سیاست پرداخت معوقه در مدل کنترل موجودی کالای فاسدشدنی با تقاضای کوادراتیک با درنظرگرفتن کمبود پس‌افت

نوع مقاله: مقاله پژوهشی

نویسندگان

1 مربی، دانشگاه صنعتی قوچان.

2 استادیار، دانشگاه صنعتی شاهرود.

3 مربی، دانشگاه تربت حیدریه.

چکیده

در اﯾﻦ پژوهش یک مدل جامع برای برنامه‌ریزی و ﮐﻨﺘﺮل ﻣﻮﺟﻮدی ﮐﺎﻻﻫﺎی ﻓﺴﺎدﭘﺬﯾﺮ ﺑﺎ مجاز­بودن بروز ﮐﻤﺒﻮد ارائه شده است. تابع تقاضا دارای ماهیت کوادراتیک ‌‌(تابع درجه دوم زمان)‌ است. در اﯾﻦ ﻣﺪل ﺳﯿﺴﺘﻢ ﻣﻮﺟﻮدی‌، برنامه‌ریزی برای تأمین یک ﮐﺎﻻ با نرخ ﻓﺴﺎد ﺛﺎﺑﺖ و کمبود به‌صورت پس‌افت کامل انجام می‌شود. هدف از مدل پیشنهادی، تعیین زمان چرخه‌ مناسب سفارش به‌منظور بیشینه‌کردن سود کل سیستم موجودی است. ﻣﺪلﺳﺎزی ﻣﺴﺌﻠﻪ در دو قالب مدت‌زمان اتمام موجودی انبار، پیش و پس از زمان ابلاغی از جانب تأمین‌کننده به خرده‌فروش برای تسویه‌حساب‌ها ارائه شده است. مدل پیشنهادی با استفاده از یک الگوریتم روش حل دﻗﯿﻖ توسعه‌یافته حل شده است. نتایج محاسباتی حاکی از کارایی مدل پیشنهادی به‌منظور برنامه‌ریزی تأمین کالاهای فسادپذیر است.

کلیدواژه‌ها


1. Abad, P. L. (2001). Optimal price and order size for a reseller under partial backordering. Computers & Operations Research, 28, 53-65.

2. Aggarwal S. P., & Jaggi C. K., (1995). Ordering policies of deteriorating items under permissible delay in payments. Journal of the Operational Research Society, 46(5), 658-662.

3. Aggarwal, S. P. (1978). A note on an order-level inventory model for a system with constant rate of deterioration. Opsearch, 15, 184-187.

4. Bakker, M., Riezebos, J., & Teunter, R. H. (2012). Review of inventory systems with deterioration since 2001. European Journal of Operational Research, 221, 275-284.

5. Balkhi, Z. T., & Benkherouf, L. (2004). On an inventory model for deteriorating items with stock dependent and time-varying demand rates. Computers & Operations Research, 31, 223-240.

6. Bhunia A. K., & Maiti, M. (1998). Deterministic inventory model for deteriorating items with finite rate of replenishment dependent on inventory level. Computers & Operations Research, 25(11), 997-1006.

7. Bhunia, A. K., & Maiti, M. (1999). An inventory model of deteriorating items with lot-size dependent replenishment cost and a linear trend in demand. Applied Mathematical Modelling, 23, 301-308.

8. Chakrabarty, T., Giri, B. C., & Chaudhuri, K. S. (1998). An EOQ model for items with weibull distribution deterioration, shortages and trended demand: an extension of philip's model. Computers & Operations Research, 25(7-8), 649-657.

9. Chang, C.-T. (2004). An EOQ model with deteriorating items under inflation when supplier credits linked to order quantity [J]. International Journal of Production Economics, 88, 307-316.

10. Cheikhrouhou, N., Sarkar, B., Ganguly, B., Malik, A.I., Balisten, R., & Lee, Y.H., (2017). Optimization of sample size and order size in an inventory model with quality inspection and return of defective items. Ann. Oper. Res. 265, 1-23.

