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Optimization of inventory system with defects, rework failure and two types of errors under crisp and fuzzy approach
Department of Industrial Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran |
In this paper, a new approach was applied to a single-item single-source ($ SISS $) system at the "$ EOQ-type $" mode considering imperfect items and uncertainty environment. The mentioned method was intended to produce an optimum order/production quantity as well as taking care of imperfect processes. The imperfect proportion of the received lot size was described by an imperfect inspection process. That is, two-way inspection errors may be committed by the inspector as separate items. Thus, this survey was aimed to maximize the benefit in the traditional inventory systems. The incorporation of both defects and defective classifications (Type-$ I\&II $ errors) was illustrated, in a way that the defects were returned by the consumers. Moreover, this inventory model had an extra step in the scope of inspection; which occurred after the rework process with no inspection error. To get closer to the practical circumstances and to consider the uncertainty, the model was formulated in the fuzzy environment. The demand, rework, and inspection rates of the inventory system were considered as the triangular fuzzy numbers where the output factors of the inventory system were obtained via nonlinear parametric programming and Zadeh's extension principle. Finally, this scenario was illustrated through a mathematical model. The concavity of the objective function was also calculated and the total profit function was presented to clarify the solution procedure by numerical examples.
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References:
[1] |
M. Ben-Daya, M.A. Darwish and A. Rahim,
Two-stage imperfect production systems with inspection errors, Int. J. Oper. Quant. Manag., 9 (2003), 117-131.
|
[2] |
B. Bharani,
Fuzzy economic production quantity model for a sustainable system via geometric programming, J. Glob. Res. Math. Arch., 5 (2018), 26-33.
|
[3] |
L. E. Cárdenas-Barrón,
The derivation of EOQ/EPQ inventory models with two backorders costs using analytic geometry and algebra, Appl. Math. Model., 35 (2011), 2394-2407.
doi: 10.1016/j.apm.2010.11.053. |
[4] |
L. E. Cárdenas-Barrón,
An easy method to derive EOQ and EPQ inventory models with backorders, Comput. Math. with Appl., 59 (2010), 948-952.
doi: 10.1016/j.camwa.2009.09.013. |
[5] |
L. E. Cárdenas-Barrón,
A simple method to compute economic order quantities: Some observations, Appl. Math. Model., 34 (2010), 1684-1688.
doi: 10.1016/j.apm.2009.08.024. |
[6] |
L. E. Cárdenas-Barrón,
Optimal manufacturing batch size with rework in a single-stage production system-a simple derivation, Comput. Ind. Eng., 55 (2008), 758-765.
|
[7] |
L. E. Cárdenas-Barrón,
Economic production quantity with rework process at a single-stage manufacturing system with planned backorders, Comput. Ind. Eng., 57 (2009), 1105-1113.
doi: 10.1016/j.cie.2009.04.020. |
[8] |
L. E. Cárdenas-Barrón,
Observation on: "Economic production quantity model for items with imperfect quality", Int. J. Production Economics, 64 (2000), 59-64.
|
[9] |
L. E. Cárdenas-Barrón,
The economic production quantity (EPQ) with shortage derived algebraically, Int. J. Prod. Econ., 70 (2001), 289-292.
|
[10] |
H. C. Chang,
An application of fuzzy sets theory to the EOQ model with imperfect quality items, Comput. Oper. Res., 31 (2004), 2079-2092.
doi: 10.1016/S0305-0548(03)00166-7. |
[11] |
H.-C. Chang and C.-H. Ho,
Exact closed-form solutions for "optimal inventory model for items with imperfect quality and shortage backordering", Omega, 38 (2010), 233-237.
doi: 10.1016/j.omega.2009.09.006. |
[12] |
S.-P. Chen,
Parametric nonlinear programming approach to fuzzy queues with bulk service, Eur. J. Oper. Res., 163 (2005), 434-444.
doi: 10.1016/j.ejor.2003.10.041. |
[13] |
S.-P. Chen,
Solving fuzzy queueing decision problems via a parametric mixed integer nonlinear programming method, Eur. J. Oper. Res., 177 (2007), 445-457.
doi: 10.1016/j.ejor.2005.09.040. |
[14] |
T. C. E. Cheng,
An economic order quantity model with demand-dependent unit production cost and imperfect production processes, IIE Trans., 23 (1991), 23-28.
doi: 10.1080/07408179108963838. |
[15] |
S. W. Chiu,
Robust planning in optimization for production system subject to random machine breakdown and failure in rework, Comput. Oper. Res., 37 (2010), 899-908.
doi: 10.1016/j.cor.2009.03.016. |
[16] |
Y. P. Chiu,
Determining the optimal lot size for the finite production model with random defective rate, the rework process, and backlogging, Eng. Optim., 35 (2003), 427-437.
doi: 10.1080/03052150310001597783. |
[17] |
S. W. Chiu, S.-L. Wang and Y.-S.P. Chiu,
Determining the optimal run time for EPQ model with scrap, rework, and stochastic breakdowns, Eur. J. Oper. Res., 180 (2007), 664-676.
doi: 10.1016/j.ejor.2006.05.005. |
[18] |
S. W. Chiu, Y. P. Chiu and B. P. Wu,
An economic production quantity model with the steady production rate of scrap items, J. Chaoyang Univ. Technol., 8 (2003), 225-235.
