# American Institute of Mathematical Sciences

October  2015, 11(4): 1041-1058. doi: 10.3934/jimo.2015.11.1041

## Production planning in a three-stock reverse-logistics system with deteriorating items under a continuous review policy

 1 Industrial Engineering Department, College of Engineering, King Saud University, P.O Box 800, Riyadh 11421, Saudi Arabia 2 Fairleigh Dickinson University, Silberman College of Business, Department of Information Systems and Decision Sciences, 842 Cambie Street, Vancouver, BC, V6B 2P6, Canada

Received  November 2013 Revised  August 2014 Published  March 2015

We consider in this paper a reverse supply chain with three stocks. Newly manufactured items are stored in the first stock. The second stock is reserved for remanufactured items, while the third stock contains the items that are returned from the market. One of our main assumptions is that remanufactured items are not as-good-as-new. We also assume that new and remanufactured items are subject to deterioration and to dynamic demands, that customer return rate is also dynamic, and that the firm adopts a continuous-review policy. Using optimal control theory, we obtain the explicit expressions of the optimal manufacturing rate, remanufacturing rate, disposal rate, and inventory levels in all three stocks. Numerical examples and sensitivity analyses illustrate the results obtained.
Citation: Abdelghani Bouras, Lotfi Tadj. Production planning in a three-stock reverse-logistics system with deteriorating items under a continuous review policy. Journal of Industrial and Management Optimization, 2015, 11 (4) : 1041-1058. doi: 10.3934/jimo.2015.11.1041
##### References:
 [1] J. Aitken and A. Harrison, Supply governance structures for reverse logistics systems, International Journal of Operations & Production Management, 33 (2013), 745-764. [2] A. A. Al-Babtain, Optimal control of reverse logistics model with logistic demand and return rates, Applied Mathematical Sciences, 4 (2010), 2561-2568. [3] A. Alshamrani, Adaptive control of a reverse logistic inventory model with uncertain deteriorations and disposal rates, Advances in Operations Research, 1-11. [4] W. Bei and S. Linyan, A review of reverse logistics, Applied Sciences (APPS), 7 (2005), 16-29. [5] D. F. Blumberg, Introduction to Management of Reverse Logistics and Closed Loop Supply Chain Processes, CRC Press, 2004. [6] T. Clottey, W. C. Benton and R. Srivastava, Forecasting product returns for remanufacturing operations, Decision Sciences, 43 (2012), 589-614. [7] M. P. De Brito, Managing Reverse Logistics or Reversing Logistics Management?, ERIM PhD Series; EPS-2004-035-LIS, Erasmus Research Institute of Management (ERIM), 2004. [8] M. P. De Brito, S. D. P. Flapper and R. Dekker, Reverse logistics, Econometric Institute Research Papers. [9] R. Dekker, M. Fleischmann, K. Inderfurth and L. N. Van Wassenhove (eds.), Reverse Logistics. Quantitative Models in Closed-Loop Supply Chains, Springer-Verlag, Berlin, 2004. [10] I. Dobos, Optimal production-inventory strategies for a HMMS-type reverse logistics system, International Journal of Production Economics, 81 (2003), 351-360. [11] I. Dobos, Készletmodellek a visszutas logisztikában= Inventory Models in Reverse Logistics, PhD thesis, Budapesti Corvinus Egyetem, 2007. [12] H. Dyckhoff, R. Lackes and J. Reese, Supply Chain Management and Reverse Logistics, Springer, 2004. [13] A. M. A. El Saadany, Inventory Management in Reverse Logistics with Imperfect Production, Learning, Lost Sales, Subassemblies, and Price/Quality Considerations, PhD thesis, Mechanical Engineering, Ryerson University, Toronto, Canada, 2009. [14] L. Feng, J. Zhang and W. Tang, Optimal control of production and remanufacturing for a recovery system with perishable items, International Journal of Production Research, 51 (2013), 3177-3994. [15] O. S. S. Filho, Suboptimal production planning policies for closed-loop system with uncertain levels of demand and return, in Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011. [16] S. D. P. Flapper and T. S. Spengler (eds.) , Product recovery, Special issue of OR Spectrum, 28 (2006), 53-71. [17] S. D. P. Flapper, J. E. E. Van Nunen and L. N. Van Wassenhove, Managing Closed-Loop Supply Chain, Springer, Berlin, 2005. [18] M. Fleischmann, Quantitative Models for Reverse Logistics, PhD thesis, Erasmus University Rotterdam, the Netherlands, 2000. [19] A. Foul, An advertising inventory system with product recovery, International Mathematical Forum, 5 (2010), 125-138. [20] A. Foul, A. Al-Gohary