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Two-warehouse inventory model for non-instantaneous deteriorating items with stock-dependent demand and inflation using particle swarm optimization

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Abstract

We investigate a two-warehouse inventory model for non-instantaneous deteriorating items with partial backlogging and stock-dependent demand under inflationary conditions. Shortages are allowed. The backlogging rate is variable and depends on the waiting time for the next replenishment. This paper seeks to determine an optimal replenishment policy that minimizes the present value of the total cost per unit time. The necessary and sufficient conditions for the existence and uniqueness of the optimal solution are found. The corresponding problems are formulated and solved with particle swarm optimization. Numerical experimentation and post-optimality analysis are conducted.

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References

  • Bhunia, A. K., & Shaikh, A. A. (2011a). A two warehouse inventory model for deteriorating items with time dependent partial backlogging and variable demand dependent on marketing strategy and time. International Journal of Inventory Control and Management, 1, 95–110.

    Google Scholar 

  • Bhunia, A. K., & Shaikh, A. A. (2011b). A deterministic model for deteriorating items with displayed inventory level dependent demand rate incorporating marketing decisions with transportation cost. International Journal of Industrial Engineering Computations, 2, 547–562.

    Google Scholar 

  • Bhunia, A. K., Shaikh, A. A., Maiti, A. K., & Maiti, M. (2013). A two warehouse deterministic inventory model for deteriorating items with a linear trend in time dependent demand over finite time horizon by elitist real-coded genetic algorithm. International Journal Industrial Engineering and Computations, 4, 241–258.

    Article  Google Scholar 

  • Bhunia, A. K., Mahato, S. K., Shaikh, A. A., & Jaggi, C. K. (2014a). A deteriorating inventory model with displayed stock-level-dependent demand and partially backlogged shortages with all unit discount facilities via particle swarm optimization. International Journal of Systems Science: Operations and Logistics, 1(3), 164–180.

    Google Scholar 

  • Bhunia, A. K., & Shaikh, A. A. (2014b). A deterministic inventory model for deteriorating items with selling price dependent demand and three-parameter Weibull distributed deterioration. International Journal of Industrial Engineering Computations, 5, 497–510.

    Article  Google Scholar 

  • Bhunia, A. K., & Shaikh, A. A. (2015). An application of PSO in a two-warehouse inventory model for deteriorating item under permissible delay in payment with different inventory policies. Applied Mathematics and Computation, 256, 831–850.

    Article  Google Scholar 

  • Bhunia, A. K., Shaikh, A. A., & Gupta, R. K. (2015a). A study on two-warehouse partially backlogged deteriorating inventory models under inflation via particle swarm optimization. International Journal of Systems Science, 46(6), 1036–1050.

    Article  Google Scholar 

  • Bhunia, A. K., Shaikh, A. A., Pareek, S., & Dhaka, V. (2015b). A memo on stock model with partial backlogging under delay in payments. Uncertain Supply Chain Management, 3, 11–20.

    Article  Google Scholar 

  • Bhunia, A. K., Shaikh, A. A., Sharma, G., & Pareek, S. (2015c). A two storage inventory model for deteriorating items with variable demand and partial backlogging. Journal of Industrial and Production Engineering, 32(4), 263–272.

  • Bhunia, A. K., Shaikh, A. A., & Sahoo, L. (2016). A two-warehouse inventory model for deteriorating item under permissible delay in payment via particle swarm optimisation. International Journal of Logistics Systems and Management, 24(1), 45–69.

    Article  Google Scholar 

  • Cárdenas-Barrón, L. E., Chung, K. J., & Treviño-Garza, G. (2014). Celebrating a century of the economic order quantity model in honor of Ford Whitman Harris. International Journal of Production Economics, 155, 1–7.

    Article  Google Scholar 

  • Cárdenas-Barrón, L. E., & Sana, S. S. (2015). Multi-item EOQ inventory model in a two-layer supply chain while demand varies with promotional effort. Applied Mathematical Modelling, 39(21), 6725–6737.

    Article  Google Scholar 

  • Chung, C. J., & Wee, H. M. (2008). An integrated production-inventory deteriorating model for pricing policy considering imperfect production, inspection planning and warranty-period-and stock-level-dependent demand. International Journal of System Science, 39(8), 823–837.

    Article  Google Scholar 

  • Clerc, M. (1999). The swarm and queen: towards a deterministic and adaptive particle swarm optimization. In Proceedings of IEEE congress on evolutionary computation (pp. 1951–1957). Washington: DC, USA.

  • Clerc, M., & Kennedy, J. F. (2002). The particle swarm: Explosion, stability, and convergence in a multi-dimensional complex space. IEEE Transactions of Evolutionary Computing, 6, 58–73.

    Article  Google Scholar 

  • Coelho, L. S. (2010). Gaussian quantum-behaved particle swarm optimization approaches for constrained engineering design problems. Expert Systems with Applications, 37, 1676–1683.

    Article  Google Scholar 

  • Covert, R. P., & Philip, G. C. (1973). An EOQ model for items with Weibull distribution deterioration. AIIE Transactions, 5(4), 323–326.