11. Chu, P., & Chen, P. S. (2002). A note on inventory replenishment policies for deteriorating items in an exponentially declining market. Computers & Operations Research, 29, 1827-1842.

12. Chung K.-J. & Liao, J.-J. (2004). Lot-sizing decisions under trade credit depending on the ordering quantity. Computers & Operations Research, 31, 909-928.

13. Chung, K. J., & Liao, J.-J. (2006). The optimal ordering policy in a DCF analysis for deteriorating items when trade credit depends on the order quantity. International Journal of Production Economics, 100, 116-130.

14. Chung, K.-J. & Liao, J.-J. (2004). Lot-sizing decisions under trade credit depending on the ordering quantity. Computers & Operations Research, 31, 909-928.

15. Dye, C.-Y., & Ouyang, L.-Y. (2005). An EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging. European Journal of Operational Research, 163, 776-783.

16. Dye, C.-Y., Chang, H.-J., & Teng, J.-T. (2006). A deteriorating inventory model with time-varying demand and shortage-dependent partial backlogging. European Journal of Operational Research, 172, 417-429.

17. Dye, C.-Y. Hsieh, T.-P., & Ouyang. L.-Y. (2007). Determining optimal selling price and lot size with a varying rate of deterioration and exponential partial backlogging. European Journal of Operational Research, 181, 668-678.

18. Farughi, H., Khanlarzade, N., & Yegane, B. (2014). Pricing and inventory control policy for non- instantaneous deteriorating items with time-and price-dependent demand and partial backlogging. Decision Science Letters, 3(3), 325-334.

19. Ghare, P. M., & Schrader, G. F. (1963). A model for exponentially decaying inventory. Journal of Industrial Engineering, 14(5), 238-43.

20. Goyal, S. K., & Giri, B. C. (2001). Recebt trends in modeling of deteriorating inventory. European Journal of Operational Research, 134, 1-16.

21. Gu, F. W., & Zhou, S. Y. (2007). A replenishment policy for deteriorating items which are permissible delay in payment. Logistics Technology, 26(9), 48-51.

22. Gupta, R., & Vrat, P. (1994). Inventory model with multi-items under constraint systems for stock dependent consumption rate. Operations Research, 24, 41-42

23. Harris, F.W. (1913). How many parts to make at once, Factory. The Magazine of Management, 10(2), 135-136.

24. Hou, K.-L. (2006). An inventory model for deteriorating items with stock-dependent consumption rate and shortages under inflation and time discounting. European Journal of Operational Research, 168, 463-474.

25. Huang, K.-N., & Liao, J.-J. (2008). A simple method to locate the optimal solution for exponentially deteriorating items under trade credit financing. Computers and Mathematics with Applications, 56(4), 965-977.

26. Jamal, A. M. M., Sarker, B. R., & Wang, S. J. (2000). Optimal payment time for a retailer under permitted delay of payment by the wholesaler. International Journal of Production Economics, 66, 59-66.

27. Janssen, L., Claus, T., & Sauer, J. (2016). Literature review of deteriorating inventory models by key topics from 2012 to 2015. International Journal of Production Economics, 182, 86-112.

28. Jindal, P., & Solanki, A. (2016). Integrated vendor-buyer inventory models with inflation and time value of money in controllable lead-time. Decision Science Letters, 5(1), 81-94.

29. Kalpakam S., & Shanthi, S. (2000). A perishable system with modified base stock policy and random supply quantity. Computers & Mathematics with Applications. 39, 79-89.

30. Kalpakam S., & Shanthi, S. (2001). A perishable inventory system with modified (S-1, S) policy and arbitrary processing times. Computers & Operations Research, 28, 45 3-471.

31. Khanlarzade, N., Yegane, B., Kamalabadi, I., & Farughi, H. (2014). Inventory control with deteriorating items: A state-of-the-art literature review. International Journal of Industrial Engineering Computations, 5(2), 179-198.

32. Khanra, S., & Chaudhuri, K. S. (2003). A note on an order-level inventory model for a deteriorating item with time-dependent quadratic demand. Computers & Operations Research, 30, 1901-1916.

