
-
Previous Article
Multi-item deteriorating two-echelon inventory model with price- and stock-dependent demand: A trade-credit policy
- JIMO Home
- This Issue
-
Next Article
Note on : Supply chain inventory model for deteriorating items with maximum lifetime and partial trade credit to credit risk customers
An inventory model with imperfect item, inspection errors, preventive maintenance and partial backlogging in uncertainty environment
Department of Industrial Engineering, Faculty of Engineering Kharazmi University, 15719-14911 Tehran, Iran |
In this paper investigate a production system with the defective quality process and preventive maintenance to establish the inspection policy and optimum inventory level for production items with considering uncertainty environment. The shortage occurs because of preventive maintenance and is considered as partial backlogging. Through the production process, at a random moment, the production of items from the state in-control turns into an out-of-control mode, so that parts of the defective product are manufactured an in-control state and outside of the control process mode. The online item inspection process begins after a time variable through the production period. The human inspection process has also been considered for the classify of defective goods. Uninspected products are accepted to the customer/buyer with minimal repair warranty and the defective items classify by the inspector at fixed cost before being shipped subject to salvaged items. Also, the inspection process of manufactured goods includes a human inspection error. Therefore, two types of classification errors (Type Ⅰ & Ⅱ) are considered to be more realistic than the proposed model. The input parameters of the model are considered as a triangular fuzzy environment, and the output parameters of the model are solved by the Zadeh's extension principle and nonlinear parametric programming. As a final point, a numerical example by graphical representations is obtainable to illustrate the proposed model.
References:
[1] |
M. Al-Salamah,
Economic production quantity in batch manufacturing with imperfect quality, imperfect inspection, and destructive and non-destructive acceptance sampling in a two-tier market, Comput. Ind. Eng., 93 (2016), 275-285.
doi: 10.1016/j.cie.2015.12.022. |
[2] |
A. Baykasoǧlu, K. Subulan and F. S. Karaslan,
A new fuzzy linear assignment method for multi-attribute decision making with an application to spare parts inventory classification, Appl. Soft Comput. J., 42 (2016), 1-17.
doi: 10.1016/j.asoc.2016.01.031. |
[3] |
B. Bouslah, A. Gharbi and R. Pellerin,
Integrated production, sampling quality control and maintenance of deteriorating production systems with AOQL constraint, Omega (United Kingdom), 61 (2016), 110-126.
doi: 10.1016/j.omega.2015.07.012. |
[4] |
S.-C. Chang, J.-S. Yao and H.-M. Lee,
Economic reorder point for fuzzy backorder quantity, Omega (United Kingdom), 109 (1998), 183-202.
doi: 10.1016/S0377-2217(97)00069-6. |
[5] |
Y. C. Chen,
An optimal production and inspection strategy with preventive maintenance error and rework, J. Manuf. Syst., 32 (2013), 99-106.
doi: 10.1016/j.jmsy.2012.07.010. |
[6] |
K. J. Chung, C. C. Her and S. D. Lin,
A two-warehouse inventory model with imperfect quality production processes, Comput. Ind. Eng., 56 (2009), 193-197.
doi: 10.1016/j.cie.2008.05.005. |
[7] |
S. K. De and S. S. Sana,
Fuzzy order quantity inventory model with fuzzy shortage quantity and fuzzy promotional index, Econ. Model., 31 (2013), 351-358.
doi: 10.1016/j.econmod.2012.11.046. |
[8] |
M. Farhangi, S. T. A. Niaki and B. Maleki Vishkaei,
Closed-form equations for optimal lot sizing in deterministic EOQ models with exchangeable imperfect quality items, Sci. Iran., 22 (2015), 2621-2634.
|
[9] |
Z. Hauck and J. Vörös,
Lot sizing in case of defective items with investments to increase the speed of quality control, Omega (United Kingdom), 52 (2015), 180-189.
doi: 10.1016/j.omega.2014.04.004. |
[10] |
J. T. Hsu and L. F. Hsu,
Two EPQ models with imperfect production processes, inspection errors, planned backorders, and sales returns, Comput. Ind. Eng., 64 (2013), 389-402.
doi: 10.1016/j.cie.2012.10.005. |
[11] |
J. T. Hsu and L. F. Hsu,
An EOQ model with imperfect quality items inspection errors shortage backordering and sales returns, Intern. J. Prod. Econ., 143 (2013), 162-170.
doi: 10.1016/j.ijpe.2012.12.025. |
[12] |
J. S. Hu, H. Zheng, C. Y. Guo and Y. P. Ji,
Optimal production run length with imperfect production processes and backorder in fuzzy random environment, Comput. Ind. Eng., 59 (2010), 9-15.
doi: 10.1016/j.cie.2010.01.012. |
[13] |
H. Ishii and T. Konno,
A stochastic inventory problem with fuzzy shortage cost, Eur. J. Oper. Res., 106 (1998), 90-94.
doi: 10.1016/S0377-2217(97)00173-2. |
[14] |
M. Y. Jaber and S. K. Goyal,
Economic production quantity model for items with imperfect quality subject to learning effects, Int. J. Prod. Econ., 115 (2008), 143-150.
doi: 10.1016/j.ijpe.2008.05.007. |
[15] |
D. K. Jana, B. Das and M. Maiti,
Multi-item partial backlogging inventory models over random planninghorizon in random fuzzy environment, Appl. Soft Comput. J., 21 (2014), 12-27.