and A. Essayed, Optimal control of HMMS-model with deteriorating items, International Mathematical Forum, 4 (2009), 1515-1528. [21] A. Foul and L. Tadj, Optimal control of a hybrid periodic-review production inventory system with disposal, International Journal of Operational Research, 2 (2007), 481-494. doi: 10.1504/IJOR.2007.014175. [22] A. Gharbi, R. Pellerin and J. Sadr, Production rate control for stochastic remanufacturing systems, International Journal of Production Economics, 112 (2008), 37-47. [23] M. Gharote, Inventory Models for Reverse Logistics, Master's thesis, Industrial Engineering and Operations Research, Indian Institute of Technology Bombay, India, 2004. [24] V. D. R. Guide and L. N. Van Wassenhove, Business Aspects of Closed-Loop Supply Chains, vol. 2, Carnegie Mellon University Press Pittsburgh, PA, 2003. [25] V. D. R. Guide and L. N. Van Wassenhove, Or forum-the evolution of closed-loop supply chain research, Operations Research, 57 (2009), 10-18. [26] V. D. R. Guide, T. P. Harrison and L. N. Van Wassenhove, The challenge of closed-loop supply chains, Interfaces, 33 (2003), 3-6. [27] A. Gunasekaran and T. C. E. Cheng (eds.), New perspectives and challenges, Special Issue of Omega, 36, Issue 4. [28] R. Hedjar, M. Bounkhel and L. Tadj, Receding horizon control of a hybrid production system with deteriorating items, Nonlinear Analysis: Theory, Methods & Applications, 63 (2005), 405-422. doi: 10.1016/j.na.2005.05.027. [29] M. Y. Jaber and A. El Saadany, The production, remanufacture and waste disposal model with lost sales, International Journal of Production Economics, 120 (2009), 115-124. [30] V. Jain (ed.), Sustainable supply chain management and reverse logistics, Special Issue of International Journal of Production Research, 50, issue 5. [31] P. Jie, Production Planning and Inventory Control of Two-Product Recovery System in Reverse Logistics, PhD thesis, Department of Industrial and Systems Engineering, National University of Singapore, Singapore, 2010. [32] Jonrinaldi, Modelling of Coordinating Production and Inventory Cycles in a Manufacturing Supply Chain Involving Reverse Logistics, PhD thesis, University of Exeter, South West England, 2012. [33] M. L. Junior and M. G. Filho, Production planning and control for remanufacturing: Literature review and analysis, Production Planning & Control, 23 (2012), 419-435. [34] D. Kannan, A. Diabat, M. Alrefaei, K. Govindand and G. Yonge, A carbon footprint based reverse logistics network design model, Resources, Conservation and Recycling, 67 (2012), 75-79. [35] J.-P. Kenné, P. Dejax and A. Gharbi, Production planning of a hybrid manufacturing-remanufacturing system under uncertainty within a closed-loop supply chain, International Journal of Production Economics, 135 (2012), 81-93. [36] W. Kerr and C. Ryan, Eco-efficiency gains from remanufacturing. a case study of photocopier remanufacturing at fuji xerox australia, Journal of Cleaner Production, 9 (2001), 75-81. [37] G. P. Kiesmüller, A new approach for controlling a hybrid stochastic manufacturing/remanufacturing system with inventories and different leadtimes, European Journal of Operational Research, 147 (2003), 62-71. [38] G. P. Kiesmüller, Optimal control of a one product recovery system with leadtimes, International Journal of Production Economics, 81 (2003), 333-340. [39] G. P. Kiesmüller and C. W. Scherer, Computational issues in a stochastic finite horizon one product recovery inventory model, European Journal of Operational Research, 146 (2003), 553-579. doi: 10.1016/S0377-2217(02)00249-7. [40] G. P. Kiesmüller, S. Minner and R. Kleber, Optimal control of a one product recovery system with backlogging, IMA Journal of applied mathematics in business and industry, 11 (2000), 189-207. [41] M. Klausner, W. M. Grimm and C. Hendrickson, Reuse of electric motors in consumer products, Journal of Industrial Ecology, 2 (1998), 89-102. [42] R. Kleber, The integral decision on production/remanufacturing technology and investment time in product recovery, OR spectrum, 28 (2006), 21-51. doi: 10.1007/s00291-005-0011-6. [43] R. Kleber, S. Minner and G. P. Kiesmüller, A continuous time inventory model for a product recovery system with multiple options, International Journal of Production Economics, 79 (2002), 121-141. [44] A. Langevin and D. Riopel (eds.), Logistics Systems: Design and Optimization, Springer, Berlin, 2005. doi: 10.1007/b106452. [45] Y. Li, J. Zhang, J. Chen and X. Cai, Optimal solution structure for multi-period production planning with returned