American Institute of Mathematical Sciences

Advanced
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

Xiaochen Sun 1, , Fei Hu 1, , Yancong Zhou 2, and  Cheng-Chew Lim 3,

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.
Keywords: legislation constraint., stochastic dynamic programming, Inventory, acquisition pricing, manufacturing and remanufacturing system.
Mathematics Subject Classification: Primary: 90B05, 90B30; Secondary: 93E2.
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]

Ardeshir Ahmadi, Hamed Davari-Ardakani. A multistage stochastic programming framework for cardinality constrained portfolio optimization. Numerical Algebra, Control & Optimization, 2017, 7 (3) : 359-377. doi: 10.3934/naco.2017023
[2]

Ziteng Wang, Shu-Cherng Fang, Wenxun Xing. On constraint qualifications: Motivation, design and inter-relations. Journal of Industrial & Management Optimization, 2013, 9 (4) : 983-1001. doi: 10.3934/jimo.2013.9.983
[3]

Alexandr Mikhaylov, Victor Mikhaylov. Dynamic inverse problem for Jacobi matrices. Inverse Problems & Imaging, 2019, 13 (3) : 431-447. doi: 10.3934/ipi.2019021
[4]

Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev. Linear programming solutions of periodic optimization problems: approximation of the optimal control. Journal of Industrial & Management Optimization, 2007, 3 (2) : 399-413. doi: 10.3934/jimo.2007.3.399
[5]

Simone Cacace, Maurizio Falcone. A dynamic domain decomposition for the eikonal-diffusion equation. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 109-123. doi: 10.3934/dcdss.2016.9.109
[6]

Xianchao Xiu, Ying Yang, Wanquan Liu, Lingchen Kong, Meijuan Shang. An improved total variation regularized RPCA for moving object detection with dynamic background. Journal of Industrial & Management Optimization, 2020, 16 (4) : 1685-1698. doi: 10.3934/jimo.2019024
[7]

Yuncherl Choi, Taeyoung Ha, Jongmin Han, Sewoong Kim, Doo Seok Lee. Turing instability and dynamic phase transition for the Brusselator model with multiple critical eigenvalues. Discrete & Continuous Dynamical Systems - A, 2021  doi: 10.3934/dcds.2021035
[8]

J. Frédéric Bonnans, Justina Gianatti, Francisco J. Silva. On the convergence of the Sakawa-Shindo algorithm in stochastic control. Mathematical Control & Related Fields, 2016, 6 (3) : 391-406. doi: 10.3934/mcrf.2016008
[9]

Diana Keller. Optimal control of a linear stochastic Schrödinger equation. Conference Publications, 2013, 2013 (special) : 437-446. doi: 10.3934/proc.2013.2013.437
[10]

Seung-Yeal Ha, Dongnam Ko, Chanho Min, Xiongtao Zhang. Emergent collective behaviors of stochastic kuramoto oscillators. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 1059-1081. doi: 10.3934/dcdsb.2019208
[11]

María J. Garrido-Atienza, Bohdan Maslowski, Jana  Šnupárková. Semilinear stochastic equations with bilinear fractional noise. Discrete & Continuous Dynamical Systems - B, 2016, 21 (9) : 3075-3094. doi: 10.3934/dcdsb.2016088
[12]

M. Grasselli, V. Pata. Asymptotic behavior of a parabolic-hyperbolic system. Communications on Pure & Applied Analysis, 2004, 3 (4) : 849-881. doi: 10.3934/cpaa.2004.3.849
[13]

Elena Bonetti, Pierluigi Colli, Gianni Gilardi. Singular limit of an integrodifferential system related to the entropy balance. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 1935-1953. doi: 10.3934/dcdsb.2014.19.1935
[14]

Dmitry Treschev. A locally integrable multi-dimensional billiard system. Discrete & Continuous Dynamical Systems - A, 2017, 37 (10) : 5271-5284. doi: 10.3934/dcds.2017228
[15]

Dugan Nina, Ademir Fernando Pazoto, Lionel Rosier. Controllability of a 1-D tank containing a fluid modeled by a Boussinesq system. Evolution Equations & Control Theory, 2013, 2 (2) : 379-402. doi: 10.3934/eect.2013.2.379
[16]

Yanqin Fang, Jihui Zhang. Multiplicity of solutions for the nonlinear Schrödinger-Maxwell system. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1267-1279. doi: 10.3934/cpaa.2011.10.1267
[17]

Xu Zhang, Xiang Li. Modeling and identification of dynamical system with Genetic Regulation in batch fermentation of glycerol. Numerical Algebra, Control & Optimization, 2015, 5 (4) : 393-403. doi: 10.3934/naco.2015.5.393
[18]

Guo-Bao Zhang, Ruyun Ma, Xue-Shi Li. Traveling waves of a Lotka-Volterra strong competition system with nonlocal dispersal. Discrete & Continuous Dynamical Systems - B, 2018, 23 (2) : 587-608. doi: 10.3934/dcdsb.2018035
[19]

Nhu N. Nguyen, George Yin. Stochastic partial differential equation models for spatially dependent predator-prey equations. Discrete & Continuous Dynamical Systems - B, 2020, 25 (1) : 117-139. doi: 10.3934/dcdsb.2019175
[20]

Longxiang Fang, Narayanaswamy Balakrishnan, Wenyu Huang. Stochastic comparisons of parallel systems with scale proportional hazards components equipped with starting devices. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2021004

2019 Impact Factor: 1.366

Tools

Metrics

  • PDF downloads (68)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences