CHAPTER 2. MAXIMIZE PRODUCER PROFIT UNDER INSTRUMENT WITH
2.5 Comparing the Expected Profit Per Unit Time for Complete Inspection Plan and Process Control
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2.5 Comparing the Expected Profit Per Unit Time for Complete Inspection Plan and Process Control.
We would like to find the difference of profit for complete inspection plan and PC. So we calculate the difference of two profits first,
D*
IS1−SPC= EPR
*IS1− EPR
*SPC,D*
IS2−SPC= EPR
*IS2− EPR
*SPC. Then do sensitivity analysis forI S1 S P C
D * − and
I S2 S P C
D * − to find out which process parameters and design parameters are significant.
The response figure and table are applied to find the significant parameters of D *I S1−S P C and
I S1 S P C D * − .
(I) Response figure and table of D *I S1−S P C
Figure 2.21 Response figure of
I S1 S P C
D * −
for each parameter
Table 2.27 Response table of
I S1 S P C D * −
δ δ
1δ
2δ
3σ
x(θ, m) (R, C
pr, IC, P
PM) k
Plevel1
3559.487 3396.299 2506.769 2556.133 3779.256 3175.025 7539.241 3347.814level2
2872.422 2871.474 3594.601 3446.951 2907.024 2845.517 867.583 2836.458level3
2326.437 2490.573 2656.977 2755.262 2072.066 2737.805 351.522 2574.074diff
1233.05 905.726 1087.831 890.819 1707.19 437.22 7187.719 773.74(R,P
0-P
1) e a b T
2-T
1C
sr-C
flevel1
7539.241 2362.361 3347.814 3075.419 2787.839 2142.027level2
867.583 3276.705 2836.458 2735.46 3104.835 3322.787level3
351.522 3119.28 2574.074 2947.467 2865.671 3293.532diff
7187.719 914.344 773.74 339.959 316.996 1180.759‧ 國
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Based on Table 2.27, If the difference between the maximal and minimal values of the three levels of a parameter is larger than 5000, then the parameter is determined to be significant. We found (R, Cpr, IC, PPM) and (R,P0-P1) are significantly influence D *I S1−S P C. When (R, Cpr, IC, PPM) or (R,P0-P1) increases,
I S1 S P C
D * − decreases.
(II) Response figure and table of D *I S2−S P C
Figure 2.22 Response figure of
I S2 S P C
D * −
for each parameter
Table 2.28 Response table of
I S2 S P C D * −
δ δ1 δ2 δ3 σx (θ, m) (R, Csc, IC, PPMH) γ kP
level1 3518.81 3275.768 2842.36 2950.179 3561.328 3139 6522.236 3309.945 2077.816 level2 2841.361 3152.212 3379.375 3385.133 2861.87 3013.658 1170.008 2645.207 2525.414 level3 1605.078 1537.27 1743.514 1629.938 1542.051 1812.591 273.005 2010.098 3362.019 diff 1913.731 1738.498 1635.86 1755.195 2019.277 1326.409 6249.231 1299.847 1284.202
P0-P1 e a b T2-T1 Csr-Cf
level1 6522.236 2502.537 3309.945 2077.816 1722.977 1582.905 level2 1170.008 3274.824 2645.207 2525.414 3392.12 3252.22 level3 273.005 2187.888 2010.098 3362.019 2850.152 3130.124
diff 6249.231 1086.936 1299.847 1284.202 1669.143 1669.315
Based on Table 2.28, If the difference between the maximal and minimal values of the three levels of a parameter is larger than 5000, then the parameter is determined to be significant. We found (R, Cpr, IC, PPM) and (R,P0-P1) are significantly influence D *I S2−S P C . When (R, Cpr, IC, PPM) or (R,P0-P1) increases, D *I S2−S P C decreases.
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number of productions of per unit time (R), and the profit of per item under in-control andout-of-control process (P0, P1) are critical parameters that affect D *I S2−S P C and D *I S2−S P C . Therefore, producer should appropriately control production and adjust sale prices to maximize
I S2 S P C D * − and
I S2 S P C D * − .
Table 2.29 Summary table of sensitivity analyses for
I S1 S P C
↓︰represent if parameter is increasing then response is significant and with decrease trend.
N︰represent parameter is not significant for response.
For the significant parameters ( R, Cpr, Csc, IC, PPM, P0 and P1 ), we sketch the plot for the level values that correspond to the response values (D *IS1−SP C,D *I S2−S P C ). The intersection points on the x-axis are calculated to determine the range of R, Cpr, Csc, IC, PPM, P0 and P1 to let the producer profit of complete inspection is larger than the producer profit of PC.