doi: 10.1016/j.asoc.2014.02.021. |
[16] |
S. Karmakar, S. K. De and A. Goswami,
A pollution sensitive dense fuzzy economic production quantity model with cycle time dependent production rate, J. Clean. Prod., 154 (2017), 139-150.
doi: 10.1016/j.jclepro.2017.03.080. |
[17] |
N. Kazemi, E. Shekarian, L. E. Cárdenas-Barrón and E. U. Olugu,
Incorporating human learning into a fuzzy EOQ inventory model with backorders, Comput. Ind. Eng., 87 (2015), 540-542.
doi: 10.1016/j.cie.2015.05.014. |
[18] |
M. Khan, M. Y. Jaber and M. Bonney,
An economic order quantity (EOQ) for items with imperfect quality and inspection errors, Int. J. Prod. Econ., 133 (2011), 113-118.
doi: 10.1016/j.ijpe.2010.01.023. |
[19] |
M. Khan, M. Y. Jaber and M. I. M. Wahab,
Economic order quantity model for items with imperfect quality with learning in inspection, Int. J. Prod. Econ., 124 (2010), 87-96.
doi: 10.1016/j.ijpe.2009.10.011. |
[20] |
C. Krishnamoorthi,
An inventory model for product life cycle with maturity stage and defective items, Opsearch, 49 (2012), 209-222.
doi: 10.1007/s12597-012-0075-4. |
[21] |
T. Y. Lin,
Coordination policy for a two-stage supply chain considering quantity discounts and overlapped delivery with imperfect quality, Comput. Ind. Eng., 66 (2013), 53-62.
doi: 10.1016/j.cie.2013.06.012. |
[22] |
J. Liu and H. Zheng,
Fuzzy economic order quantity model with imperfect items, shortages and inspection errors, Syst. Eng. Procedia, 4 (2012), 282-289.
doi: 10.1016/j.sepro.2011.11.077. |
[23] |
W. N. Ma, D. C. Gong and G. C. Lin,
An optimal common production cycle time for imperfect production processes with scrap, Math. Comput. Model., 52 (2010), 724-737.
doi: 10.1016/j.mcm.2010.04.024. |
[24] |
B. Pal, S. S. Sana and K. Chaudhuri,
A mathematical model on EPQ for stochastic demand in an imperfect production system, J. Manuf. Syst., 32 (2013), 260-270.
doi: 10.1016/j.jmsy.2012.11.009. |
[25] |
S. Papachristos and I. Konstantaras,
Economic ordering quantity models for items with imperfect quality, Int. J. Prod. Econ., 100 (2006), 148-154.
doi: 10.1016/j.ijpe.2004.11.004. |
[26] |
M. A. Rahim and H. Ohta,
An integrated economic model for inventory and quality control problems, Eng. Optim., 37 (2005), 65-81.
doi: 10.1080/0305215042000268598. |
[27] |
J. Sadeghi, S. M. Mousavi and S. T. A. Niaki,
Optimizing an inventory model with fuzzy demand, backordering, and discount using a hybrid imperialist competitive algorithm, Appl. Math. Model., 40 (2016), 7318-7335.
doi: 10.1016/j.apm.2016.03.013. |
[28] |
M. K. Salameh and M. Y. Jaber,
Economic production quantity model for items with imperfect quality, Int. J. Prod. Econ., 64 (2000), 59-64.
doi: 10.1016/S0925-5273(99)00044-4. |
[29] |
N. K. Samal and D. K. Pratihar,
Optimization of variable demand fuzzy economic order quantity inventory models without and with backordering, Comput. Ind. Eng., 78 (2014), 148-162.
doi: 10.1016/j.cie.2014.10.006. |
[30] |
S. S. Sana,
A production-inventory model of imperfect quality products in a three-layer supply chain, Decis. Support Syst., 50 (2011), 539-547.
doi: 10.1016/j.dss.2010.11.012. |
[31] |
J. Taheri-Tolgari, A. Mirzazadeh and F. Jolai,
An inventory model for imperfect items under inflationary conditions with considering inspection errors, Comput. Math. with Appl., 63 (2012), 1007-1019.
doi: 10.1016/j.camwa.2011.09.050. |
[32] |
J. Wu, K. Skouri, J. T. Teng and Y. Hu,
Two inventory systems with trapezoidal-type demand rate and time-dependent deterioration and backlogging, Expert Syst. Appl., 46 (2016), 367-379.
doi: 10.1016/j.eswa.2015.10.048. |
show all references
References:
[1] |
M. Al-Salamah,
Economic production quantity in batch manufacturing with imperfect quality, imperfect inspection, and destructive and non-destructive acceptance sampling in a two-tier market, Comput. Ind. Eng., 93 (2016), 275-285.
doi: 10.1016/j.cie.2015.12.022. |
[2] |
A. Baykasoǧlu, K. Subulan and F. S. Karaslan,
A new fuzzy linear assignment method for multi-attribute decision making with an application to spare parts inventory classification, Appl. Soft Comput. J., 42 (2016), 1-17.
doi: 10.1016/j.asoc.2016.01.031. |
[3] |
B. Bouslah, A. Gharbi and R. Pellerin,
Integrated production, sampling quality control and maintenance of deteriorating production systems with AOQL constraint, Omega (United Kingdom), 61 (2016), 110-126.