    Article  Google Scholar 

  • Das, D., Roy, A., & Kar, S. (2015). A multi-warehouse partial backlogging inventory model for deteriorating items under inflation when a delay in payment is permissible. Annals of Operations Research, 226(1), 133–162.

    Article  Google Scholar 

  • Eberhart, R. C., & Kennedy, J. F. (1995). A new optimizer using particle swarm theory. Proceedings of the sixth international symposium on micro machine and human science (pp. 39–43). Japan: Nagoya.

  • Gao, Y., Zhang, G., Lu, J., & Wee, H. M. (2011). Particle swarm optimization for bi-level pricing problems in supply chains. Journal of Global Optimization, 51(2), 245–254.

    Article  Google Scholar 

  • Ghare, P. M., & Schrader, G. F. (1963). A model for exponentially decaying inventory. Journal of Industrial Engineering, 14(5), 238–243.

    Google Scholar 

  • Hartley, V. R. (1976). Operations research: A managerial emphasis. Santa Monica: Good Year.

    Google Scholar 

  • Jaggi, C. K., & Verma, P. (2010). An optimal replenishment policy for non-instantaneous deteriorating items with two storage facilities. International Journal of Services Operations and Informatics, 5(3), 209–230.

    Article  Google Scholar 

  • Jaggi, C. K., Pareek, S., Khanna, A., & Sharma, R. (2014a). Credit financing in a two-warehouse environment for deteriorating items with price-sensitive demand and fully backlogged shortages. Applied Mathematical Modelling, 38(21–22), 5315–5333.

    Article  Google Scholar 

  • Jaggi, C. K., & Tiwari, S. (2014b). Two warehouse inventory model for non-instantaneous deteriorating items with price dependent demand and time varying holding cost. In Om Parakash (Ed.), Mathematical Modelling and Applications (pp. 225–238). Germany: Lambert.

    Google Scholar 

  • Jaggi, C. K., Sharma, A., & Tiwari, S. (2015a). Credit financing in economic ordering policies for non-instantaneous deteriorating items with price dependent demand under permissible delay in payments: A new approach. International Journal of Industrial Engineering Computations, 6(4), 481–502.

    Article  Google Scholar 

  • Jaggi, C. K., Tiwari, S., & Shafi, A. (2015b). Effect of deterioration on two-warehouse inventory model with imperfect quality. Computers and Industrial Engineering, 88, 378–385.

    Article  Google Scholar 

  • Jaggi, C. K., Tiwari, S., & Goel, S. K. (2017a). Credit financing in economic ordering policies for non-instantaneous deteriorating items with price dependent demand and two storage facilities. Annals of Operations Research, 248(1), 253–280.

    Article  Google Scholar 

  • Jaggi, C. K., Cárdenas-Barrón, L. E., Tiwari, S., & Shafi, A. (2017b). Two-warehouse inventory model with imperfect quality items under deteriorating conditions and permissible delay in payments. Scientia Iranica, Transactions E: Industrial Engineering, 24(1), 390–412.

    Google Scholar 

  • Kennedy, J. F., & Eberhart, R. C. (1995). Particle swarm optimization. Proceedings of the IEEE international conference on neural networks (Vol. IV, pp. 1942–1948). Australia: Perth.

  • Lee, C. C. (2006). Two-warehouse inventory model with deterioration under FIFO dispatching policy. European Journal of Operational Research, 174(2), 861–873.

    Article  Google Scholar 

  • Lo, S. T., Wee, H. M., & Huang, W. C. (2007). An integrated production-inventory model with imperfect production processes and Weibull distribution deterioration under inflation. International Journal of Production Economics, 106(1), 248–260.

    Article  Google Scholar 

  • Ouyang, L. Y., Wu, K. S., & Yang, C. T. (2006). A study on an inventory model for non-instantaneous deteriorating items with permissible delay in payments. Computers and Industrial Engineering, 51(4), 637–651.

    Article  Google Scholar 

  • Ouyang, L. Y., Wu, K. S., & Yang, C. T. (2008). Retailer’s ordering policy for non-instantaneous deteriorating items with quantity discount, stock dependent demand and stochastic backorder rate. Journal of the Chinese Institute of Industrial Engineers, 25(1), 62–72.

    Article  Google Scholar 

  • Pal, P., Das, C. B., Panda, A., & Bhunia, A. K. (2005). An application of real-coded genetic algorithm (for mixed integer non-linear programming in an optimal two-warehouse inventory policy for deteriorating items with a linear trend in demand and a fixed planning horizon). International Journal of Computer Mathematics, 82(2), 163–175.

    Article  Google Scholar 

  • Pan, D., Ci, Y., He, M., & He, H. (2013). An improved quantum-behaved particle swarm optimization algorithm based on random weight. Journal of Software, 8, 1327–1332.

    Google Scholar 

  • Sana, S. S. (2010). Optimal selling price and lotsize with time varying deterioration and partial backlogging. Applied Mathematics and Computation, 217(1), 185–194.

    Article  Google Scholar 

  • Sana, S. S. (2015). An EOQ model for stochastic demand for limited capacity of own warehouse. Annals of Operations Research, 233(1), 383–399.

