<sup>1</sup> ð Þ <sup>k</sup>þ<sup>1</sup> <sup>&</sup>lt;TC[k]\*,

$$\text{\textbullet - If } \underset{\bullet \text{---}}{\text{TC}} \underset{\bullet \text{---}}{\text{TC}} \underset{\bullet \text{---}}{\text{TC}} \text{\textbullet } \underset{\bullet \text{---}}{\text{Set } i} \text{\textbullet } \stackrel{i}{i} = i + \text{\textbullet}, \text{\textbullet back to Step-11.}$$

$$\text{- If } TC\_{\left[i\_{(k+1)}(k+1)\right]} \text{ } TC\_{\lceil k \rceil} \text{'', observe whether } k \text{ = g,}$$