doi: 10.1016/j.omega.2015.07.012. |
[4] |
S.-C. Chang, J.-S. Yao and H.-M. Lee,
Economic reorder point for fuzzy backorder quantity, Omega (United Kingdom), 109 (1998), 183-202.
doi: 10.1016/S0377-2217(97)00069-6. |
[5] |
Y. C. Chen,
An optimal production and inspection strategy with preventive maintenance error and rework, J. Manuf. Syst., 32 (2013), 99-106.
doi: 10.1016/j.jmsy.2012.07.010. |
[6] |
K. J. Chung, C. C. Her and S. D. Lin,
A two-warehouse inventory model with imperfect quality production processes, Comput. Ind. Eng., 56 (2009), 193-197.
doi: 10.1016/j.cie.2008.05.005. |
[7] |
S. K. De and S. S. Sana,
Fuzzy order quantity inventory model with fuzzy shortage quantity and fuzzy promotional index, Econ. Model., 31 (2013), 351-358.
doi: 10.1016/j.econmod.2012.11.046. |
[8] |
M. Farhangi, S. T. A. Niaki and B. Maleki Vishkaei,
Closed-form equations for optimal lot sizing in deterministic EOQ models with exchangeable imperfect quality items, Sci. Iran., 22 (2015), 2621-2634.
|
[9] |
Z. Hauck and J. Vörös,
Lot sizing in case of defective items with investments to increase the speed of quality control, Omega (United Kingdom), 52 (2015), 180-189.
doi: 10.1016/j.omega.2014.04.004. |
[10] |
J. T. Hsu and L. F. Hsu,
Two EPQ models with imperfect production processes, inspection errors, planned backorders, and sales returns, Comput. Ind. Eng., 64 (2013), 389-402.
doi: 10.1016/j.cie.2012.10.005. |
[11] |
J. T. Hsu and L. F. Hsu,
An EOQ model with imperfect quality items inspection errors shortage backordering and sales returns, Intern. J. Prod. Econ., 143 (2013), 162-170.
doi: 10.1016/j.ijpe.2012.12.025. |
[12] |
J. S. Hu, H. Zheng, C. Y. Guo and Y. P. Ji,
Optimal production run length with imperfect production processes and backorder in fuzzy random environment, Comput. Ind. Eng., 59 (2010), 9-15.
doi: 10.1016/j.cie.2010.01.012. |
[13] |
H. Ishii and T. Konno,
A stochastic inventory problem with fuzzy shortage cost, Eur. J. Oper. Res., 106 (1998), 90-94.
doi: 10.1016/S0377-2217(97)00173-2. |
[14] |
M. Y. Jaber and S. K. Goyal,
Economic production quantity model for items with imperfect quality subject to learning effects, Int. J. Prod. Econ., 115 (2008), 143-150.
doi: 10.1016/j.ijpe.2008.05.007. |
[15] |
D. K. Jana, B. Das and M. Maiti,
Multi-item partial backlogging inventory models over random planninghorizon in random fuzzy environment, Appl. Soft Comput. J., 21 (2014), 12-27.
doi: 10.1016/j.asoc.2014.02.021. |
[16] |
S. Karmakar, S. K. De and A. Goswami,
A pollution sensitive dense fuzzy economic production quantity model with cycle time dependent production rate, J. Clean. Prod., 154 (2017), 139-150.
doi: 10.1016/j.jclepro.2017.03.080. |
[17] |
N. Kazemi, E. Shekarian, L. E. Cárdenas-Barrón and E. U. Olugu,
Incorporating human learning into a fuzzy EOQ inventory model with backorders, Comput. Ind. Eng., 87 (2015), 540-542.
doi: 10.1016/j.cie.2015.05.014. |
[18] |
M. Khan, M. Y. Jaber and M. Bonney,
An economic order quantity (EOQ) for items with imperfect quality and inspection errors, Int. J. Prod. Econ., 133 (2011), 113-118.
doi: 10.1016/j.ijpe.2010.01.023. |
[19] |
M. Khan, M. Y. Jaber and M. I. M. Wahab,
Economic order quantity model for items with imperfect quality with learning in inspection, Int. J. Prod. Econ., 124 (2010), 87-96.
doi: 10.1016/j.ijpe.2009.10.011. |
[20] |
C. Krishnamoorthi,
An inventory model for product life cycle with maturity stage and defective items, Opsearch, 49 (2012), 209-222.
doi: 10.1007/s12597-012-0075-4. |
[21] |
T. Y. Lin,
Coordination policy for a two-stage supply chain considering quantity discounts and overlapped delivery with imperfect quality, Comput. Ind. Eng., 66 (2013), 53-62.
doi: 10.1016/j.cie.2013.06.012. |
[22] |
J. Liu and H. Zheng,
Fuzzy economic order quantity model with imperfect items, shortages and inspection errors, Syst. Eng. Procedia, 4 (2012), 282-289.
doi: 10.1016/j.sepro.2011.11.077. |
[23] |
W. N. Ma, D. C. Gong and G. C. Lin,
An optimal common production cycle time for imperfect production processes with scrap, Math. Comput. Model., 52 (2010), 724-737.
doi: 10.1016/j.mcm.2010.04.024. |
[24] |
B. Pal, S. S. Sana and K. Chaudhuri,
A mathematical model on EPQ for stochastic demand in an imperfect production system, J. Manuf. Syst., 32 (2013), 260-270.