|
[19] |
S. W. Chiu,
Production lot size problem with failure in repair and backlogging derived without derivatives, Eur. J. Oper. Res., 188 (2008), 610-615.
doi: 10.1016/j.ejor.2007.04.049. |
[20] |
Y.-S. P. Chiu, K.-K. Chen, F.-T. Cheng and M.-F. Wu,
Optimization of the finite production rate model with scrap, rework and stochastic machine breakdown, Comput. Math. with Appl., 59 (2010), 919-932.
doi: 10.1016/j.camwa.2009.10.001. |
[21] |
Y.-S. P. Chiu, K.-K. Chen and C.-K. Ting,
Replenishment run time problem with machine breakdown and failure in rework, Expert Syst. Appl., 39 (2012), 1291-1297.
doi: 10.1016/j.eswa.2011.08.005. |
[22] |
Y.-S. P. Chiu, S.-C. Liu, C.-L. Chiu and H.-H. Chang,
Mathematical modeling for determining the replenishment policy for EMQ model with rework and multiple shipments, Math. Comput. Model., 54 (2011), 2165-2174.
doi: 10.1016/j.mcm.2011.05.025. |
[23] |
S. W. Chiu, C.-K. Ting and Y.-S.P. Chiu,
Optimal production lot sizing with rework, scrap rate, and service level constraint, Math. Comput. Model., 46 (2007), 535-549.
doi: 10.1016/j.mcm.2006.11.031. |
[24] |
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. |
[25] |
K.-J. Chung and Y.-F. Huang,
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Parameter/unit | ||||||
unit/cycle | day | day | day | day | $/year | |
Value | 1611 | 5.88 | 0.03 | 5.77 | 11.68 | 1079591 |
Parameter/unit | ||||||
unit/cycle | day | day | day | day | $/year | |
Value | 1611 | 5.88 | 0.03 | 5.77 | 11.68 | 1079591 |
Fuzzy number: |
||||
General Data | Symbol | |||
Rework and inspection rate re-workable items | 65000 | 800000 | 1000000 | |
Demand rate | 40000 | 50000 | 60000 | |
Rework and inspection rate of serviceable items | 520000 | 640000 | 800000 | |
Screening rate for order size | 80000 | 100000 | 150000 |
Fuzzy number: |
||||
General Data | Symbol | |||
Rework and inspection rate re-workable items | 65000 | 800000 | 1000000 | |
Demand rate | 40000 | 50000 | 60000 | |
Rework and inspection rate of serviceable items | 520000 | 640000 | 800000 | |
Screening rate for order size | 80000 | 100000 | 150000 |
Left and right bound of |
Left and right bound of |
||
|
0 | [102631,2434893] | [1586,1980] |
0.1 | [183152,2282247] | [1587,1918] | |
0.2 | [267488,2133404] | [1588,1865] | |
0.3 | [355640,1988365] | [1590,1865] | |
0.4 | [447608,1847131] | [1592,1778] | |
0.5 | [543393,1709699] | [1594,1742] | |
0.6 | [642996,1576071] | [1596,1710] | |
0.7 | [746417,1446247] | [1599,1682] | |
0.8 | [853656,1320226] | [1602,1656] | |
0.9 | [964714,1198007] | [1606,1632] | |
1 | [1079592,1079592] | [1611,1611] |
Left and right bound of |
Left and right bound of |
||
|
0 | [102631,2434893] | [1586,1980] |
0.1 | [183152,2282247] | [1587,1918] | |
0.2 | [267488,2133404] | [1588,1865] | |
0.3 | [355640,1988365] | [1590,1865] | |
0.4 | [447608,1847131] | [1592,1778] | |
0.5 | [543393,1709699] | [1594,1742] | |
0.6 | [642996,1576071] | [1596,1710] | |
0.7 | [746417,1446247] | [1599,1682] | |
0.8 | [853656,1320226] | [1602,1656] | |
0.9 | [964714,1198007] | [1606,1632] | |
1 | [1079592,1079592] | [1611,1611] |
Defuzzification method | ||
Variable | Signed distance/ |
Centroid/ |
E[TPU] | 1174177 | 1205705 |
1697 | 1726 | |
12.67 | 13 | |
6.16 | 6.26 | |
0.031 | 0.032 | |
6.48 | 6.72 |
Defuzzification method | ||
Variable | Signed distance/ |
Centroid/ |
E[TPU] | 1174177 | 1205705 |
1697 | 1726 | |
12.67 | 13 | |
6.16 | 6.26 | |
0.031 | 0.032 | |
6.48 | 6.72 |
Fuzzy mode: defuzzification method | Crisp mode | ||
Variable | Signed distance/ |
Centroid/ |
|
E[TPU] | 1174177 | 1205705 | 1079591 |
1697 | 1726 | 1611 | |
E[TPU]/ |
692 | 699 | 670 |
Fuzzy mode: defuzzification method | Crisp mode | ||
Variable | Signed distance/ |
Centroid/ |
|
E[TPU] | 1174177 | 1205705 | 1079591 |
1697 | 1726 | 1611 | |
E[TPU]/ |
692 | 699 | 670 |
Type-1 fuzzy number | ||
Crisp mode | Signed distance/ |
Centroid/ |
Components: ( |
Type-1 fuzzy number | ||
Crisp mode | Signed distance/ |
Centroid/ |
Components: ( |
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