# American Institute of Mathematical Sciences

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 and 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), 222-232. doi: 10.1016/j.ijpe.2011.08.007. [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), 407-420. [3] S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, Cambridge, 2004. doi: 10.1017/CBO9780511804441. [4] R. Dekker, M. Fleischmann, K. Inderfurth and L. N. V. Wassenhove, Reverse Logistics: Quantitative Models for Closed-Loop Supply Chains, Springer-Verlag, Heidelberg, 2004. [5] I. Dobos and K. Richter, A production/recycling model with stationary demand and return rates, Cent Eur. J Oper. Res., 11 (2003), 35-46. [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), 1-17. [7] M. R. Galbreth and J. D. Blackburn, Optimal acquisition and sorting policies for remanufacturing, Prod. Oper. Manag., 15 (2006), 384-392. [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), 3779-3800. [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), 303-316. [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), 1161-1183. doi: 10.1016/j.jom.2007.01.017. [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), 55-63. [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), 73-87. doi: 10.1016/S0925-5273(00)00080-3. [13] F. Hillier and J. Lieberman, Introduction to Operations Research, $4^{nd}$ Edition, Holden-Day, Oakland, California, 1986. [14] E. L. Porteus, Foundation of Stochastic Inventory Theory, Stanford University Press, Palo Alto, California, 2002. [15] S. M. Ross, Introduction to Stochastic Dynamic Programming, Academic Press, New York, 1983. [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), 933-947. doi: 10.1007/s00170-013-4954-5. [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), 6978-6998. [18] X. Zhou and Y. Yu, Optimal product acquisition, pricing, and inventory management for systems with remanufacturing, Oper. Res., 59 (2011), 514-521. doi: 10.1287/opre.1100.0898.

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), 222-232. doi: 10.1016/j.ijpe.2011.08.007. [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), 407-420. [3] S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, Cambridge, 2004. doi: 10.1017/CBO9780511804441. [4] R. Dekker, M. Fleischmann, K. Inderfurth and L. N. V. Wassenhove, Reverse Logistics: Quantitative Models for Closed-Loop Supply Chains, Springer-Verlag, Heidelberg, 2004. [5] I. Dobos and K. Richter, A production/recycling model with stationary demand and return rates, Cent Eur. J Oper. Res., 11 (2003), 35-46. [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), 1-17. [7] M. R. Galbreth and J. D. Blackburn, Optimal acquisition and sorting policies for remanufacturing, Prod. Oper. Manag., 15 (2006), 384-392. [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), 3779-3800. [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), 303-316. [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), 1161-1183. doi: 10.1016/j.jom.2007.01.017. [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), 55-63. [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), 73-87. doi: 10.1016/S0925-5273(00)00080-3. [13] F. Hillier and J. Lieberman, Introduction to Operations Research, $4^{nd}$ Edition, Holden-Day, Oakland, California, 1986. [14] E. L. Porteus, Foundation of Stochastic Inventory Theory, Stanford University Press, Palo Alto, California, 2002. [15] S. M. Ross, Introduction to Stochastic Dynamic Programming, Academic Press, New York, 1983. [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), 933-947. doi: 10.1007/s00170-013-4954-5. [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), 6978-6998. [18] X. Zhou and Y. Yu, Optimal product acquisition, pricing, and inventory management for systems with remanufacturing, Oper. Res., 59 (2011), 514-521. doi: 10.1287/opre.1100.0898.
 [1] Mahdi Karimi, Seyed Jafar Sadjadi. Optimization of a Multi-Item Inventory model for deteriorating items with capacity constraint using dynamic programming. Journal of Industrial and Management Optimization, 2022, 18 (2) : 1145-1160. doi: 10.3934/jimo.2021013 [2] Kai Li, Yan Li, Jing Liu, Nenggui Zhao. Two-sided vertical competition considering product quality in a manufacturing-remanufacturing system. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021187 [3] Md Sadikur Rahman, Subhajit Das, Amalesh Kumar Manna, Ali Akbar Shaikh, Asoke Kumar Bhunia, Ali Ahmadian, Soheil Salahshour. A new approach based on inventory control using interval differential equation with application to manufacturing system. Discrete and Continuous Dynamical Systems - S, 2022, 15 (2) : 457-480. doi: 10.3934/dcdss.2021117 [4] Hassen Aydi, Ayman Kachmar. Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint. II. Communications on Pure and Applied Analysis, 2009, 8 (3) : 977-998. doi: 10.3934/cpaa.2009.8.977 [5] Jing Zhao, Jie Wei, Yongjian Li. Pricing and remanufacturing decisions for two substitutable products with a common retailer. Journal of Industrial and Management Optimization, 2017, 13 (2) : 1125-1147. doi: 10.3934/jimo.2016065 [6] Ata Allah Taleizadeh, Hadi Samimi, Biswajit Sarkar, Babak Mohammadi. Stochastic machine breakdown and discrete delivery in an imperfect inventory-production system. Journal of Industrial and Management Optimization, 2017, 13 (3) : 1511-1535. doi: 10.3934/jimo.2017005 [7] Yongjian Wang, Fei Wang. Effects of the carbon credits buy-back policy on manufacturing/remanufacturing decisions of the capital-constrained manufacturer. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021198 [8] 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 and Management Optimization, 2020, 16 (6) : 2603-2623. doi: 10.3934/jimo.2019072 [9] Benrong Zheng, Xianpei Hong. Effects of take-back legislation on pricing and coordination in a closed-loop supply chain. Journal of Industrial and Management Optimization, 2022, 18 (3) : 1603-1627. doi: 10.3934/jimo.2021035 [10] Pedro Piñeyro, Omar Viera. Inventory policies for the economic lot-sizing problem with remanufacturing and final disposal options. Journal of Industrial and Management Optimization, 2009, 5 (2) : 217-238. doi: 10.3934/jimo.2009.5.217 [11] Yanhua Feng, Xuhui Xia, Lei Wang, Zelin Zhang. Pricing and coordination of competitive recycling and remanufacturing supply chain considering the quality of recycled products. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021089 [12] 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 and Management Optimization, 2020, 16 (2) : 965-990. doi: 10.3934/jimo.2018188 [13] Nguyen Huu Du, Nguyen Thanh Dieu, Tran Dinh Tuong. Dynamic behavior of a stochastic predator-prey system under regime switching. Discrete and Continuous Dynamical Systems - B, 2017, 22 (9) : 3483-3498. doi: 10.3934/dcdsb.2017176 [14] Andrzej Nowakowski, Jan Sokolowski. On dual dynamic programming in shape control. Communications on Pure and Applied Analysis, 2012, 11 (6) : 2473-2485. doi: 10.3934/cpaa.2012.11.2473 [15] Jérôme Renault. General limit value in dynamic programming. Journal of Dynamics and Games, 2014, 1 (3) : 471-484. doi: 10.3934/jdg.2014.1.471 [16] Lizhao Yan, Fei Xu, Yongzeng Lai, Mingyong Lai. Stability strategies of manufacturing-inventory systems with unknown time-varying demand. Journal of Industrial and Management Optimization, 2017, 13 (4) : 2033-2047. doi: 10.3934/jimo.2017030 [17] Jiang-Xia Nan, Deng-Feng Li. Linear programming technique for solving interval-valued constraint matrix games. Journal of Industrial and Management Optimization, 2014, 10 (4) : 1059-1070. doi: 10.3934/jimo.2014.10.1059 [18] Li Deng, Wenjie Bi, Haiying Liu, Kok Lay Teo. A multi-stage method for joint pricing and inventory model with promotion constrains. Discrete and Continuous Dynamical Systems - S, 2020, 13 (6) : 1653-1682. doi: 10.3934/dcdss.2020097 [19] Jean-Michel Coron, Matthias Kawski, Zhiqiang Wang. Analysis of a conservation law modeling a highly re-entrant manufacturing system. Discrete and Continuous Dynamical Systems - B, 2010, 14 (4) : 1337-1359. doi: 10.3934/dcdsb.2010.14.1337 [20] Jérome Lohéac, Jean-François Scheid. Time optimal control for a nonholonomic system with state constraint. Mathematical Control and Related Fields, 2013, 3 (2) : 185-208. doi: 10.3934/mcrf.2013.3.185

2020 Impact Factor: 1.801