doi: 10.1016/j.jmsy.2012.11.009. |
[25] |
S. Papachristos and I. Konstantaras,
Economic ordering quantity models for items with imperfect quality, Int. J. Prod. Econ., 100 (2006), 148-154.
doi: 10.1016/j.ijpe.2004.11.004. |
[26] |
M. A. Rahim and H. Ohta,
An integrated economic model for inventory and quality control problems, Eng. Optim., 37 (2005), 65-81.
doi: 10.1080/0305215042000268598. |
[27] |
J. Sadeghi, S. M. Mousavi and S. T. A. Niaki,
Optimizing an inventory model with fuzzy demand, backordering, and discount using a hybrid imperialist competitive algorithm, Appl. Math. Model., 40 (2016), 7318-7335.
doi: 10.1016/j.apm.2016.03.013. |
[28] |
M. K. Salameh and M. Y. Jaber,
Economic production quantity model for items with imperfect quality, Int. J. Prod. Econ., 64 (2000), 59-64.
doi: 10.1016/S0925-5273(99)00044-4. |
[29] |
N. K. Samal and D. K. Pratihar,
Optimization of variable demand fuzzy economic order quantity inventory models without and with backordering, Comput. Ind. Eng., 78 (2014), 148-162.
doi: 10.1016/j.cie.2014.10.006. |
[30] |
S. S. Sana,
A production-inventory model of imperfect quality products in a three-layer supply chain, Decis. Support Syst., 50 (2011), 539-547.
doi: 10.1016/j.dss.2010.11.012. |
[31] |
J. Taheri-Tolgari, A. Mirzazadeh and F. Jolai,
An inventory model for imperfect items under inflationary conditions with considering inspection errors, Comput. Math. with Appl., 63 (2012), 1007-1019.
doi: 10.1016/j.camwa.2011.09.050. |
[32] |
J. Wu, K. Skouri, J. T. Teng and Y. Hu,
Two inventory systems with trapezoidal-type demand rate and time-dependent deterioration and backlogging, Expert Syst. Appl., 46 (2016), 367-379.
doi: 10.1016/j.eswa.2015.10.048. |


















Triangular Fuzzy Number: [a, b, c] | ||||
General Data | Symbol | a | b | c |
Production rate | 300 | 500 | 700 | |
Annual demand rate | 250 | 450 | 650 | |
Setup cost | 400 | 600 | 800 | |
Holding cost | 1.5 | 2.5 | 4 | |
Variable cost | 75 | 100 | 125 | |
Inspection cost | 0.75 | 1 | 1.25 | |
Repair cost for warranty | 35 | 50 | 65 | |
Salvage cost | 10 | 15 | 20 | |
Cost of falsely accepted imperfect item | 23 | 28 | 33 | |
Cost of falsely rejected perfect item | 7 | 10 | 13 | |
Maintenance cost | 75 | 100 | 125 | |
Shortage cost | 5.5 | 6.5 | 7.5 | |
Fraction of product shortage that is backorder | 0.6 | 0.75 | 0.9 | |
Percentage of defective products/in control | 0.05 | 0.15 | 0.25 | |
Percentage of defective products/out-of-control | 0.05 | 0.30 | 0.60 |
Triangular Fuzzy Number: [a, b, c] | ||||
General Data | Symbol | a | b | c |
Production rate | 300 | 500 | 700 | |
Annual demand rate | 250 | 450 | 650 | |
Setup cost | 400 | 600 | 800 | |
Holding cost | 1.5 | 2.5 | 4 | |
Variable cost | 75 | 100 | 125 | |
Inspection cost | 0.75 | 1 | 1.25 | |
Repair cost for warranty | 35 | 50 | 65 | |
Salvage cost | 10 | 15 | 20 | |
Cost of falsely accepted imperfect item | 23 | 28 | 33 | |
Cost of falsely rejected perfect item | 7 | 10 | 13 | |
Maintenance cost | 75 | 100 | 125 | |
Shortage cost | 5.5 | 6.5 | 7.5 | |
Fraction of product shortage that is backorder | 0.6 | 0.75 | 0.9 | |
Percentage of defective products/in control | 0.05 | 0.15 | 0.25 | |
Percentage of defective products/out-of-control | 0.05 | 0.30 | 0.60 |
General Data | Symbol | Probability Density Function |
Type-Ⅰ error | ||
Type-Ⅱ error | ||
Preventive maintenance time | ||
Time after which the production process shifts in control to out-of-control state |
