Manufacturer-retailer integrated inventory model with controllable lead time and service level constraint under the effect of learning-forgetting in setup cost

Document Type : Article

Authors

1 Department of Mathematics, Vardhaman College, Bijnor-246701 (U.P.), India

2 Department of Mathematics, CCS University, Meerut-250001(U.P.), India

3 Department of Mathematics, Gurukula Kangari Vishwavidyalaya, Hairdwar-249404 (U.K.), India

4 Department of Industrial and Systems Engineering, School of Engineering and Sciences Tecnologico de Monterrey, E. Garza Sada 2501 Sur, C.P. 64849, Monterrey, Nuevo Leon, Mexico

Abstract

This research paper builds a manufacturer-retailer integrated inventory model to compute jointly the optimal values for the order quantity, the lead time, the reorder point and the number of shipments taking into consideration the effect of learning-forgetting phenomenon on the setup cost. The fabrication process of manufacturer is not perfect and certain level of product quality can attain with an additional cost. Service level constraint is incorporated into the inventory model to evade the backorder which gives negative impact to company reputation. The lead time is reduced with the help of crashing cost. The proposed inventory model is illustrated with the help of an example. From this example, it is detected that centralized decision is better than decentralized one. It is also observed from the analysis that players have to compromise with their profit if they decide to increment the service level and quality of the product. Due to the effect of learning-forgetting on the setup cost, profit of the centralized system increases.

Keywords


References:
[1] Goyal, S. K. “An integrated inventory model for a single supplier-single customer problem”. International Journal of Production Research, 15(1), 107-111 (1977)..
[2] Banerjee, A. (1986). A joint economic‐lot‐size model for purchaser and vendor. Decision sciences, 17(3), 292-311.
[3] Goyal, S.K.  A joint economic-lot-size model for purchaser and vendor: A comment. Decision Sciences, 19(1), 236-241 (1988).
[4] Pan, J. C. H., & Yang, J. S. “A study of an integrated inventory with controllable lead time”. International Journal of Production Research, 40(5), 1263-1273 (2002).
[5] Goyal, S. K. “A note on: On controlling the controllable lead time component in the integrated inventory models”. International Journal of Production Research, 41(12), 2873-2875 (2003). 
[6] Yang, P. C., & Wee, H. M. “Economic ordering policy of deteriorated item for vendor and buyer: an integrated approach”. Production Planning & Control, 11(5), 474-480 (2000).
[7] Affisco, J. F., Paknejad, M. J., & Nasri, F. (2002). Quality improvement and setup reduction in the joint economic lot size model. European Journal of Operational Research, 142(3), 497-508.

[8] Chang, H. C., Ouyang, L. Y., Wu, K. S., & Ho, C. H. “Integrated vendor–buyer cooperative inventory models with controllable lead time and ordering cost reduction”, European Journal of Operational Research, 170(2), 481-495 (2006).

[9] Hoque, M. A., & Goyal, S. K. “A heuristic solution procedure for an integrated inventory system under controllable lead-time with equal or unequal sized batch shipments between a vendor and a buyer”. International Journal of Production Economics, 102(2), 217-225 (2006).

[10] Chan, C. K., & Kingsman, B. G. “Coordination in a single-vendor multi-buyer supply chain by synchronizing delivery and production cycles”. Transportation Research Part E: Logistics and Transportation Review, 43(2), 90-111 (2007).

