Phase Wise Supply Chain Model of EOQ with Normal Life Time for Queued Customers: A Computational Approach
ABSTRACT
In this paper, we mainly aim to compute the optimal inventory in the phase wise supply chain for queued customers in the interval of lower and upper bounds with particular life of the items. Important performance measures such as total optimal cost of the system and total expected delivery have also been computed by applying the dynamic programming and Drichlet theorem. Finally, numerical demonstration and sensitivity analysis have also been presented to gain the better perspective of the model.
In this paper, we mainly aim to compute the optimal inventory in the phase wise supply chain for queued customers in the interval of lower and upper bounds with particular life of the items. Important performance measures such as total optimal cost of the system and total expected delivery have also been computed by applying the dynamic programming and Drichlet theorem. Finally, numerical demonstration and sensitivity analysis have also been presented to gain the better perspective of the model.
Cite this paper
S. Mishra and P. Mishra, "Phase Wise Supply Chain Model of EOQ with Normal Life Time for Queued Customers: A Computational Approach," American Journal of Operations Research, Vol. 2 No. 3, 2012, pp. 296-307. doi: 10.4236/ajor.2012.23036.
S. Mishra and P. Mishra, "Phase Wise Supply Chain Model of EOQ with Normal Life Time for Queued Customers: A Computational Approach," American Journal of Operations Research, Vol. 2 No. 3, 2012, pp. 296-307. doi: 10.4236/ajor.2012.23036.
References
[1] J. M. Chen and C. S. Lin, “An Optimal Replenishment Model for Inventory Items with Normally Distributed Deterioration,” Production Planning and Control, Vol. 13, No. 5, 2002, pp. 470-480. Hdoi:10.1080/09537280210144446 [2] Abel, “Availability, Affordability and Accessibility of Food Khartoum,” Geohjournal, Vol. 34, 2004, pp. 253-255. [3] S. Osaki, “Stochastic System Reliability Modeling,” Word Scientific Publishing, Co.Pte.Ltd., 1985. [4] M. Schwarz, C. Sauer, H. Daduna, R. Kulik and R. Szekli, “M/M/1 Queueing Systems with Inventory,” Queueing System, Vol. 54, No. 1, 2006, pp. 55-78. Hdoi:10.1007/s11134-006-8710-5 [5] G. P. Cachon and F. Q. Zhang, “Obtaining Fast Service in a Queueing System via Performance-Based Allocation of Demand,” Management Science, Vol. 53, No. 3, 2007, pp. 408-420. Hdoi:10.1287/mnsc.1060.0636 [6] S. S. Mishra and D. K. Yadav, “Cost and Profit Analysis of M/Ek/1 Queueing System with Removable Service Station,” Bulgarian Journal of Applied Mathematical Sciences, Vol. 2, 2008, pp. 2777-2789. [7] S. S. Mishra, “Computational Approach to the Cost Analysis of Dual Machine Interference Model with General Arrival Distribution,” PAMM, Vol. 7, No. 1, 2007, pp. 2060073-2060074. Hdoi:10.1002/pamm.200701034 [8] Ravindran and Philips, “O.R. Principle and Practice,” Solberg, New York, 2001. [9] S. Viswanathan and K. Mathur, “Integrating Routing and Inventory Decisions in One-Warehouse Multiretailer Multiproduct Distribution Systems,” Management Science, Vol. 40, 1997, pp. 320-338 [10] S. M. R. Iravani and C. P. Teo, “Asymptotically Optimal Schedules for Single-Server Flow Shop Problems with Setup Costs and Times,” Operations Research Letters, Vol. 33, No. 4, 2005, pp.421-430. Hdoi:10.1016/j.orl.2004.08.007 [11] R. Bellman, “Some Problem in the Theory of Dynamic Programming,” Econometrica, Vol. 22, No. 1, 1954, pp. 37-48. Hdoi:10.2307/1909830 [12] A. A. Batabyal, “The Queuing Theoretic Approach to Groundwater Management,” Ecological Modeling, Vol. 85, 1996, pp. 219-227. [13] J. E. Freund, “Mathematical Statistics,” Prentice Hall, Inc., New Jersey, 1992. [14] S. S. Mishra and P. K. Singh, “Computational Approach to an Inventory Model with Ramp-Type Demand and Linear Deterioration,” International Journal of Operations Research, Vol. 15, No. 3, 2012, pp. 337-357. [15] S. S. Mishra and P. K. Singh, “Computational Approach to EOQ Model with Power Form Stock-Dependent Demand and Cubic Deterioration,” American Journal of Operations Research, Vol. 1, 2011, pp. 5-13. [16] S. J. Ryan Daniel, Chandrasekhar and Rajendran, “International Transaction in Operation Research,” Weily Inter Science, Vol. 12, 2005, pp. 101-127. [17] L. Sheremetov and L. Rocha-Mier, “Supply Chain Network Optimization Based on Collective-Intelligence and Agent Technologies,” Human Systems Management, Vol. 27, 2008, pp. 31-47. [18] K. Shaul, Bar-Lev, P. Mahmut and D. Perry, “On the EOQ Model with Inventory-Level-Dependent Demand Rate and Random Yield,” Operation Research, Vol. 6, 1994, pp. 167-176. [19] E. Erel, “The Effect of Continuous Price Change in the EOQ,” Omaga, Vol. 20, 2002, pp. 523-527. Hdoi:10.1016/0305-0483(92)90026-4 [20] M. Wu and L. S. Pheng, “Modeling Just-in-Time Purchasing in the Ready Mixed Concrete Industry,” International Journal of Production Economic, Vol. 107, 2007, pp. 190-201. [21] D. R. Towill, “Logistics Information Management,” MCB UP Ltd., Vol. 9, 1996, pp. 41-53. [22] T. Pirttil? and V.-M. Virolainen, “An Overview of the State and Problems of Inventory Management in Finland,” International Journal of Production Economics, Vol. 26, 1992, pp. 17-220.