General Data | Symbol | Probability Density Function |
Type-Ⅰ error | ||
Type-Ⅱ error | ||
Preventive maintenance time | ||
Time after which the production process shifts in control to out-of-control state |
Lower and upper bound of |
Lower and upper bound of |
Lower and upper bound of | |||||
0 | 300 | 700 | 250 | 650 | 400 | 800 | |
0.1 | 320 | 680 | 270 | 630 | 420 | 780 | |
0.2 | 340 | 660 | 290 | 610 | 440 | 760 | |
0.3 | 360 | 640 | 310 | 590 | 460 | 740 | |
0.4 | 380 | 620 | 330 | 570 | 480 | 720 | |
0.5 | 400 | 600 | 350 | 550 | 500 | 700 | |
0.6 | 420 | 580 | 370 | 530 | 520 | 680 | |
0.7 | 440 | 560 | 390 | 510 | 540 | 660 | |
0.8 | 460 | 540 | 410 | 490 | 560 | 640 | |
0.9 | 480 | 520 | 430 | 470 | 580 | 620 | |
1 | 500 | 500 | 450 | 450 | 600 | 600 |
Lower and upper bound of |
Lower and upper bound of |
Lower and upper bound of | |||||
0 | 300 | 700 | 250 | 650 | 400 | 800 | |
0.1 | 320 | 680 | 270 | 630 | 420 | 780 | |
0.2 | 340 | 660 | 290 | 610 | 440 | 760 | |
0.3 | 360 | 640 | 310 | 590 | 460 | 740 | |
0.4 | 380 | 620 | 330 | 570 | 480 | 720 | |
0.5 | 400 | 600 | 350 | 550 | 500 | 700 | |
0.6 | 420 | 580 | 370 | 530 | 520 | 680 | |
0.7 | 440 | 560 | 390 | 510 | 540 | 660 | |
0.8 | 460 | 540 | 410 | 490 | 560 | 640 | |
0.9 | 480 | 520 | 430 | 470 | 580 | 620 | |
1 | 500 | 500 | 450 | 450 | 600 | 600 |
Lower and upper bound of |
Lower and upper bound of |
Lower and upper bound of | |||||
0 | 1.5 | 4 | 75 | 125 | 0.75 | 1.25 | |
0.1 | 1.6 | 3.85 | 77.5 | 122.5 | 0.775 | 1.225 | |
0.2 | 1.7 | 3.7 | 80 | 120 | 0.8 | 1.2 | |
0.3 | 1.8 | 3.55 | 82.5 | 117.5 | 0.825 | 1.175 | |
0.4 | 1.9 | 3.4 | 85 | 115 | 0.85 | 1.15 | |
0.5 | 2 | 3.25 | 87.5 | 112.5 | 0.875 | 1.125 | |
0.6 | 2.1 | 3.1 | 90 | 110 | 0.9 | 1.1 | |
0.7 | 2.2 | 2.95 | 92.5 | 107.5 | 0.925 | 1.075 | |
0.8 | 2.3 | 2.8 | 95 | 105 | 0.95 | 1.05 | |
0.9 | 2.4 | 2.65 | 97.5 | 102.5 | 0.975 | 1.025 | |
1 | 2.5 | 2.5 | 100 | 100 | 1 | 1 |
Lower and upper bound of |
Lower and upper bound of |
Lower and upper bound of | |||||
0 | 1.5 | 4 | 75 | 125 | 0.75 | 1.25 | |
0.1 | 1.6 | 3.85 | 77.5 | 122.5 | 0.775 | 1.225 | |
0.2 | 1.7 | 3.7 | 80 | 120 | 0.8 | 1.2 | |
0.3 | 1.8 | 3.55 | 82.5 | 117.5 | 0.825 | 1.175 | |
0.4 | 1.9 | 3.4 | 85 | 115 | 0.85 | 1.15 | |
0.5 | 2 | 3.25 | 87.5 | 112.5 | 0.875 | 1.125 | |
0.6 | 2.1 | 3.1 | 90 | 110 | 0.9 | 1.1 | |
0.7 | 2.2 | 2.95 | 92.5 | 107.5 | 0.925 | 1.075 | |
0.8 | 2.3 | 2.8 | 95 | 105 | 0.95 | 1.05 | |
0.9 | 2.4 | 2.65 | 97.5 | 102.5 | 0.975 | 1.025 | |
1 | 2.5 | 2.5 | 100 | 100 | 1 | 1 |
Lower and upper bound of |
Lower and upper bound of |
Lower and upper bound of | |||||
0 | 35 | 65 | 10 | 20 | 23 | 33 | |
0.1 | 36.5 | 63.5 | 10.5 | 19.5 | 23.5 | 32.5 | |
0.2 | 38 | 62 | 11 | 19 | 24 | 32 | |
0.3 | 39.5 | 60.5 | 11.5 | 18.5 | 24.5 | 31.5 | |
0.4 | 41 | 59 | 12 | 18 | 25 | 31 | |
0.5 | 42.5 | 57.5 | 12.5 | 17.5 | 25.5 | 30.5 | |
0.6 | 44 | 56 | 13 | 17 | 26 | 30 | |
0.7 | 45.5 | 54.5 | 13.5 | 16.5 | 26.5 | 29.5 | |
0.8 | 47 | 53 | 14 | 16 | 27 | 29 | |
0.9 | 48.5 | 51.5 | 14.5 | 15.5 | 27.5 | 28.5 | |
1 | 50 | 50 | 15 | 15 | 28 | 28 |
Lower and upper bound of |
Lower and upper bound of |
Lower and upper bound of | |||||
0 | 35 | 65 | 10 | 20 | 23 | 33 | |
0.1 | 36.5 | 63.5 | 10.5 | 19.5 | 23.5 | 32.5 | |
0.2 | 38 | 62 | 11 | 19 | 24 | 32 | |
0.3 | 39.5 | 60.5 | 11.5 | 18.5 | 24.5 | 31.5 | |
0.4 | 41 | 59 | 12 | 18 | 25 | 31 | |
0.5 | 42.5 | 57.5 | 12.5 | 17.5 | 25.5 | 30.5 | |