[11] Sajadieh, M. S., Jokar, M. R. A., & Modarres, M. “Developing a coordinated vendor–buyer model in two-stage supply chains with stochastic lead-times”. Computers & Operations Research, 36(8), 2484-2489 (2009).
[12] Ben-Daya, M., Darwish, M., & Ertogral, K. “The joint economic lot sizing problem: Review and extensions”. European Journal of Operational Research, 185(2), 726-742 (2008).
[13] Lin, Y. J. “An integrated vendor–buyer inventory model with backorder price discount and effective investment to reduce ordering cost”. Computers & Industrial Engineering, 56(4), 1597-1606 (2009).
[14] Ye, F., & Xu, X. “Cost allocation model for optimizing supply chain inventory with controllable lead time”. Computers & Industrial Engineering, 59(1), 93-99 (2010).
[15] Li, Y., Xu, X., & Ye, F. Supply chain coordination model with controllable lead time and service level constraint. Computers & Industrial Engineering, 61(3), 858-864 (2011).
[16] Yadav, D., Singh, S. R., & Kumari, R. “Application of minimax distribution free procedure and Chebyshev inequality for backorder discount inventory model with effective investment to reduce lead-time and defuzzification by signed distance method”. International Journal of Operational Research, 15(4), 371-390 (2012).
[17] Arkan, A., & Hejazi, S. R. “Coordinating orders in a two echelon supply chain with controllable lead time and ordering cost using the credit period”. Computers & Industrial Engineering, 62(1), 56-69 (2012).
[18] Song, H. M., Yang, H., & Bensoussan, A. “Optimizing production and inventory decisions in a supply chain with lot size, production rate and lead time interactions”. Applied Mathematics and Computation, 224, 150-165 (2013).
[19] Heydari, J. “Coordinating supplier׳ s reorder point: A coordination mechanism for supply chains with long supplier lead time”. Computers & Operations Research, 48, 89-101 (2014).
[20] Zhu, S. X. “Integration of capacity, pricing, and lead-time decisions in a decentralized supply chain”. International Journal of Production Economics, 164, 14-23 (2015).
[21] Sarkar, B., & Mahapatra, A. S. “Periodic review fuzzy inventory model with variable lead time and fuzzy demand”. International Transactions in Operational Research, 24(5), 1197-1227 (2017).
[22] Heydari, J., Zaabi-Ahmadi, P., & Choi, T. M. “Coordinating supply chains with stochastic demand by crashing lead times”. Computers & Operations Research, 100, 394-403 (2018).
[24] Ouyang, L. Y., & Wu, K. S. “Mixture inventory model involving variable lead time with a service level constraint”. Computers & Operations Research, 24(9), 875-882 (1997).

[25] Jha, J. K., & Shanker, K. “Two-echelon supply chain inventory model with controllable lead time and service level constraint”. Computers & Industrial Engineering, 57(3), 1096-1104 (2009).

[26] Bijvank, M., & Vis, I. F. “Lost-sales inventory systems with a service level criterion”. European Journal of Operational Research, 220(3), 610-618 (2012).
[27] Sarkar, B., Chaudhuri, K., & Moon, I. “Manufacturing setup cost reduction and quality improvement for the distribution free continuous-review inventory model with a service level constraint”. Journal of Manufacturing Systems, 34, 74-82 (2015).
[28] Shin, D., Guchhait, R., Sarkar, B., & Mittal, M. “Controllable lead time, service level constraint, and transportation discounts in a continuous review inventory model”. RAIRO-Operations Research, 50(4-5), 921-934 (2016).
[29] Albrecht, M. “Optimization of safety stocks in models with an order service level objective or constraint”. European Journal of Operational Research, 263(3), 900-909 (2017).
[30] Gruson, M., Cordeau, J. F., & Jans, R. “The impact of service level constraints in deterministic lot sizing with backlogging”. Omega, 79, 91-103 (2018).
[31] Sakulsom, N., & Tharmmaphornphilas, W. “Heuristics for a periodic-review policy in a two-echelon inventory problem with seasonal demand”. Computers & Industrial Engineering, 133, 292-302 (2019).

[32] Cárdenas-Barrón, L.E., Reynoso, J. Edvardsson, B., Cabrera, K. Inventory model optimization revisited: Understanding service inventories to improve performance, Scientia Iranica, DOI: 10.24200/sci.2018.50333.1639, (In press).