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58 Figure 2.23
I S1 S P C D * −
and
I S2 S P C
D * −
under different process parameters and design parameters value
Figure 2.23 (a) D*
IS SPC1−and
I S2 S P C D * −
under different production quantity
Figure 2.23 (b) D*
IS SPC1−under different perfect repair cost per item
From Figure 2.23 (a), we found that,
(1) when R > 0, the profit are larger for producer conducts perfect repair for the nonconforming item instead of PC.
(2) when R > 0, the profit are larger for producer conducts selling low price for the nonconforming item instead of PC.
From Figure 2.23 (b), we found that, when 0 < Cpr < 40.22, the profit are larger for producer conducts perfect repair for the nonconforming item instead of PC. This suggests that, when cost of product perfect repair is larger than 40.22, then it is better for producer conducting PC.
Figure 2.23 (c)
I S2 S P C
D * −
under different nonconforming item cost
Figure 2.23 (d)
I S1 S P C D * −
and
I S2 S P C D * −
under different inspection cost
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From Figure 2.23 (c), we found that, when 0 < Csc < 23.04, the profit are larger for producer conducts selling low price action instead of PC. This suggests that, when cost of per nonconforming item is larger than 23.04, then it is better for producer conducting PC.
From Figure 2.23 (d), we found that,
(1) When 0 < IC < 1.61, producer profit is larger when perfect repair is adopted than when PC is adopted. This suggests that, when inspection cost of producer take perfect repair action is larger than 1.61, then it is better for producer conducting PC.
(2) When 0 < IC < 1.27, producer profit is larger when sell low price is adopted than when PC is adopted. This suggests that, when inspection cost of producer sell different price action is larger than 1.27, then it is better for producer conducting PC.
Figure 2.23 (e)
I S1 S P C D * −
and
I S2 S P C
D * −
under different sell price of conforming items
From Figure 2.23 (e), we found that,
(1) When 0 < PPM < 107.03, profit is larger when perfect repair is adopted than when PC is adopted.
This suggests that, when per item selling price of producer take perfect repair action is larger than 107.03, then it is better for producer conducting PC.
(2) When 0 < PPMH < 97.61, profit is larger when sell low price is adopted than when PC is adopted.
This suggests that, when per item high selling price of producer take sell different price action is larger than 97.61, then it is better for producer conducting PC.
‧ 國
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N a tio na
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60 Figure 2.23 (f)
I S1 S P C D * −
and
I S2 S P C D * −
under different in-control profit per item of PC
Figure 2.23 (g)
I S1 S P C D * −
and
I S2 S P C
D * −
under different out-of-control profit per item of PC
From Figure 2.23 (f), we found that,
(1) When 0 < P0 < 83.62, profit is larger when perfect repair is adopted than when PC is adopted. This suggests that, when the profit per item under in-control process is larger than 83.62, then it is better for producer conducting PC.
(2) When 0 < P0 < 76.09, profit is larger when sell low price is adopted than when PC is adopted.
This suggests that, when the profit per item under in-control process is larger than 76.09, then it is better for producer conducting PC.
From Figure 2.19 (g), we found that,
(1) When 0 < P1 < 65.22, profit is larger when perfect repair is adopted than when PC is adopted. This suggests that, when the profit per item under out-of-control process is larger than 65.22, then it is better for producer conducting PC.
(2) When 0 < P1 < 59.57, profit is larger when sell low price is adopted than when PC is adopted.
This suggests that, when the profit per item under out-of-control process is larger than 59.57, then it is better for producer conducting PC.
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Table 2.30 Parameters range for producer conducting complete inspection plan under different η combination values
Significant Parameters
Before changed η values (0.5, 0.14, 0.08) Changed η values (0.5, 0.85, 0.95)
Conducting Perfect Repair Action
Conducting Sell at Low Price Action
Conducting Perfect Repair Action
Conducting Sell at Low Price Action
R R > 0 R > 0 R > 0 R > 0
Cpr 0 < Cpr < 40.22 - 0 < Cpr < 40.77 -
Csc - 0 < Csc < 23.04 - 0 < Csc < 26.29
IC 0 < IC < 1.61 0 < IC < 1.27 0 < IC < 1.65 0 < IC < 1.57 PPM ( PPMH ) 0 < PPM < 107.03 0 < PPMH < 97.61 0 < PPM < 107.95 0 < PPMH < 105.71 P0 0 < P0 < 83.62 0 < P0 < 76.09 0 < P0 < 84.36 0 < P0 < 82.57 P1 0 < P1 < 65.22 0 < P1 < 59.57 0 < P1 < 65.77 0 < P1 < 64.43
In section 2.3.1-3 we changed the proportion of the expected in-control time, η, and found that when η increases then the expected profit per unit time increases for producer. We also compare the significant parameters in the difference of producer adopting inspection profit and process control profit for the changed η value and before the changed η value, and found the significant parameters are same. Furthermore, Table 2.30 lists the ranges of parameters where perfect repair profit and sell at low price profit are higher than process control profit, and found the widths of the parameters ranges for changed η value are wider than those before changing η value.