0.6 | 44 | 56 | 13 | 17 | 26 | 30 | |
0.7 | 45.5 | 54.5 | 13.5 | 16.5 | 26.5 | 29.5 | |
0.8 | 47 | 53 | 14 | 16 | 27 | 29 | |
0.9 | 48.5 | 51.5 | 14.5 | 15.5 | 27.5 | 28.5 | |
1 | 50 | 50 | 15 | 15 | 28 | 28 |
Lower and upper bound of |
Lower and upper bound of |
Lower and upper bound of |
|||||
0 | 7 | 13 | 75 | 125 | 5.5 | 7.5 | |
0.1 | 7.3 | 12.7 | 77.5 | 122.5 | 5.6 | 7.4 | |
0.2 | 7.6 | 12.4 | 80 | 120 | 5.7 | 7.3 | |
0.3 | 7.9 | 12.1 | 82.5 | 117.5 | 5.8 | 7.2 | |
0.4 | 8.2 | 11.8 | 85 | 115 | 5.9 | 7.1 | |
0.5 | 8.5 | 11.5 | 87.5 | 112.5 | 6 | 7 | |
0.6 | 8.8 | 11.2 | 90 | 110 | 6.1 | 6.9 | |
0.7 | 9.1 | 10.9 | 92.5 | 107.5 | 6.2 | 6.8 | |
0.8 | 9.4 | 10.6 | 95 | 105 | 6.3 | 6.7 | |
0.9 | 9.7 | 10.3 | 97.5 | 102.5 | 6.4 | 6.6 | |
1 | 10 | 10 | 100 | 100 | 6.5 | 6.5 |
Lower and upper bound of |
Lower and upper bound of |
Lower and upper bound of |
|||||
0 | 7 | 13 | 75 | 125 | 5.5 | 7.5 | |
0.1 | 7.3 | 12.7 | 77.5 | 122.5 | 5.6 | 7.4 | |
0.2 | 7.6 | 12.4 | 80 | 120 | 5.7 | 7.3 | |
0.3 | 7.9 | 12.1 | 82.5 | 117.5 | 5.8 | 7.2 | |
0.4 | 8.2 | 11.8 | 85 | 115 | 5.9 | 7.1 | |
0.5 | 8.5 | 11.5 | 87.5 | 112.5 | 6 | 7 | |
0.6 | 8.8 | 11.2 | 90 | 110 | 6.1 | 6.9 | |
0.7 | 9.1 | 10.9 | 92.5 | 107.5 | 6.2 | 6.8 | |
0.8 | 9.4 | 10.6 | 95 | 105 | 6.3 | 6.7 | |
0.9 | 9.7 | 10.3 | 97.5 | 102.5 | 6.4 | 6.6 | |
1 | 10 | 10 | 100 | 100 | 6.5 | 6.5 |
Lower and upper bound of |
Lower and upper bound of |
Lower and upper bound of |
|||||
0 | 0.6 | 0.9 | 0.05 | 0.25 | 0.05 | 0.6 | |
0.1 | 0.615 | 0.885 | 0.06 | 0.24 | 0.075 | 0.57 | |
0.2 | 0.63 | 0.87 | 0.07 | 0.23 | 0.1 | 0.54 | |
0.3 | 0.645 | 0.855 | 0.08 | 0.22 | 0.125 | 0.51 | |
0.4 | 0.66 | 0.84 | 0.09 | 0.21 | 0.15 | 0.48 | |
0.5 | 0.675 | 0.825 | 0.1 | 0.2 | 0.175 | 0.45 | |
0.6 | 0.69 | 0.81 | 0.11 | 0.19 | 0.2 | 0.42 | |
0.7 | 0.705 | 0.795 | 0.12 | 0.18 | 0.225 | 0.39 | |
0.8 | 0.72 | 0.78 | 0.13 | 0.17 | 0.25 | 0.36 | |
0.9 | 0.735 | 0.765 | 0.14 | 0.16 | 0.275 | 0.33 | |
1 | 0.75 | 0.75 | 0.15 | 0.15 | 0.3 | 0.3 |
Lower and upper bound of |
Lower and upper bound of |
Lower and upper bound of |
|||||
0 | 0.6 | 0.9 | 0.05 | 0.25 | 0.05 | 0.6 | |
0.1 | 0.615 | 0.885 | 0.06 | 0.24 | 0.075 | 0.57 | |
0.2 | 0.63 | 0.87 | 0.07 | 0.23 | 0.1 | 0.54 | |
0.3 | 0.645 | 0.855 | 0.08 | 0.22 | 0.125 | 0.51 | |
0.4 | 0.66 | 0.84 | 0.09 | 0.21 | 0.15 | 0.48 | |
0.5 | 0.675 | 0.825 | 0.1 | 0.2 | 0.175 | 0.45 | |
0.6 | 0.69 | 0.81 | 0.11 | 0.19 | 0.2 | 0.42 | |
0.7 | 0.705 | 0.795 | 0.12 | 0.18 | 0.225 | 0.39 | |
0.8 | 0.72 | 0.78 | 0.13 | 0.17 | 0.25 | 0.36 | |
0.9 | 0.735 | 0.765 | 0.14 | 0.16 | 0.275 | 0.33 | |
1 | 0.75 | 0.75 | 0.15 | 0.15 | 0.3 | 0.3 |
Lower and upper bound of |
Lower and upper bound of |
Lower and upper bound of |
|||||
0 | 87.0133 | 145.1221 | 261.5060 | 334.5721 | 0 | 1 | |
0.1 | 89.9842 | 142.218 | 268.8547 | 332.0059 | 0 | 0.6745 | |
0.2 | 92.9146 | 139.3142 | 276.4437 | 329.4848 | 0 | 0.4356 | |
0.3 | 95.8269 | 136.4106 | 282.4803 | 327.0103 | 0 | 0.3054 | |
0.4 | 98.7300 | 133.5071 | 287.6358 | 324.5838 | 0 | 0.2221 | |
0.5 | 101.627 | 130.6038 | 292.2257 | 322.2072 | 0 | 0.1640 | |
0.6 | 104.522 | 127.7005 | 296.4265 | 319.8825 | 0 | 0.1211 | |
0.7 | 107.414 | 124.7973 | 300.3485 | 317.6118 | 0 | 0.0882 | |
0.8 | 110.305 | 121.8939 | 304.0651 | 315.3975 | 0 | 0.0622 | |
0.9 | 113.195 | 118.9902 | 307.6279 | 313.2330 | 0.0096 | 0.0412 | |
1 | 116.0856 | 116.0856 | 311.0745 | 311.0745 | 0.0239 | 0.0239 |
Lower and upper bound of |
