International Journal of Nonlinear Analysis and Applications
Proposing a lower bound for a nonlinear scheduling problem in supply chain
Document Type : Research Paper
Authors
Department of Industrial Engineering, Faculty of Materials and Industrial Engineering, Semnan University, Semnan 35195-363, Iran
Abstract
This paper proposes a nonlinear programming model for a scheduling problem in the supply chain. Due to the nonlinear structure of the developed model and its NP-hard structure, a lower bound is developed. Four lemmas and a theorem are presented and proved to determine the lower bound. The proposed problem is inspired from a three stage supply chain commonly used in various industries.
Keywords
[1] W. Roux, S. Dauzere-Peres and J.B. Lasserre, Planning and scheduling in a multisite environment, Prod. Plan. Cont. 10 (1999) 19–28.
[2] Y.-C. Chang and C.-Y. Lee, Machine scheduling with job delivery coordination, Europ. J. Oper. Res. 158 (2004) 470–487.
[3] S. H. Zegordi and M. A. Beheshti Nia, Integrating production and transportation scheduling in a two-stage supply chain considering order assignment, The Int. J. Adv. Manu. Tech. 44 (2009) 928–939.
[4] S. H. Zegordi, I. N. K. Abadi and M. A. B. Nia, A novel genetic algorithm for solving production and transportation scheduling in a two stage supply chain, Comput. Indust. Engin. 58 (2010) 373–381.
[5] A.D. Yimer and K. Demirli, A genetic approach to two-phase optimization of dynamic supply chain scheduling, Comput. Indust. Engin. 58 (2010) 411–422.
[6] B. Scholz-Reiter, E.M. Frazzon and T. Makuschewitz, Integrating manufacturing and logistic systems along global supply chains, CIRP J. Manu. Sci. Tech. 2 (2010) 216–223.
[7] H. Osman and K. Demirli, Economic lot and delivery scheduling problem for multi-stage supply chains, Int. J. Prod. Econ. 136 (2012) 275–286.
[8] I. Averbakh and M. Baysan, Approximation algorithm for the on-line multi-customer two-level supply chain scheduling problem, Oper. Res. Lett. 41 (2013) 710–714.
[9] S. Kabra, M.A. Shaik and A.S. Rathore, Multi-period scheduling of a multi-stage multi-product bio-pharmaceutical process, Comput. Chem. Engin. 57 (2013) 95–103.
[10] C.A. Ullrich, Integrated machine scheduling and vehicle routing with time windows, Europ. J. Oper. Res. 227 (2013) 152–165.
[11] A. Thomas, J. Venkateswaran, G. Singh and M. Krishnamoorthy, A resource constrained scheduling problem with multiple independent producers and a single linking constraint: A coal supply chain example, Europ. J. Oper. Res. 236 (2014) 946–956.
[12] E. Selvarajah and R. Zhang, Supply chain scheduling at the manufacturer to minimize inventory holding and delivery costs, Int. J. Prod. Econ. 147 (2014) 117–124.
[13] T. Sawik, Coordinated supply chain scheduling, Int. J. Prod. Econ. 120 (2009) 437–451.
[14] J. Pei, P.M. Pardalos, X. Liu, W. Fan and S. Yang, Serial batching scheduling of deteriorating jobs in a two-stage supply chain to minimize the makespan, Europ. J. Oper. Res. 244 (2015) 13–25.
[15] M. Rasti-Barzoki and S.R. Hejazi, Pseudo-polynomial dynamic programming for an integrated due date assignment, resource allocation, production, and distribution scheduling model in supply chain scheduling, Appl. Math. Mod. 39 (2015) 3280–3289.
[2] Y.-C. Chang and C.-Y. Lee, Machine scheduling with job delivery coordination, Europ. J. Oper. Res. 158 (2004) 470–487.
[3] S. H. Zegordi and M. A. Beheshti Nia, Integrating production and transportation scheduling in a two-stage supply chain considering order assignment, The Int. J. Adv. Manu. Tech. 44 (2009) 928–939.
[4] S. H. Zegordi, I. N. K. Abadi and M. A. B. Nia, A novel genetic algorithm for solving production and transportation scheduling in a two stage supply chain, Comput. Indust. Engin. 58 (2010) 373–381.
[5] A.D. Yimer and K. Demirli, A genetic approach to two-phase optimization of dynamic supply chain scheduling, Comput. Indust. Engin. 58 (2010) 411–422.
[6] B. Scholz-Reiter, E.M. Frazzon and T. Makuschewitz, Integrating manufacturing and logistic systems along global supply chains, CIRP J. Manu. Sci. Tech. 2 (2010) 216–223.
[7] H. Osman and K. Demirli, Economic lot and delivery scheduling problem for multi-stage supply chains, Int. J. Prod. Econ. 136 (2012) 275–286.
[8] I. Averbakh and M. Baysan, Approximation algorithm for the on-line multi-customer two-level supply chain scheduling problem, Oper. Res. Lett. 41 (2013) 710–714.
[9] S. Kabra, M.A. Shaik and A.S. Rathore, Multi-period scheduling of a multi-stage multi-product bio-pharmaceutical process, Comput. Chem. Engin. 57 (2013) 95–103.
[10] C.A. Ullrich, Integrated machine scheduling and vehicle routing with time windows, Europ. J. Oper. Res. 227 (2013) 152–165.
[11] A. Thomas, J. Venkateswaran, G. Singh and M. Krishnamoorthy, A resource constrained scheduling problem with multiple independent producers and a single linking constraint: A coal supply chain example, Europ. J. Oper. Res. 236 (2014) 946–956.
[12] E. Selvarajah and R. Zhang, Supply chain scheduling at the manufacturer to minimize inventory holding and delivery costs, Int. J. Prod. Econ. 147 (2014) 117–124.
[13] T. Sawik, Coordinated supply chain scheduling, Int. J. Prod. Econ. 120 (2009) 437–451.
[14] J. Pei, P.M. Pardalos, X. Liu, W. Fan and S. Yang, Serial batching scheduling of deteriorating jobs in a two-stage supply chain to minimize the makespan, Europ. J. Oper. Res. 244 (2015) 13–25.
[15] M. Rasti-Barzoki and S.R. Hejazi, Pseudo-polynomial dynamic programming for an integrated due date assignment, resource allocation, production, and distribution scheduling model in supply chain scheduling, Appl. Math. Mod. 39 (2015) 3280–3289.
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Volume 12, Issue 1
May 2021Pages 1073-1085
- Receive Date: 22 September 2016
- Revise Date: 05 March 2017
- Accept Date: 18 July 2017
- First Publish Date: 05 April 2021