An EPQ model for an imperfect production process with fuzzy cycle time and quality screening

Ozturk, H.; Aytar, S.; Senel, F. A.

doi:10.22111/ijfs.2019.4917

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	An EPQ model for an imperfect production process with fuzzy cycle time and quality screening
Iranian Journal of Fuzzy Systems
مقاله 14، دوره 16، شماره 5، آذر و دی 2019، صفحه 169-185 اصل مقاله (746.02 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22111/ijfs.2019.4917
نویسندگان
H. Ozturk^* ¹؛ S. Aytar²؛ F. A. Senel³
¹Suleyman Demirel University, Department of Business Administration, 32260, Isparta, Turkey
²Suleyman Demirel University, Department of Mathematics, 32260, Isparta, Turkey
³Suleyman Demirel University, Department of Computer Engineering, , 32260, Isparta, Turkey
چکیده
This study has developed a production inventory model where the cycle time is fuzzy, the existence of defective products is assumed in each batch and product screening is performed both in-production and after-production. Triangular fuzzy numbers serve to model uncertainties in the cycle time, and a fuzzified total inventory profit function is created by the defuzzification method known as the signed distance method. The classical approach is used to determine the optimal policy, with the ideal cycle time matched to the total profit. Although assuming asymmetric triangular fuzzy numbers prevents the calculation of a clear analytical solution, the method approaches as closely as possible to an analytical solution. A numerical solution to only one equation is needed to obtain the optimal configuration. Conversely, there is a positive trade-off, with an analytical solution to the optimization problem if there is an assumption of symmetrical triangular fuzzy numbers. The proposed model is illustrated by a numerical example. The paper presents results and sensitivity analyses, in both tables and graphic illustrations. The effects on total profit are discussed in relation to various parameters. From the numerical studies, it is observed that the level of fuzziness influences the cycle time and an approximately linear relationship, in the opposite direction, was found between the total profit and the level of fuzziness, when it was increased.
کلیدواژه‌ها
Inventory؛ EPQ؛ cycle time؛ rework؛ quality control؛ signed distance defuzzification method؛ process industry؛ supply chain management

مراجع
[1] A. Andriolo, D. Battini, R. W. Grubbstrom, A. Persona, F. Sgarbossa, A century of evolution from Harris's basic lot size model: Survey and research agenda, International Journal of Production Economics, 155 (2014), 16-38. [2] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96. [3] A. Baykasoglu, T. Gocken, Solution of a fully fuzzy multi-item economic order quantity problem by using fuzzy ranking functions, Engineering Optimization, 39 (2007), 919-39. [4] K. M. Bjork, The economic production quantity problem with a finite production rate and fuzzy cycle time, Proceedings of the 41st Annual Hawaii International Conference on System Sciences, (2008), 68-77. [5] K. M. Bjork, An analytical solution to a fuzzy economic order quantity problem, International Journal Approximate Reasoning, 50 (2009), 485-493. [6] K. M. Bjork, A multi-item fuzzy economic production quantity problem with a finite production rate, International Journal of Production Economics, 135 (2012), 702-707. [7] K. M. Bjork, C. Carlsson, The outcome of imprecise lead times on the distributors, Proceedings of the 38th Annual Hawaii International Conference on System Sciences, (2005), 81-90. [8] K. M. Bjork, C. Carlsson, The effect of flexible lead times on a paper producer, International Journal of Production Economics, 107 (2007), 139-150. [9] M. E. Bredahl, J. R. Northen, A. Boecker, M. A. Normile, Consumer demand sparks the growth of quality assurance schemes in the European food sector, Changing Structure of the Global Food Consumption and Trade: US Department of Agriculture, Agriculture and Trade Report, (2001), 90-102. [10] J. G. Brown, A note on fuzzy sets, Information and Control, 18 (1971), 32-39. [11] C. Carlsson, R. Fuller, Soft computing and the bullwhip effect, Economics and Complexity, 2 (1999), 1-26. [12] D. Chakraborty, D. K. Jana, T. K. Roy, Multi-item integrated supply chain model for deteriorating items with stock dependent demand under fuzzy random and bifuzzy environments, Computers and Industrial Engineering, 88 (2015), 166-180. [13] H. C. Chang, An application