Lower and upper bound of |
Lower and upper bound of |
|||||
0 | 87.0133 | 145.1221 | 261.5060 | 334.5721 | 0 | 1 | |
0.1 | 89.9842 | 142.218 | 268.8547 | 332.0059 | 0 | 0.6745 | |
0.2 | 92.9146 | 139.3142 | 276.4437 | 329.4848 | 0 | 0.4356 | |
0.3 | 95.8269 | 136.4106 | 282.4803 | 327.0103 | 0 | 0.3054 | |
0.4 | 98.7300 | 133.5071 | 287.6358 | 324.5838 | 0 | 0.2221 | |
0.5 | 101.627 | 130.6038 | 292.2257 | 322.2072 | 0 | 0.1640 | |
0.6 | 104.522 | 127.7005 | 296.4265 | 319.8825 | 0 | 0.1211 | |
0.7 | 107.414 | 124.7973 | 300.3485 | 317.6118 | 0 | 0.0882 | |
0.8 | 110.305 | 121.8939 | 304.0651 | 315.3975 | 0 | 0.0622 | |
0.9 | 113.195 | 118.9902 | 307.6279 | 313.2330 | 0.0096 | 0.0412 | |
1 | 116.0856 | 116.0856 | 311.0745 | 311.0745 | 0.0239 | 0.0239 |
Lower and upper bound of |
Lower and upper bound of |
||||
0 | 0.176880867 | 5.9687669 | 9.23117E-06 | 0.000239 | |
0.1 | 0.366359442 | 5.691024185 | 1.82229E-05 | 0.000228 | |
0.2 | 0.652038831 | 5.417609624 | 3.09138E-05 | 0.000218 | |
0.3 | 0.947627216 | 5.148450421 | 4.33739E-05 | 0.000208 | |
0.4 | 1.25140767 | 4.883472592 | 5.57048E-05 | 0.000197 | |
0.5 | 1.562433439 | 4.622600569 | 6.79622E-05 | 0.000187 | |
0.6 | 1.880135101 | 4.365756781 | 8.01786E-05 | 0.000177 | |
0.7 | 2.204158168 | 4.112861206 | 9.23724E-05 | 0.000166 | |
0.8 | 2.534281476 | 3.863830732 | 0.000104554 | 0.000156 | |
0.9 | 2.870373498 | 3.546574322 | 0.000116726 | 0.000143 | |
1 | 3.212363938 | 3.212363938 | 0.000128889 | 0.000129 |
Lower and upper bound of |
Lower and upper bound of |
||||
0 | 0.176880867 | 5.9687669 | 9.23117E-06 | 0.000239 | |
0.1 | 0.366359442 | 5.691024185 | 1.82229E-05 | 0.000228 | |
0.2 | 0.652038831 | 5.417609624 | 3.09138E-05 | 0.000218 | |
0.3 | 0.947627216 | 5.148450421 | 4.33739E-05 | 0.000208 | |
0.4 | 1.25140767 | 4.883472592 | 5.57048E-05 | 0.000197 | |
0.5 | 1.562433439 | 4.622600569 | 6.79622E-05 | 0.000187 | |
0.6 | 1.880135101 | 4.365756781 | 8.01786E-05 | 0.000177 | |
0.7 | 2.204158168 | 4.112861206 | 9.23724E-05 | 0.000166 | |
0.8 | 2.534281476 | 3.863830732 | 0.000104554 | 0.000156 | |
0.9 | 2.870373498 | 3.546574322 | 0.000116726 | 0.000143 | |
1 | 3.212363938 | 3.212363938 | 0.000128889 | 0.000129 |
Defuzzification method | ||
Variable | Centroid | Signed distance |
116.07 | 116.08 | |
302.38 | 304.56 | |
0.3413 | 0.262 | |
Hessian matrix |
3.1193 | 3.1426 |
Hessian matrix |
0.0001 | 0.0001 |
Defuzzification method | ||
Variable | Centroid | Signed distance |
116.07 | 116.08 | |
302.38 | 304.56 | |
0.3413 | 0.262 | |
Hessian matrix |
3.1193 | 3.1426 |
Hessian matrix |
0.0001 | 0.0001 |
[1] |
Biswajit Sarkar, Bimal Kumar Sett, Sumon Sarkar. Optimal production run time and inspection errors in an imperfect production system with warranty. Journal of Industrial and Management Optimization, 2018, 14 (1) : 267-282. doi: 10.3934/jimo.2017046 |
[2] |
Guiyang Zhu. Optimal pricing and ordering policy for defective items under temporary price reduction with inspection errors and price sensitive demand. Journal of Industrial and Management Optimization, 2022, 18 (3) : 2129-2161. doi: 10.3934/jimo.2021060 |
[3] |
Shuhua Zhang, Longzhou Cao, Zuliang Lu. An EOQ inventory model for deteriorating items with controllable deterioration rate under stock-dependent demand rate and non-linear holding cost. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021156 |
[4] |