    Article  Google Scholar 

  • Sana, S. S., & Goyal, S. K. (2015). (Q, r, L) model for stochastic demand with lead-time dependent partial backlogging. Annals of Operations Research, 233(1), 401–410.

    Article  Google Scholar 

  • Sarma, K. V. S. (1987). A deterministic order level inventory model for deteriorating items with two storage facilities. European Journal of Operational Research, 29(1), 70–73.

    Article  Google Scholar 

  • Saxena, N., Singh, S. R., & Sana, S. S. (2016). A green supply chain model of vendor and buyer for remanufacturing items. RAIRO-Operations Research. doi:10.1051/ro/2016077.

  • Sun, J., Feng, B., & Xu, W. B. (2004a). Particle swarm optimization with particles having quantum behavior. In: IEEE Proceedings of congress on evolutionary computation (pp. 325–331).

  • Sun, J., Xu, W. B., & Feng, B. (2004b). A global search strategy of quantum-behaved particle swarm optimization. In: Proceedings of the 2004 IEEE conference on cybernetics and intelligent systems (pp. 111-116).

  • Sun, J., Xu, W. B., & Feng, B. (2005). Adaptive parameter selection of quantum-behaved particle swarm optimization on global level. Advances in Intelligent Computing, Lecture Notes in Computer Science, 3644, 420–428.

    Article  Google Scholar 

  • Taleizadeh, A. A., Wee, H. M., & Sadjadi, S. J. (2010). Multi-product production quantity model with repair failure and partial backordering. Computers and Industrial Engineering, 59(1), 45–54.

    Article  Google Scholar 

  • Tiwari, S., Cárdenas-Barrón, L. E., Khanna, A., & Jaggi, C. K. (2016). Impact of trade credit and inflation on retailer’s ordering policies for non-instantaneous deteriorating items in a two-warehouse environment. International Journal of Production Economics, 176, 154–169.

    Article  Google Scholar 

  • Wee, H. M., Yu, J. C., & Law, S. T. (2005). Two-warehouse inventory model with partial backordering and Weibull distribution deterioration under inflation. Journal of the Chinese Institute of Industrial Engineers, 22(6), 451–462.

    Article  Google Scholar 

  • Wee, H. M., Lo, S. T., Yu, J., & Chen, H. C. (2008). An inventory model for ameliorating and deteriorating items taking account of time value of money and finite planning horizon. International Journal of Systems Science, 39(8), 801–807.

    Article  Google Scholar 

  • Wu, K. S., Ouyang, L. Y., & Yang, C. T. (2006). An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging. International Journal of Production Economics, 101(2), 369–384.

    Article  Google Scholar 

  • Wu, K. S., Ouyang, L. Y., & Yang, C. T. (2009). Coordinating replenishment and pricing policies for non-instantaneous deteriorating items with price-sensitive demand. International Journal of Systems Science, 40(12), 1273–1281.

    Article  Google Scholar 

  • Xi, M., Sun, J., & Xu, W. (2008). An improved quantum-behaved particle swarm optimization algorithm with weighted mean best position. Applied Mathematics and Computation, 205, 751–759.

    Article  Google Scholar 

  • Yang, H. L. (2004). Two-warehouse inventory models for deteriorating items with shortages under inflation. European Journal of Operational Research, 157(2), 344–356.

    Article  Google Scholar 

  • Yang, H. L. (2006). Two-warehouse partial backlogging inventory models for deteriorating items under inflation. International Journal of Production Economics, 103(1), 362–370.

    Article  Google Scholar 

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Acknowledgements

The authors are thankful to the valuable, constructive and detailed suggestions provided by three anonymous referees. The first author is grateful to his parents, wife, children Aditi Tiwari and Aditya Tiwari for their valuable support during the development of this paper.

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Authors and Affiliations

  1. Department of Operational Research, Faculty of Mathematical Sciences, New Academic Block, University of Delhi, Delhi, 110007, India

    Sunil Tiwari & Chandra K. Jaggi

  2. NUS Business School and the Logistics Institute-Asia Pacific, National University of Singapore, Singapore, Singapore

    Sunil Tiwari & Mark Goh

  3. Department of Mathematics, The University of Burdwan, Burdwan, West Bengal, 713104, India

    Asoke Kumar Bhunia

  4. School of Engineering and Sciences, Tecnológico de Monterrey, E. Garza Sada 2501 Sur, C.P. 64849, Monterrey, Nuevo León, Mexico

    Ali Akbar Shaikh

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  1. Sunil Tiwari
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  2. Chandra K. Jaggi
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  3. Asoke Kumar Bhunia
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  4. Ali Akbar Shaikh
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  5. Mark Goh
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Correspondence to Ali Akbar Shaikh.

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Tiwari, S., Jaggi, C.K., Bhunia, A.K. et al. Two-warehouse inventory model for non-instantaneous deteriorating items with stock-dependent demand and inflation using particle swarm optimization. Ann Oper Res 254, 401–423 (2017). https://doi.org/10.1007/s10479-017-2492-5

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