of fuzzy sets theory to the EOQ model with imperfect quality items, Computers and Operations Research, 31 (2004), 2079-2092. [14] T. H. Chen, Y. C. Tsao, Optimal lot-sizing integration policy under learning and rework effects in a manufacturer-retailer chain, International Journal of Production Economics, 155 (2014), 239-248. [15] S. H. Chen, C. C. Wang, R. Arthur, Backorder fuzzy inventory model under function principle, Information Sciences, 95 (1996), 71-79. [16] S. W. Chiu, An optimization problem of manufacturing systems with stochastic machine breakdown and rework process, Applied Stochastic Models in Business and Industry, 24 (2008), 203-219. [17] B. Cui, W. Zeng, Approximate reasoning with interval-valued fuzzy sets, Fifth International Conference on Fuzzy Systems and Knowledge Discovery, (2008), 60-64. [18] A. De Luca, S. Termini, Algebraic properties of fuzzy sets, Journal of Mathematical Analysis and Applications, 40 (1972), 373-386. [19] P. Diamond, P. Kloeden, Metric spaces of fuzzy sets: Theory and applications, World scientific, 1994. [20] D. Dubois, H. Prade, Operations on fuzzy numbers, International Journal of Systems Science, 9 (1978), 613-626. [21] S. D. P. Flapper, J. C. Fransoo, R. A. C. M. Broekmeulen, K. Inderfurth, Planning and control of rework in the process industries: A review, Production Planning and Control, 13 (2002), 26-34. [22] S. B. Gershwin, How do quantity and quality really interact? Precise models instead of strong opinions, IFAC Proceedings Volumes, 39 (2006), 33-39. [23] C. H. Glock, M. Y. Jaber, A multi-stage production-inventory model with learning and forgetting effects, rework and scrap, Computers and Industrial Engineering, 64 (2013), 708-720. [24] J. A. Goguen, L-Fuzzy sets, Journal of Mathematical Analysis and Applications, 18 (1967), 145-174. [25] M. B. Gorza lczany, A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems, 21 (1987), 1-17. [26] S. K. Goyal, A. Gunasekaran, T. Martikainen, P. Yli-Olli, Integrating production and quality control policies: A survey, European Journal of Operational Research, 69 (1993), 1-13. [27] R. W. Grubbstrom, B. G. Kingsman, Ordering and inventory policies for step changes in the unit item cost: A discounted cash flow approach, Management Science, 50 (2004), 253-267. [28] A. L. Guiffrida, Fuzzy inventory models, in Inventory Management Non-Classical Views, FL, Boca Raton: CRC Press, (2009), 173-198. [29] H. Gurnani, Z. Drezner, R. Akella, Capacity planning under different inspection strategies, European Journal of Operational Research, 89 (1996), 2-12. [30] P. A. Hayek, M. K. Salameh, Production lot sizing with the reworking of imperfect quality items produced, Production Planning and Control, 12 (2001), 584-590. [31] F. Herrera, E. Herrera-Viedma, Linguistic decision analysis: Steps for solving decision problems under linguistic information, Fuzzy Sets and Systems, 115 (2000), 67-82. [32] S. Islam, T. K. Roy, Fuzzy multi-item economic production quantity model under space constraint: A geometric programming approach, Applied Mathematics and Computation, 184 (2007), 326-335. [33] A. M. Jamal, B. R. Sarker, S. Mondal, Optimal manufacturing batch size with rework process at a single-stage production system, Computer and Industrial Engineering, 47 (2004), 77-89. [34] O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems, 24 (1987), 301-317. [35] C. W. Kang, M. Ullah, B. Sarkar, Human errors incorporation in work-in-process group manufacturing system, Scientia Iranica, 24 (2017), 2050-2061. [36] A. Kaufman, M. M. Gupta, Introduction to fuzzy arithmetic, New York, USA: Van Nostrand Reinhold Company, 1991. [37] N. Kazemi E. Ehsani, M. Y. Jaber, An inventory model with backorders with fuzzy parameters and decision variables, International Journal of Approximate Reasoning, 51 (2010), 964-972. [38] I. Konstantaras, K. Skouri, M. Y. Jaber, Inventory models for imperfect quality items with shortages and learning in inspection, Applied Mathematical Modelling, 36 (2012), 5334-5343. [39] H. M. Lee, J. S. Yao, Economic production quantity for fuzzy demand quantity, and fuzzy production quantity, European Journal of Operational Research, 109 (1998), 203-211. [40] F. T. Lin, Fuzzy job-shop scheduling based on ranking level (/spl lambda/, 1) interval-valued fuzzy numbers, IEEE Transactions on Fuzzy Systems, 10 (2002), 510-522. [41] W. N. Ma, D. C. Gong, G. C. Lin, An optimal common production cycle time for imperfect production processes with scrap, Mathematical and Computer Modelling, 52 (2010), 724-737. [42] J. Mezei, K. M. Bjork, An economic production quantity problem with backorders and fuzzy cycle times, Journal of Intelligent and Fuzzy Systems, 28 (2015), 1861-1868. [43] M. Mizumoto, K. Tanaka, Some properties of fuzzy sets of type 2, Information and Control, 31 (1976), 312-340. [44] S. P. Mondal, Interval valued intuitionistic fuzzy number and its application in differential equation, Journal of Intelligent and Fuzzy Systems, 34 (2018), 677-687. [45] L. Moussawi-Haidar, M. Salameh, W. Nasr, Production lot sizing with quality screening and rework, Applied Mathematical Modelling, 40 (2016), 3242-3256. [46] H. Ozturk, A note on production lot sizing with quality screening and rework, Applied Mathematical Modelling, 43 (2017), 659-69. [47] S. Papachristos, I. Konstantaras, Economic ordering quantity models for items with imperfect quality, International Journal of Production Economics, 100 (2006), 148-154. [48] K. S. Park, Fuzzy-set theoretic interpretation of economic order quantity, IEEE Transactions on Systems, Man and Cybernetics, 17 (1987), 1082-1084. [49] S. Paul, D. Jana, S. P. Mondal, P. Bhattacharya, Optimal harvesting of two species mutualism model with interval parameters, Journal of Intelligent and Fuzzy Systems, 33 (2017), 1991-2005. [50] E. L. Porteus, Optimal lot sizing, process quality improvement and setup cost reduction, Operations Research, 34 (1986), 137-144. [51] M. J. Rosenblatt, H. L. Lee, Economic production cycles with imperfect production processes, IIE Transactions, 18 (1986), 48-55. [52] J. Sadeghi, S. T. A. Niaki, M. R. Malekian, S. Sadeghi, Optimising multi-item economic production quantity model with trapezoidal fuzzy demand and backordering: Two tuned meta-heuristics, European Journal of Industrial Engineering, 10(2) (2016), 170-195. [53] M. K. Salameh, M. Y. Jaber, Economic production quantity model for items with imperfect quality, International Journal of Production Economics, 64 (2000), 59-64. [54] B. Sarkar, An inventory model with reliability in an imperfect production process, Applied Mathematics and Computation, 218 (2012), 4881-4891. [55] B. K. Sett, S. Sarkar, B. Sarkar, Optimal buer inventory and inspection errors in an imperfect production system with preventive maintenance, The International Journal of Advanced Manufacturing Technology, 90 (2017), 545-560. [56] C. Suntag, Inspection and inspection quality management, Milwaukee: ASQC, 1993. [57] A. A. Taleizadeh, S. J. Sadjadi, S. T. A. Niaki, Multi product EPQ model with single machine, backordering and immediate rework process, European Journal of Industrial Engineering, 5 (2011), 388-411. [58] J. T. Teng, H. L. Yang, M. S. Chern, Economic order quantity models for deteriorating items and partial backlogging when demand is quadratic in time, European Journal of Industrial Engineering, 5 (2011), 198-214. [59] I. B. Turksen, Interval valued fuzzy sets based on normal forms, Fuzzy Sets and Systems, 20 (1986), 191-210. [60] M. Ullah, C. W. Kang, Effect of rework, rejects and inspection on lot size with work-in-process inventory, International Journal of Production Research, 52 (2014), 2448-2460. [61] M. Vujosevic, D. Petrovic, R. Petrovic, EOQ formula when inventory cost is fuzzy, International Journal of Production Economics, 45 (1996), 499-504. 62] H. M. Wee, W. T. Wang, P. C. Yang, A production quantity model for imperfect quality items with shortage and screening constraint, International Journal Production Research, 51 (2013), 1869-1884. [63] J. S. Yao, K. Wu, Ranking fuzzy numbers based on decomposition principle and signed distance, Fuzzy Sets and Systems, 116 (2000), 275-88. [64] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353. [65] L. A. Zadeh, Some reflections on soft computing, granular computing and their roles in the conception, design and utilization of information/intelligent systems, Soft Computing, 2 (1998), 23-25. [66] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning{II, Information Sciences, 8 (1975), 301-357. [67] W. Zeng, H. Li, Relationship between similarity measure and entropy of interval valued fuzzy sets, Fuzzy Sets and Systems, 157(11) (2006), 1477-1484. [68] X. Zhang, Y. Gerchak, Joint lot sizing and inspection policy in an EOQ model with random yield, IIE Transactions, 22 (1990), 41-4
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An EPQ model for an imperfect production process with fuzzy cycle time and quality screening