33. Kim, M. S., & Sarkar, B. (2017). Multi-stage cleaner production process with quality improvement and lead-time dependent ordering cost. J. Clean. Prod., 144, 572-590.

34. Lashgari, M., Taleizadeh, A. A., & Ahmadi, A. (2016). Partial up-stream advanced payment and partial down- stream delayed payment in a three-level supply chain. Annals of Operations Research, 238, 329-354.

35. Li, L.-F., Huang, P.-Q., & Luo, J.-W. (2004). A study of inventory management for deteriorating items. Systems Engineering, 22(3), 25-30.

36. Mahapatra, N. K. (2005). Decision process for multiobjective, multi-item production-inventory system via interactive fuzzy satisficing technique. Computers and Mathematics with Applications, 49, 805-821.

37. Mandal, B. N., & Phaujdar, S. (1989). An inventory model for deteriorating items and stock-dependent consumption rate. Journal of the Operational Research Society, 40, 483-488.

38. Mashud, A., Khan, M., Uddin, M., & Islam, M. (2018). A non-instantaneous inventory model having different deterioration rates with stock and price dependent demand under partially backlogged shortages. Uncertain Supply Chain Management, 6(1), 49-64.

39. Noh, J. S., Kin, J. S., & Sarkar, B. (2016). Stochastic joint replenishment problem with quantity discounts and minimum order constraints. Res. Oper. https://doi.org/10.1007/s12351-016-0281-6.

40. Ouyang, L. Y., Wu, K. S., & Yang, C. T. (2006). A study on an inventory model for non-instantaneous deteriorating items with permissible delay in payments. Computers & Industrial Engineering, 51, 637-651

41. P.-H. Hsu, H. M. Wee, & H.-M. Teng. (2007). Optimal ordering decision for deteriorating items with expiration date and uncertain lead time. Computers & Industrial Engineering, 52, 448-458.

42. Padmanabhan, G., & Vrat, P. (1995). EOQ models for perishable items under stock dependent selling rate. European Journal of Operational Research, 86(2), 281-292.

43. Pal, A. K., Bhunia, A. K., & Mukherjee, R. N. (2006). Optimal lot size model for deteriorating items with demand rate dependent on displayed stock level (DSL) and partial backordering. European Journal of Operational Research, 175, 977-991.

44. Palanivel, M., & Uthayakumar, R. (2014). An EOQ model for non-instantaneous deteriorating items with power demand, time dependent holding cost, partial backlogging and permissible delay in payments. World Academy of Science, Engineering and Technology. International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, 8(8), 1127-1137.

45. Panda, S., Senapati, S., & Basu, M. (2008). Optimal replenishment policy for perishable seasonal products in a season with ramp-type time dependent demand. Computers & Industrial Engineering, 54, 301-314.

46. Papachristos, S., & Skouri. K. (2003). An inventory model with deteriorating items, quantity discount, pricing and time-dependent partial backlogging. International Journal of Production Economics, 83, 247-256

47. Papachristos, S., & Skouri, K. (2000). An optimal replenishment policy for deteriorating items with time-varying demand and partial-exponential type-backlogging. Operations Researh Letters, 27, 175-184.

48. Raafat, F. (1991). Survey of literature on continuously deteriorating inventory models. Journal of Operational Research Society, 42, 89-94.

49. Rabbani, M., Rezaei, H., Lashgari, M., & Farrokhi-Asl, H. (2018). Vendor managed inventory control system for deteriorating items using metaheuristic algorithms. Decision Science Letters, 7(1), 25-38.

50. Sarkar, B. (2016). Supply chain coordination with variable backorder, inspections, and discount policy for fixed lifetime products. Math. Probl. Eng. 14.

51. Sarker, B. R., Jamal, A. M. M., & Wang, S. J., (2000). Supply chain models for perishable products under inflation and permissible delay in payment. Computer & Operation Research, 27, 59-75.

52. Sett, B. K., Sarkar, S., Sarkar, B., & Yun, W. Y., (2016). Optimal replenishment policy with variable deterioration for fixed lifetime products. Sci. Iran. SCIE, 23(5), 2318-2329.