products remanufacturing, Asia-Pacific Journal of Operational Research, 27 (2010), 629-648. doi: 10.1142/S0217595910002910. [46] L. L. Lim, Optimal Control of a Hybrid Production/Remanufacturing System Using one Shared Resource, Master's thesis, Industrial Engineering and Innovation Sciences Department, Eindhoven University of Technology, Eindhoven, the Netherlands and Industrial Engineering School, Grenoble Institute of Technology, Grenoble, France, 2008. [47] F. Liu, Reverse Logistics Matters: Impact of Resource Commitment on Reverse Logistics and Customer Loyalty, Master's thesis, Faculty of Business Administration, University of Maastricht, Maastricht, the Netherlands, 2010. [48] Y. Lu, Optimal Acquisition and Sorting Policies for Remanufacturing Over Single and Multiple Periods, Master's thesis, Department of Mechanical and Industrial Engineering, University of Massachusetts Amherst, Amherst, Massachusetts, 2009. [49] S. Minner and G. P. Kiesmüller, Dynamic product acquisition in closed loop supply chains, International Journal of Production Research, 50 (2012), 2836-2851. [50] S. Minner and R. Kleber, Optimal control of production and remanufacturing in a simple recovery model with linear cost functions, OR Spektrum, 23 (2001), 3-24. doi: 10.1007/PL00013344. [51] R. Montemanni (ed.), Optimization methods in logistics, Special Issue of Journal of Applied Operational Research. [52] S. D. Morgan and R. J. Gagnon, A systematic literature review of remanufacturing scheduling, International Journal of Production Research, 51 (2013), 4853-4879. [53] K. Nakashima, H. Arimitsu, T. Nose and S. Kuriyama, Optimal control of a remanufacturing system, International Journal of Production Research, 42 (2004), 3619-3625. [54] N. A. Nik Ab Halim, Y. Sabariah and A. Haim Hilman, Reverse logistics adoption among malaysian manufacturers, in International Conference on Management, Economics and Social Sciences (ICMESS'2011) Bangkok Dec., 2011. [55] M. Olovsson and L. Khalil, Reverse Logistics Study at Volvo CE CST Europe, Master's thesis, Mälardalen University, Västeras, Sweden, 2008. [56] R. Pellerin, J. Sadr, A. Gharbi and R. Malhamé, A production rate control policy for stochastic repair and remanufacturing systems, International Journal of Production Economics, 121 (2009), 39-48. [57] L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, John Wiley & Sons, New York, NY, 1962. [58] C. Prahinski and C. Kocabasoglu, Empirical research opportunities in reverse supply chains, Omega, 34 (2006), 519-532. [59] M. Préjean, Half-soles, kettles and cures: Milestones in the tire retreading and repairing industry, American Retreaders' Association, Louisville, KY. [60] D. S. Rogers, R. S. Tibben-Lembke and Council and R. L. Executive, Going Backwards: Reverse Logistics Trends and Practices, vol. 2, Reverse Logistics Executive Council Pittsburgh, PA, 1999. [61] B. S. Sahay (ed.), 3PL, 4PL and Reverse Logistics, Part 2, Special issues on in the International Journal of Physical Distribution and Logistics Management, 36, issue 7. [62] B. S. Sahay (ed.), 3PL, 4PL and Reverse Logistics, Part 1, Special issues on in the International Journal of Physical Distribution and Logistics Management, 36, issue 9. [63] J. Sarkis (ed.), Greening the Supply Chain, Springer, 2006. [64] P. S. Sethi and G. L. Thompson, Optimal Control Theory: Applications to Management Science and Economics, 2nd ed., Kluwer Academic Publishers, Boston, MA, 2000. [65] D. W. Steeneck and S. C. Sarin, Pricing and production planning for reverse supply chain: A review, International Journal of Production Research, 51 (2013), 6972-6989. [66] L. Van Stek, Using Reverse Logistics for Failed Spare Parts: A New Opportunity for Vanderlande Industries, Master's thesis, Industrial Engineering and Management, University of Twente, Enschede, Netherlands, 2012. [67] V. Verter and T. Boyaci (eds.), Reverse logistics, Special Issue of Computers & Operations Research, 34, issue 2. [68] J. Wan, Roles of Postponement in Supply Chain Strategies, PhD thesis, University of Cambridge, Cambridge, England, 2009. [69] Z. Y. Wang, Integration of Reverse Logistics within New Product Design: The Cases study in Chinese Electric and Electronic Equipment (EEE) Industry, Master's thesis, Department of Industrial Engineering and Operations Management, University of Nottingham, Nottingham, England., 2008. [70] H. Zerhouni, Intégration des Flux Inverses dans la Gestion des Stocks et de la Production}, PhD thesis, Institut National Polytechnique de Grenoble, France, 2009.