[33] Rosenblatt, M. J., & Lee, H. L. “Economic production cycles with imperfect production processes”. IIE transactions, 18(1), 48-55 (1986).
[34] Teng, J. T., & Thompson, G. L. “Optimal strategies for general price-quality decision models of new products with learning production costs”. European Journal of Operational Research, 93(3), 476-489 (1996).
[35] Salameh, M. K., & Jaber, M. Y. “Economic production quantity model for items with imperfect quality”. International Journal of Production Economics, 64(1-3), 59-64 (2000).
[36] Jaber, M. Y., & Bonney, M. “Lot sizing with learning and forgetting in set-ups and in product quality”. International Journal of Production Economics, 83(1), 95-111 (2003).
[37] Yang, J. S., & Pan, J. C. H. “Just-in-time purchasing: an integrated inventory model involving deterministic variable lead time and quality improvement investment”. International Journal of Production Research, 42(5), 853-863 (2004).
[38] Ouyang, L. Y., Wu, K. S., & Ho, C. H. “An integrated vendor–buyer inventory model with quality improvement and lead time reduction”. International Journal of Production Economics, 108(1-2), 349-358 (2007).

[39] Chen, C. K., Lo, C. C., & Liao, Y. X. “Optimal lot size with learning consideration on an imperfect production system with allowable shortages”. International Journal of Production Economics, 113(1), 459-469 (2008).

[40] Hsu, W. K. K., & Yu, H. F. “EOQ model for imperfective items under a one-time-only discount”. Omega, 37(5), 1018-1026 (2009).
[41] Roy, M. D., Sana, S. S., & Chaudhuri, K. “An economic order quantity model of imperfect quality items with partial backlogging”. International Journal of Systems Science, 42(8), 1409-1419 (2011).
[42] Pal, B., Sana, S. S., & Chaudhuri, K. “Joint pricing and ordering policy for two echelon imperfect production inventory model with two cycles”. International Journal of Production Economics, 155, 229-238 (2014).
[43] Jaber, M. Y., Zanoni, S., & Zavanella, L. E. “Economic order quantity models for imperfect items with buy and repair options”. International Journal of Production Economics, 155, 126-131 (2014).
[44] Kumar, R. S., & Goswami, A. “EPQ model with learning consideration, imperfect production and partial backlogging in fuzzy random environment”. International Journal of Systems Science, 46(8), 1486-1497 (2015).
[45] Giri, B. C., & Glock, C. H. “A closed-loop supply chain with stochastic product returns and worker experience under learning and forgetting”. International Journal of Production Research, 55(22), 6760-6778 (2017).

[46] Jaggi, C.K., Cárdenas-Barrón, L.E., Tiwari, S., Shafi, A. “Two-warehouse inventory model for deteriorating items with imperfect quality under the conditions of permissible delay in payments”, Scientia Iranica, 24(1), 390-412 (2017).

[47] Nobil, A.H., Sedigh, A.H.A., Cárdenas-Barrón, L.E., “Multi-machine economic production quantity for items with scrapped and rework with shortages and allocation decisions”, Scientia Iranica, 25(4), 2331-2346(2018).
[48] Gautam, P., & Khanna, A. “An imperfect production inventory model with setup cost reduction and carbon emission for an integrated supply chain”. Uncertain Supply Chain Management, 6(3), 271-286 (2018).
[49] Gautam, P., Kishore, A., Khanna, A., & Jaggi, C. K. “Strategic defect management for a sustainable green supply chain”. Journal of Cleaner Production, 233, 226-241 (2019).
[50] Khanna, A., Gautam, P., & Jaggi, C. K. “Coordinating vendor-buyer decisions for imperfect quality items considering trade credit and fully backlogged shortages”. In AIP Conference Proceedings, 1715(1), 020065. AIP Publishing (2016).
[51] Khanna, A., Gautam, P., & Jaggi, C. K. “Inventory modeling for deteriorating imperfect quality items with selling price dependent demand and shortage backordering under credit financing”. International Journal of Mathematical, Engineering and Management Sciences, 2(2), 110-124 (2017).
[52] Kishore, K, Gautam, P., Khanna, A., Jaggi, C.K. Investigating the effect of learning in set-up cost for imperfect production systems by utilizing two-way inspection plan for rework under screening constraints, Scientia Iranica, DOI: 10.24200/sci.2019.51333.2120 (In Press).     

