October  2015, 11(4): 1355-1373. doi: 10.3934/jimo.2015.11.1355

Optimal acquisition, inventory and production decisions for a closed-loop manufacturing system with legislation constraint

1. 

School of Science, Tianjin University, Tianjin 300072, China, China

2. 

School of Information Engineering, Tianjin University of Commerce, Tianjin 300134, China

3. 

School of Electrical and Electronic Engineering, The University of Adelaide, SA 5005

Received  March 2013 Revised  October 2014 Published  March 2015

In order to improve the utilization efficiency of resources, more and more countries have required manufacturing firms to remanufacture or reuse used products through legislation. For many firms, the profit from reusing used products may be less than the profit from producing new products, so how to make decisions under such legislation constraint is a major concern by these firms. In this paper, we study the optimal acquisition, inventory and production decision problem for such firms under a two-period setting, where firms have two different production ways: (i) production with new raw materials, and (ii) production with used products. The return quantity of used products at the second period depends on the demand of the first period and the acquisition effort. The problem is formulated as a stochastic dynamic programming model. We give the optimal production rule and the optimal inventory decision at the second period, and prove the existence of an optimal policy with a simple structure at the first period. Moreover, based on our theoretical analysis, we calculate the optimal decisions under different parameter settings, and discuss how the firm does react when facing with specific market and production conditions.
Citation: Xiaochen Sun, Fei Hu, Yancong Zhou, Cheng-Chew Lim. Optimal acquisition, inventory and production decisions for a closed-loop manufacturing system with legislation constraint. Journal of Industrial & Management Optimization, 2015, 11 (4) : 1355-1373. doi: 10.3934/jimo.2015.11.1355
References:
[1]

B. Atamer, I.Bakal and Z. Pelin BayIndIr, Optimal pricing and production decisions in utilizing reusable containers,, Int. J. Product. Econ., 143 (2013), 222. doi: 10.1016/j.ijpe.2011.08.007. Google Scholar

[2]

I. Bakal and E. Akcali, Effects of random yield in reverse supply chains with price-sensitive supply and demand,, Prod. Oper. Manag., 15 (2006), 407. Google Scholar

[3]

S. Boyd and L. Vandenberghe, Convex Optimization,, Cambridge University Press, (2004). doi: 10.1017/CBO9780511804441. Google Scholar

[4]

R. Dekker, M. Fleischmann, K. Inderfurth and L. N. V. Wassenhove, Reverse Logistics: Quantitative Models for Closed-Loop Supply Chains,, Springer-Verlag, (2004). Google Scholar

[5]

I. Dobos and K. Richter, A production/recycling model with stationary demand and return rates,, Cent Eur. J Oper. Res., 11 (2003), 35. Google Scholar

[6]

M. Fleischmann, J. Bloemhof-Ruwaard, R. Dekker, E. van der Lann, J. van Nunen and L. N. V. Wassenhove, Quantitative models for reverse logistics: A review,, Eur. J. Oper. Res., 103 (1997), 1. Google Scholar

[7]

M. R. Galbreth and J. D. Blackburn, Optimal acquisition and sorting policies for remanufacturing,, Prod. Oper. Manag., 15 (2006), 384. Google Scholar

[8]

V. D. R. Guide Jr. and V. Jayaraman, Product acquisition management: Current industry practice and a proposed framework,, Int. J. Prod. Res., 38 (2000), 3779. Google Scholar

[9]

V. D. R. Guide Jr., R. H. Teunter and L. N. V. Wassenhove, Matching demand and supply to maximize profits from remanufacturing,, Manufacturing and Service Operations Management, 5 (2003), 303. Google Scholar

[10]

I. Karakayal, H. Emir-Farinas and E. Akal, Analysis of decentralized collection and processing of end-of-life products,, J. Oper. Manag., 25 (2007), 1161. doi: 10.1016/j.jom.2007.01.017. Google Scholar

[11]

I. Karakayal, H. Emir-Farinas and E. Akal, Pricing and recovery planning for remanufacturing operations with multiple used products and multiple reusable components,, Comput. Ind. Eng., 59 (2010), 55. Google Scholar

[12]

G. P. Kiesmuller and E. A. van der Laan, An inventory model with dependent product demands and returns,, Int. J. Product. Econ., 72 (2001), 73. doi: 10.1016/S0925-5273(00)00080-3. Google Scholar

[13]

F. Hillier and J. Lieberman, Introduction to Operations Research,, $4^{nd}$ Edition, (1986). Google Scholar

[14]

E. L. Porteus, Foundation of Stochastic Inventory Theory,, Stanford University Press, (2002). Google Scholar

[15]

S. M. Ross, Introduction to Stochastic Dynamic Programming,, Academic Press, (1983). Google Scholar

[16]

X. Sun, Y. Li, G.Kannan and Y.Zhou., Integrating dynamic acquisition pricing and remanufacturing decisions under random price-sensitive returns,, Int. J. Adv. Manuf. Tech., 68 (2013), 933. doi: 10.1007/s00170-013-4954-5. Google Scholar

[17]

X. Xu, Y. Li and X. Cai, Optimal polices in hybrid manufacturing/remanufacturing systems with random price-sensitive product returns,, Int. J. Prod. Res., 50 (2012), 6978. Google Scholar

[18]

X. Zhou and Y. Yu, Optimal product acquisition, pricing, and inventory management for systems with remanufacturing,, Oper. Res., 59 (2011), 514. doi: 10.1287/opre.1100.0898. Google Scholar

show all references

References:
[1]

B. Atamer, I.Bakal and Z. Pelin BayIndIr, Optimal pricing and production decisions in utilizing reusable containers,, Int. J. Product. Econ., 143 (2013), 222. doi: 10.1016/j.ijpe.2011.08.007. Google Scholar

[2]

I. Bakal and E. Akcali, Effects of random yield in reverse supply chains with price-sensitive supply and demand,, Prod. Oper. Manag., 15 (2006), 407. Google Scholar

[3]

S. Boyd and L. Vandenberghe, Convex Optimization,, Cambridge University Press, (2004). doi: 10.1017/CBO9780511804441. Google Scholar

[4]

R. Dekker, M. Fleischmann, K. Inderfurth and L. N. V. Wassenhove, Reverse Logistics: Quantitative Models for Closed-Loop Supply Chains,, Springer-Verlag, (2004). Google Scholar

[5]

I. Dobos and K. Richter, A production/recycling model with stationary demand and return rates,, Cent Eur. J Oper. Res., 11 (2003), 35. Google Scholar

[6]

M. Fleischmann, J. Bloemhof-Ruwaard, R. Dekker, E. van der Lann, J. van Nunen and L. N. V. Wassenhove, Quantitative models for reverse logistics: A review,, Eur. J. Oper. Res., 103 (1997), 1. Google Scholar

[7]

M. R. Galbreth and J. D. Blackburn, Optimal acquisition and sorting policies for remanufacturing,, Prod. Oper. Manag., 15 (2006), 384. Google Scholar

[8]

V. D. R. Guide Jr. and V. Jayaraman, Product acquisition management: Current industry practice and a proposed framework,, Int. J. Prod. Res., 38 (2000), 3779. Google Scholar

[9]

V. D. R. Guide Jr., R. H. Teunter and L. N. V. Wassenhove, Matching demand and supply to maximize profits from remanufacturing,, Manufacturing and Service Operations Management, 5 (2003), 303. Google Scholar

[10]

I. Karakayal, H. Emir-Farinas and E. Akal, Analysis of decentralized collection and processing of end-of-life products,, J. Oper. Manag., 25 (2007), 1161. doi: 10.1016/j.jom.2007.01.017. Google Scholar

[11]

I. Karakayal, H. Emir-Farinas and E. Akal, Pricing and recovery planning for remanufacturing operations with multiple used products and multiple reusable components,, Comput. Ind. Eng., 59 (2010), 55. Google Scholar

[12]

G. P. Kiesmuller and E. A. van der Laan, An inventory model with dependent product demands and returns,, Int. J. Product. Econ., 72 (2001), 73. doi: 10.1016/S0925-5273(00)00080-3. Google Scholar

[13]

F. Hillier and J. Lieberman, Introduction to Operations Research,, $4^{nd}$ Edition, (1986). Google Scholar

[14]

E. L. Porteus, Foundation of Stochastic Inventory Theory,, Stanford University Press, (2002). Google Scholar

[15]

S. M. Ross, Introduction to Stochastic Dynamic Programming,, Academic Press, (1983). Google Scholar

[16]

X. Sun, Y. Li, G.Kannan and Y.Zhou., Integrating dynamic acquisition pricing and remanufacturing decisions under random price-sensitive returns,, Int. J. Adv. Manuf. Tech., 68 (2013), 933. doi: 10.1007/s00170-013-4954-5. Google Scholar

[17]

X. Xu, Y. Li and X. Cai, Optimal polices in hybrid manufacturing/remanufacturing systems with random price-sensitive product returns,, Int. J. Prod. Res., 50 (2012), 6978. Google Scholar

[18]

X. Zhou and Y. Yu, Optimal product acquisition, pricing, and inventory management for systems with remanufacturing,, Oper. Res., 59 (2011), 514. doi: 10.1287/opre.1100.0898. Google Scholar

[1]