show all references

##### References:
 [1] J. Aitken and A. Harrison, Supply governance structures for reverse logistics systems, International Journal of Operations & Production Management, 33 (2013), 745-764. [2] A. A. Al-Babtain, Optimal control of reverse logistics model with logistic demand and return rates, Applied Mathematical Sciences, 4 (2010), 2561-2568. [3] A. Alshamrani, Adaptive control of a reverse logistic inventory model with uncertain deteriorations and disposal rates, Advances in Operations Research, 1-11. [4] W. Bei and S. Linyan, A review of reverse logistics, Applied Sciences (APPS), 7 (2005), 16-29. [5] D. F. Blumberg, Introduction to Management of Reverse Logistics and Closed Loop Supply Chain Processes, CRC Press, 2004. [6] T. Clottey, W. C. Benton and R. Srivastava, Forecasting product returns for remanufacturing operations, Decision Sciences, 43 (2012), 589-614. [7] M. P. De Brito, Managing Reverse Logistics or Reversing Logistics Management?, ERIM PhD Series; EPS-2004-035-LIS, Erasmus Research Institute of Management (ERIM), 2004. [8] M. P. De Brito, S. D. P. Flapper and R. Dekker, Reverse logistics, Econometric Institute Research Papers. [9] R. Dekker, M. Fleischmann, K. Inderfurth and L. N. Van Wassenhove (eds.), Reverse Logistics. Quantitative Models in Closed-Loop Supply Chains, Springer-Verlag, Berlin, 2004. [10] I. Dobos, Optimal production-inventory strategies for a HMMS-type reverse logistics system, International Journal of Production Economics, 81 (2003), 351-360. [11] I. Dobos, Készletmodellek a visszutas logisztikában= Inventory Models in Reverse Logistics, PhD thesis, Budapesti Corvinus Egyetem, 2007. [12] H. Dyckhoff, R. Lackes and J. Reese, Supply Chain Management and Reverse Logistics, Springer, 2004. [13] A. M. A. El Saadany, Inventory Management in Reverse Logistics with Imperfect Production, Learning, Lost Sales, Subassemblies, and Price/Quality Considerations, PhD thesis, Mechanical Engineering, Ryerson University, Toronto, Canada, 2009. [14] L. Feng, J. Zhang and W. Tang, Optimal control of production and remanufacturing for a recovery system with perishable items, International Journal of Production Research, 51 (2013), 3177-3994. [15] O. S. S. Filho, Suboptimal production planning policies for closed-loop system with uncertain levels of demand and return, in Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011. [16] S. D. P. Flapper and T. S. Spengler (eds.) , Product recovery, Special issue of OR Spectrum, 28 (2006), 53-71. [17] S. D. P. Flapper, J. E. E. Van Nunen and L. N. Van Wassenhove, Managing Closed-Loop Supply Chain, Springer, Berlin, 2005. [18] M. Fleischmann, Quantitative Models for Reverse Logistics, PhD thesis, Erasmus University Rotterdam, the Netherlands, 2000. [19] A. Foul, An advertising inventory system with product recovery, International Mathematical Forum, 5 (2010), 125-138. [20] A. Foul, A. Al-Gohary and A. Essayed, Optimal control of HMMS-model with deteriorating items, International Mathematical Forum, 4 (2009), 1515-1528. [21] A. Foul and L. Tadj, Optimal control of a hybrid periodic-review production inventory system with disposal, International Journal of Operational Research, 2 (2007), 481-494. doi: 10.1504/IJOR.2007.014175. [22] A. Gharbi, R. Pellerin and J. Sadr, Production rate control for stochastic remanufacturing systems, International Journal of Production Economics, 112 (2008), 37-47. [23] M. Gharote, Inventory Models for Reverse Logistics, Master's thesis, Industrial Engineering and Operations Research, Indian Institute of Technology Bombay, India, 2004. [24] V. D. R. Guide and L. N. Van Wassenhove, Business Aspects of Closed-Loop Supply Chains, vol. 2, Carnegie Mellon University Press Pittsburgh, PA, 2003. [25] V. D. R. Guide and L. N. Van Wassenhove, Or forum-the evolution of closed-loop supply chain research, Operations Research, 57 (2009), 10-18. [26] V. D. R. Guide, T. P. Harrison and L. N. Van Wassenhove, The challenge of closed-loop supply chains, Interfaces, 33 (2003), 3-6. [27] A. Gunasekaran and T. C. E. Cheng (eds.), New perspectives and challenges, Special Issue of Omega, 36, Issue 4. [28] R. Hedjar, M. Bounkhel and L. Tadj, Receding horizon control of a hybrid production system with deteriorating items, Nonlinear Analysis: Theory, Methods & Applications, 63 (2005), 405-422. doi: 10.1016/j.na.2005.05.027. [29] M. Y. Jaber and A. El Saadany, The production, remanufacture and waste disposal model with lost sales, International Journal of Production Economics, 120 (2009), 115-124. [30] V. Jain (ed.), Sustainable supply chain management and reverse logistics, Special Issue of International Journal of Production Research, 50, issue 5. [31] P. Jie, Production Planning and Inventory Control of Two-Product Recovery System in Reverse Logistics, PhD thesis, Department of Industrial and Systems Engineering, National University of Singapore, Singapore, 2010. [32] Jonrinaldi, Modelling of Coordinating Production and Inventory Cycles in a Manufacturing Supply Chain Involving Reverse Logistics, PhD thesis, University of Exeter, South West England, 2012. [33] M. L. Junior and M. G. Filho, Production planning and control for remanufacturing: Literature review and analysis, Production Planning & Control, 23 (2012), 419-435. [34] D. Kannan, A. Diabat, M. Alrefaei, K. Govindand and G. Yonge, A carbon footprint based reverse logistics network design model, Resources, Conservation and Recycling, 67 (2012), 75-79. [35] J.-P. Kenné, P. Dejax and A. Gharbi, Production planning of a hybrid manufacturing-remanufacturing system under uncertainty within a closed-loop supply chain, International Journal of Production Economics, 135 (2012), 81-93. [36] W. Kerr and C. Ryan, Eco-efficiency gains from remanufacturing. a case study of photocopier remanufacturing at fuji xerox australia, Journal of Cleaner Production, 9 (2001), 75-81. [37] G. P. Kiesmüller, A new approach for controlling a hybrid stochastic manufacturing/remanufacturing system with inventories and different leadtimes, European Journal of Operational Research, 147 (2003), 62-71. [38] G. P. Kiesmüller, Optimal control of a one product recovery system with leadtimes, International Journal of Production Economics, 81 (2003), 333-340. [39] G. P. Kiesmüller and C. W. Scherer, Computational issues in a stochastic finite horizon one product recovery inventory model, European Journal of Operational Research, 146 (2003), 553-579. doi: 10.1016/S0377-2217(02)00249-7. [40] G. P. Kiesmüller, S. Minner and R. Kleber, Optimal control of a one product recovery system with backlogging, IMA Journal of applied mathematics in business and industry, 11 (2000), 189-207. [41] M. Klausner, W. M. Grimm and C. Hendrickson, Reuse of electric motors in consumer products, Journal of Industrial Ecology, 2 (1998), 89-102. [42] R. Kleber, The integral decision on production/remanufacturing technology and investment time in product recovery, OR spectrum, 28 (2006), 21-51. doi: 10.1007/s00291-005-0011-6. [43] R. Kleber, S. Minner and G. P. Kiesmüller, A continuous time inventory model for a product recovery system with multiple options, International Journal of Production Economics, 79 (2002), 121-141. [44] A. Langevin and D. Riopel (eds.), Logistics Systems: Design and Optimization, Springer, Berlin, 2005. doi: 10.1007/b106452. [45] Y. Li, J. Zhang, J. Chen and X. Cai, Optimal solution structure for multi-period production planning with returned products remanufacturing, Asia-Pacific Journal of Operational Research, 27 (2010), 629-648. doi: 10.1142/S0217595910002910. [46] L. L. Lim, Optimal Control of a Hybrid Production/Remanufacturing System Using one Shared Resource, Master's thesis, Industrial Engineering and Innovation Sciences Department, Eindhoven University of Technology, Eindhoven, the Netherlands and Industrial Engineering School, Grenoble Institute of Technology, Grenoble, France, 2008. [47] F. Liu, Reverse Logistics Matters: Impact of Resource Commitment on Reverse Logistics and Customer Loyalty, Master's