[1] J. M. Chen and C. S. Lin, “An Optimal Replenishment Model for Inventory Items with Normally Distributed Deterioration,” Production Planning and Control, Vol. 13, No. 5, 2002, pp. 470-480. Hdoi:10.1080/09537280210144446 [2] Abel, “Availability, Affordability and Accessibility of Food Khartoum,” Geohjournal, Vol. 34, 2004, pp. 253-255. [3] S. Osaki, “Stochastic System Reliability Modeling,” Word Scientific Publishing, Co.Pte.Ltd., 1985. [4] M. Schwarz, C. Sauer, H. Daduna, R. Kulik and R. Szekli, “M/M/1 Queueing Systems with Inventory,” Queueing System, Vol. 54, No. 1, 2006, pp. 55-78. Hdoi:10.1007/s11134-006-8710-5 [5] G. P. Cachon and F. Q. Zhang, “Obtaining Fast Service in a Queueing System via Performance-Based Allocation of Demand,” Management Science, Vol. 53, No. 3, 2007, pp. 408-420. Hdoi:10.1287/mnsc.1060.0636 [6] S. S. Mishra and D. K. Yadav, “Cost and Profit Analysis of M/Ek/1 Queueing System with Removable Service Station,” Bulgarian Journal of Applied Mathematical Sciences, Vol. 2, 2008, pp. 2777-2789. [7] S. S. Mishra, “Computational Approach to the Cost Analysis of Dual Machine Interference Model with General Arrival Distribution,” PAMM, Vol. 7, No. 1, 2007, pp. 2060073-2060074. Hdoi:10.1002/pamm.200701034 [8] Ravindran and Philips, “O.R. Principle and Practice,” Solberg, New York, 2001. [9] S. Viswanathan and K. Mathur, “Integrating Routing and Inventory Decisions in One-Warehouse Multiretailer Multiproduct Distribution Systems,” Management Science, Vol. 40, 1997, pp. 320-338 [10] S. M. R. Iravani and C. P. Teo, “Asymptotically Optimal Schedules for Single-Server Flow Shop Problems with Setup Costs and Times,” Operations Research Letters, Vol. 33, No. 4, 2005, pp.421-430. Hdoi:10.1016/j.orl.2004.08.007 [11] R. Bellman, “Some Problem in the Theory of Dynamic Programming,” Econometrica, Vol. 22, No. 1, 1954, pp. 37-48. Hdoi:10.2307/1909830 [12] A. A. Batabyal, “The Queuing Theoretic Approach to Groundwater Management,” Ecological Modeling, Vol. 85, 1996, pp. 219-227. [13] J. E. Freund, “Mathematical Statistics,” Prentice Hall, Inc., New Jersey, 1992. [14] S. S. Mishra and P. K. Singh, “Computational Approach to an Inventory Model with Ramp-Type Demand and Linear Deterioration,” International Journal of Operations Research, Vol. 15, No. 3, 2012, pp. 337-357. [15] S. S. Mishra and P. K. Singh, “Computational Approach to EOQ Model with Power Form Stock-Dependent Demand and Cubic Deterioration,” American Journal of Operations Research, Vol. 1, 2011, pp. 5-13. [16] S. J. Ryan Daniel, Chandrasekhar and Rajendran, “International Transaction in Operation Research,” Weily Inter Science, Vol. 12, 2005, pp. 101-127. [17] L. Sheremetov and L. Rocha-Mier, “Supply Chain Network Optimization Based on Collective-Intelligence and Agent Technologies,” Human Systems Management, Vol. 27, 2008, pp. 31-47. [18] K. Shaul, Bar-Lev, P. Mahmut and D. Perry, “On the EOQ Model with Inventory-Level-Dependent Demand Rate and Random Yield,” Operation Research, Vol. 6, 1994, pp. 167-176. [19] E. Erel, “The Effect of Continuous Price Change in the EOQ,” Omaga, Vol. 20, 2002, pp. 523-527. Hdoi:10.1016/0305-0483(92)90026-4 [20] M. Wu and L. S. Pheng, “Modeling Just-in-Time Purchasing in the Ready Mixed Concrete Industry,” International Journal of Production Economic, Vol. 107, 2007, pp. 190-201. [21] D. R. Towill, “Logistics Information Management,” MCB UP Ltd., Vol. 9, 1996, pp. 41-53. [22] T. Pirttil? and V.-M. Virolainen, “An Overview of the State and Problems of Inventory Management in Finland,” International Journal of Production Economics, Vol. 26, 1992, pp. 17-220.