Jing Zhao, Jie Wei, Yongjian Li. Pricing and remanufacturing decisions for two substitutable products with a common retailer. Journal of Industrial & Management Optimization, 2017, 13 (2) : 1125-1147. doi: 10.3934/jimo.2016065

[2]

Hassen Aydi, Ayman Kachmar. Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint. II. Communications on Pure & Applied Analysis, 2009, 8 (3) : 977-998. doi: 10.3934/cpaa.2009.8.977

[3]

Ata Allah Taleizadeh, Hadi Samimi, Biswajit Sarkar, Babak Mohammadi. Stochastic machine breakdown and discrete delivery in an imperfect inventory-production system. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1511-1535. doi: 10.3934/jimo.2017005

[4]

Chao Xu, Yinghui Dong, Zhaolu Tian, Guojing Wang. Pricing dynamic fund protection under a Regime-switching Jump-diffusion model with stochastic protection level. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-21. doi: 10.3934/jimo.2019072

[5]

Pedro Piñeyro, Omar Viera. Inventory policies for the economic lot-sizing problem with remanufacturing and final disposal options. Journal of Industrial & Management Optimization, 2009, 5 (2) : 217-238. doi: 10.3934/jimo.2009.5.217

[6]

Nguyen Huu Du, Nguyen Thanh Dieu, Tran Dinh Tuong. Dynamic behavior of a stochastic predator-prey system under regime switching. Discrete & Continuous Dynamical Systems - B, 2017, 22 (9) : 3483-3498. doi: 10.3934/dcdsb.2017176

[7]

Haibo Jin, Long Hai, Xiaoliang Tang. An optimal maintenance strategy for multi-state systems based on a system linear integral equation and dynamic programming. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-26. doi: 10.3934/jimo.2018188

[8]

Lizhao Yan, Fei Xu, Yongzeng Lai, Mingyong Lai. Stability strategies of manufacturing-inventory systems with unknown time-varying demand. Journal of Industrial & Management Optimization, 2017, 13 (4) : 2033-2047. doi: 10.3934/jimo.2017030

[9]

Andrzej Nowakowski, Jan Sokolowski. On dual dynamic programming in shape control. Communications on Pure & Applied Analysis, 2012, 11 (6) : 2473-2485. doi: 10.3934/cpaa.2012.11.2473

[10]

Jérôme Renault. General limit value in dynamic programming. Journal of Dynamics & Games, 2014, 1 (3) : 471-484. doi: 10.3934/jdg.2014.1.471

[11]

Li Deng, Wenjie Bi, Haiying Liu, Kok Lay Teo. A multi-stage method for joint pricing and inventory model with promotion constrains. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020097

[12]

Jiang-Xia Nan, Deng-Feng Li. Linear programming technique for solving interval-valued constraint matrix games. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1059-1070. doi: 10.3934/jimo.2014.10.1059

[13]

Jean-Michel Coron, Matthias Kawski, Zhiqiang Wang. Analysis of a conservation law modeling a highly re-entrant manufacturing system. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1337-1359. doi: 10.3934/dcdsb.2010.14.1337

[14]

Amin Aalaei, Hamid Davoudpour. Two bounds for integrating the virtual dynamic cellular manufacturing problem into supply chain management. Journal of Industrial & Management Optimization, 2016, 12 (3) : 907-930. doi: 10.3934/jimo.2016.12.907

[15]

Jérome Lohéac, Jean-François Scheid. Time optimal control for a nonholonomic system with state constraint. Mathematical Control & Related Fields, 2013, 3 (2) : 185-208. doi: 10.3934/mcrf.2013.3.185

[16]

Oliver Junge, Alex Schreiber. Dynamic programming using radial basis functions. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 4439-4453. doi: 10.3934/dcds.2015.35.4439

[17]

Eduardo Espinosa-Avila, Pablo Padilla Longoria, Francisco Hernández-Quiroz. Game theory and dynamic programming in alternate games. Journal of Dynamics & Games, 2017, 4 (3) : 205-216. doi: 10.3934/jdg.2017013

[18]

Rein Luus. Optimal control of oscillatory systems by iterative dynamic programming. Journal of Industrial & Management Optimization, 2008, 4 (1) : 1-15. doi: 10.3934/jimo.2008.4.1

[19]

Qing Liu, Armin Schikorra. General existence of solutions to dynamic programming equations. Communications on Pure & Applied Analysis, 2015, 14 (1) : 167-184. doi: 10.3934/cpaa.2015.14.167

[20]

Rhoda P. Agdeppa, Nobuo Yamashita, Masao Fukushima. An implicit programming approach for the road pricing problem with nonadditive route costs. Journal of Industrial & Management Optimization, 2008, 4 (1) : 183-197. doi: 10.3934/jimo.2008.4.183

2018 Impact Factor: 1.025

Metrics

  • PDF downloads (11)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]