thesis, Faculty of Business Administration, University of Maastricht, Maastricht, the Netherlands, 2010. [48] Y. Lu, Optimal Acquisition and Sorting Policies for Remanufacturing Over Single and Multiple Periods, Master's thesis, Department of Mechanical and Industrial Engineering, University of Massachusetts Amherst, Amherst, Massachusetts, 2009. [49] S. Minner and G. P. Kiesmüller, Dynamic product acquisition in closed loop supply chains, International Journal of Production Research, 50 (2012), 2836-2851. [50] S. Minner and R. Kleber, Optimal control of production and remanufacturing in a simple recovery model with linear cost functions, OR Spektrum, 23 (2001), 3-24. doi: 10.1007/PL00013344. [51] R. Montemanni (ed.), Optimization methods in logistics, Special Issue of Journal of Applied Operational Research. [52] S. D. Morgan and R. J. Gagnon, A systematic literature review of remanufacturing scheduling, International Journal of Production Research, 51 (2013), 4853-4879. [53] K. Nakashima, H. Arimitsu, T. Nose and S. Kuriyama, Optimal control of a remanufacturing system, International Journal of Production Research, 42 (2004), 3619-3625. [54] N. A. Nik Ab Halim, Y. Sabariah and A. Haim Hilman, Reverse logistics adoption among malaysian manufacturers, in International Conference on Management, Economics and Social Sciences (ICMESS'2011) Bangkok Dec., 2011. [55] M. Olovsson and L. Khalil, Reverse Logistics Study at Volvo CE CST Europe, Master's thesis, Mälardalen University, Västeras, Sweden, 2008. [56] R. Pellerin, J. Sadr, A. Gharbi and R. Malhamé, A production rate control policy for stochastic repair and remanufacturing systems, International Journal of Production Economics, 121 (2009), 39-48. [57] L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, John Wiley & Sons, New York, NY, 1962. [58] C. Prahinski and C. Kocabasoglu, Empirical research opportunities in reverse supply chains, Omega, 34 (2006), 519-532. [59] M. Préjean, Half-soles, kettles and cures: Milestones in the tire retreading and repairing industry, American Retreaders' Association, Louisville, KY. [60] D. S. Rogers, R. S. Tibben-Lembke and Council and R. L. Executive, Going Backwards: Reverse Logistics Trends and Practices, vol. 2, Reverse Logistics Executive Council Pittsburgh, PA, 1999. [61] B. S. Sahay (ed.), 3PL, 4PL and Reverse Logistics, Part 2, Special issues on in the International Journal of Physical Distribution and Logistics Management, 36, issue 7. [62] B. S. Sahay (ed.), 3PL, 4PL and Reverse Logistics, Part 1, Special issues on in the International Journal of Physical Distribution and Logistics Management, 36, issue 9. [63] J. Sarkis (ed.), Greening the Supply Chain, Springer, 2006. [64] P. S. Sethi and G. L. Thompson, Optimal Control Theory: Applications to Management Science and Economics, 2nd ed., Kluwer Academic Publishers, Boston, MA, 2000. [65] D. W. Steeneck and S. C. Sarin, Pricing and production planning for reverse supply chain: A review, International Journal of Production Research, 51 (2013), 6972-6989. [66] L. Van Stek, Using Reverse Logistics for Failed Spare Parts: A New Opportunity for Vanderlande Industries, Master's thesis, Industrial Engineering and Management, University of Twente, Enschede, Netherlands, 2012. [67] V. Verter and T. Boyaci (eds.), Reverse logistics, Special Issue of Computers & Operations Research, 34, issue 2. [68] J. Wan, Roles of Postponement in Supply Chain Strategies, PhD thesis, University of Cambridge, Cambridge, England, 2009. [69] Z. Y. Wang, Integration of Reverse Logistics within New Product Design: The Cases study in Chinese Electric and Electronic Equipment (EEE) Industry, Master's thesis, Department of Industrial Engineering and Operations Management, University of Nottingham, Nottingham, England., 2008. [70] H. Zerhouni, Intégration des Flux Inverses dans la Gestion des Stocks et de la Production}, PhD thesis, Institut National Polytechnique de Grenoble, France, 2009.
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