53. Shah Y. K., & Jaiswal, M. C. (1977). An order-level inventory model for a system with constant rate of deterioration. Opsearch, 14, 174-184.

54. Shah, N. H., Soni, H. N., & Patel, K. A. (2013). Optimizing inventory and marketing policy for non- instantaneous deteriorating items with generalized type deterioration and holding cost rates. Omega, 41(2), 421-430.

55. Shin, D., Guchhait, R., Sarkar, B., & Mittal, M., (2016). Controllable lead time, service level constraint, and transportation discount in a continuous review inventory model. RAIRO Oper. Res. 5(4), 921-934.

56. Shukla, H., Shukla, V., and Yadava, S. (2013). EOQ model for deteriorating items with exponential demand rate and shortages. Uncertain Supply Chain Management, 1(2), 67-76.

57. Singhal, S., & Singh, S. (2015). Modeling of an inventory system with multi variate demand under volume flexibility and learning. Uncertain Supply Chain Management, 3(2), 147-158.

58. Song, X. P., & Cai, X. Q. (2006). On optimal payment time for retailer under permitted delay of payment by the wholesaler. International Journal of Production Economics, 103, 246-251.

59. Soni, H. N. (2013). Optimal replenishment policies for deteriorating items with stock-sensitive demand under two level trade credit and limited capacity. Appl. Math. Model. 37, 5887-5895.

60. Tayyab, M., Sarkar, B., (2016). Optimal batch quantity in a cleaner multi-stage lean production system with random defective rate. J. Clean. Prod. 139, 922-934.

61. Tripathi, R. P., & Mishra, S. M., (2014). Inventory model for deteriorating items with inventory dependent demand rate under trade credits. J. Appl. Probab. Stat. 9(2), 25-32.

62. Tripathi, R. P., & Singh, D. (2015). Inventory model with stock-dependent demand and different holding cost function. Int. J. Ind. Syst. Eng. 21(1), 68-72.

63. Tripathi, R. P., (2014). Optimal payment time for a retailer with exponential demand under permitted credit period by the wholesaler. Appl. Math. Inf. Sci. Lett. 2(3), 91-101.

64. Zhou, W., & Lau, H. S. (2000). An economic lot-size model for deteriorating items with lot-size dependent replenishment cost and time-varying demand. Applied Mathematical Modelling, 24, 761-770.

65. Wang, S.-D., & Wang, J.-P. (2005). A multi-stage optimal inventory model for deteriorating items by considering time value and inflation rate. Operations Research and Management Science, 14(6), 142-148.

66. Wee, H.-M., & Law, S.-T. (2001). Replenishment and pricing policy for deteriorating items taking into account the time-value of money. International Journal of Production Economics, 71, 213-220.

67. Wee, H.-M. (1999). Deteriorating inventory model with quantity discount, pricing and partial backordering. International Journal of Production Economics, 59, 511-518.

68. Whitin, T. M. (1953). The Theory of Inventory Management. Princeton University Press, Princeton, NJ, USA.

69. Yang, (2005). A comparison among various partial backlogging inventory lot-size models for deteriorating items on the basis of maximum profit. International Journal of Production Economics, 96, 119-128.

70. Zhang, C., Dai, G.-X., Han, G.-H., & Li, M. (2007). Study on inventory model for deteriorating items based on trade credit and cash discount. Operations Research and Management Science, 16(6), 33-37, 41.

71. Zhang, C., DAI, G.-X., Han, G.-H., & Li, M. (2007). Study on optimal inventory model for deteriorating items based on linear trade credit. Journal of Qingdao University (Natural Science Edition), 20(3), 70-74.

72. Zhang, J., Wang, Y., Lu, L., & Tang, W. (2015). Optimal dynamic pricing and replenishment cycle for non-instantaneous deterioration items with inventory-level-dependent demand. International Journal of Production Economics, 170, 136-145.

73. Zhu, G.-P. (2001). Optimal inventory model for single perishable item. Journal of Ningxia University (Natural Science Edition), 22(1), 15-16.