[53] Dey, O., & Giri, B. C. “A new approach to deal with learning in inspection in an integrated vendor-buyer model with imperfect production process”. Computers & Industrial Engineering, 131, 515-523 (2019).

[54] Ouyang, L. Y., Chen, C. K., & Chang, H. C. “Quality improvement, setup cost and lead-time reductions in lot size reorder point models with an imperfect production process”. Computers & Operations Research, 29(12), 1701-1717 (2002).
[55] Hoque, M. A. “An alternative model for integrated vendor–buyer inventory under controllable lead time and its heuristic solution”. International journal of systems science, 38(6), 501-509 (2007).
[56] Sarkar, B., & Majumder, A. “Integrated vendor–buyer supply chain model with vendor’s setup cost reduction”. Applied Mathematics and Computation, 224, 362-371 (2013).

[57] Jha, J. K., & Shanker, K. “Single-vendor multi-buyer integrated production-inventory model with controllable lead time and service level constraints”. Applied Mathematical Modelling, 37(4), 1753-1767 (2013).

[58] Moon, I., Shin, E., & Sarkar, B. “Min–max distribution free continuous-review model with a service level constraint and variable lead time”. Applied Mathematics and Computation, 229, 310-315 (2014).
[59] Sarkar, B., & Moon, I. “Improved quality, setup cost reduction, and variable backorder costs in an imperfect production process”. International Journal of Production Economics, 155, 204-213 (2014).
[60] Sarkar, B., Mandal, B., & Sarkar, S. “Quality improvement and backorder price discount under controllable lead time in an inventory model”. Journal of Manufacturing Systems, 35, 26-36 (2015).
[61] Li, G., Kang, Y. C., & Xu, G. “Optimal decision for fashion supply chains with service level constraint and controllable lead time”. Mathematical Problems in Engineering, 2015, 758494, 1-9 (2015).
[62] Kim, M. S., & Sarkar, B. “Multi-stage cleaner production process with quality improvement and lead time dependent ordering cost”. Journal of cleaner production, 144, 572-590 (2017).
[63] Sarkar, B., Majumder, A., Sarkar, M., Dey, B. K., & Roy, G. “Two-echelon supply chain model with manufacturing quality improvement and setup cost reduction”. Journal of Industrial & Management Optimization, 13(2), 1085-1104 (2017).
[64] Wu, J. W., Lee, W. C., & Tsai, H. Y. “Computational algorithmic procedure of optimal inventory policy involving a negative exponential crashing cost and variable lead time demand”. Applied Mathematics and Computation, 184(2), 798-808 (2007).
[65] Porteus, E. L. “Optimal lot sizing, process quality improvement and setup cost reduction”. Operations research, 34(1), 137-144 (1986).
[66] Keller, G., & Noori, H. “Impact of investing in quality improvement on the lot size model”. Omega, 16(6), 595-601 (1988).
[67] Wright, T. P. “Factors affecting the cost of airplanes”. Journal of the Aeronautical Sciences, 3(4), 122-128 (1936).
[68] Loftus, G. R. Evaluating forgetting curves. Journal of Experimental Psychology: Learning, Memory, and Cognition, 11(2), 397 (1985).

[69] Gallego, G., & Moon, I. “The distribution free newsboy problem: review and extensions”. Journal of the Operational Research Society, 44(8), 825-834 (1993).