Akhlad Iqbal, Praveen Kumar. Geodesic $ \mathcal{E} $-prequasi-invex function and its applications to non-linear programming problems. Numerical Algebra, Control and Optimization, 2021 doi: 10.3934/naco.2021040 |
[5] |
Kurt Falk, Marc Kesseböhmer, Tobias Henrik Oertel-Jäger, Jens D. M. Rademacher, Tony Samuel. Preface: Diffusion on fractals and non-linear dynamics. Discrete and Continuous Dynamical Systems - S, 2017, 10 (2) : i-iv. doi: 10.3934/dcdss.201702i |
[6] |
Dmitry Dolgopyat. Bouncing balls in non-linear potentials. Discrete and Continuous Dynamical Systems, 2008, 22 (1&2) : 165-182. doi: 10.3934/dcds.2008.22.165 |
[7] |
Dorin Ervin Dutkay and Palle E. T. Jorgensen. Wavelet constructions in non-linear dynamics. Electronic Research Announcements, 2005, 11: 21-33. |
[8] |
Armin Lechleiter. Explicit characterization of the support of non-linear inclusions. Inverse Problems and Imaging, 2011, 5 (3) : 675-694. doi: 10.3934/ipi.2011.5.675 |
[9] |
Denis Serre. Non-linear electromagnetism and special relativity. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 435-454. doi: 10.3934/dcds.2009.23.435 |
[10] |
Feng-Yu Wang. Exponential convergence of non-linear monotone SPDEs. Discrete and Continuous Dynamical Systems, 2015, 35 (11) : 5239-5253. doi: 10.3934/dcds.2015.35.5239 |
[11] |
Anugu Sumith Reddy, Amit Apte. Stability of non-linear filter for deterministic dynamics. Foundations of Data Science, 2021, 3 (3) : 647-675. doi: 10.3934/fods.2021025 |
[12] |
Ahmad El Hajj, Aya Oussaily. Continuous solution for a non-linear eikonal system. Communications on Pure and Applied Analysis, 2021, 20 (11) : 3795-3823. doi: 10.3934/cpaa.2021131 |
[13] |
Tommi Brander, Joonas Ilmavirta, Manas Kar. Superconductive and insulating inclusions for linear and non-linear conductivity equations. Inverse Problems and Imaging, 2018, 12 (1) : 91-123. doi: 10.3934/ipi.2018004 |
[14] |
Emine Kaya, Eugenio Aulisa, Akif Ibragimov, Padmanabhan Seshaiyer. A stability estimate for fluid structure interaction problem with non-linear beam. Conference Publications, 2009, 2009 (Special) : 424-432. doi: 10.3934/proc.2009.2009.424 |
[15] |
Pablo Ochoa. Approximation schemes for non-linear second order equations on the Heisenberg group. Communications on Pure and Applied Analysis, 2015, 14 (5) : 1841-1863. doi: 10.3934/cpaa.2015.14.1841 |
[16] |
Eugenio Aulisa, Akif Ibragimov, Emine Yasemen Kaya-Cekin. Stability analysis of non-linear plates coupled with Darcy flows. Evolution Equations and Control Theory, 2013, 2 (2) : 193-232. doi: 10.3934/eect.2013.2.193 |
[17] |
Noufel Frikha, Valentin Konakov, Stéphane Menozzi. Well-posedness of some non-linear stable driven SDEs. Discrete and Continuous Dynamical Systems, 2021, 41 (2) : 849-898. doi: 10.3934/dcds.2020302 |
[18] |
Olusola Kolebaje, Ebenezer Bonyah, Lateef Mustapha. The first integral method for two fractional non-linear biological models. Discrete and Continuous Dynamical Systems - S, 2019, 12 (3) : 487-502. doi: 10.3934/dcdss.2019032 |
[19] |
Tarek Saanouni. Non-linear bi-harmonic Choquard equations. Communications on Pure and Applied Analysis, 2020, 19 (11) : 5033-5057. doi: 10.3934/cpaa.2020221 |
[20] |
Faustino Sánchez-Garduño, Philip K. Maini, Judith Pérez-Velázquez. A non-linear degenerate equation for direct aggregation and traveling wave dynamics. Discrete and Continuous Dynamical Systems - B, 2010, 13 (2) : 455-487. doi: 10.3934/dcdsb.2010.13.455 |
2020 Impact Factor: 1.801
Tools
Metrics
Other articles
by authors
[Back to Top]