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A Comparison between Linear Programming Model and Optimal Control Model of Production-Inventory System


Affiliations
1 Apparatus of Supervision and Scientific Evaluation, Ministry of Higher Education and Scientific Research, Iraq
 

This study compares two models of the production- inventory system - optimal control and linear programming. We derived the optimality conditions of optimal control model and formulated the linear programming model. A new method to determine the theoretical solution of the boundary value problem has been suggested. Our numerical results suggest that control on the inventory level was realized at the end of the planning period, depending on the optimal control model, while in the linear programming model, it was realized from the beginning of the planning period. Also, the method to determine the theoretical solution of the boundary value problem has proven to be efficient.

Keywords

Boundary Value Problem, Deteriorating Items, Linear Programming, Optimal Control, Production–Inventory System.
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  • Khanra, S. and Chaudhuri, K., A production-inventory model for a deteriorating item with shortage and time-dependent demand. Yugoslav J. Opera. Res., 2011, 21(1), 29–45.

  • Begum, R., Sahu, S. K. and Sahoo, R. R., An inventory model for deteriorating items with quadratic demand and partial backlogging. British J. Appl. Sci. Technol., 2012, 2(2), 112–131.

  • Jhaveri, C. A., Inventory system for deteriorating item with time dependent holding cost in declining market with partial backlogging. In Proceedings of the International Conference on Technology and Business Management. Dubai, AUE, 2013.

  • Karmakar, B. and Choudhury, K. D., Inventory models with ramptype demand for deteriorating items with partial backlogging and time-varying holding cost. Yugoslav J. Opera. Res., 2014, 24(2), 249–266.

  • Roy, A., An inventory model for deteriorating items with price dependent demand and time varying holding cost. Adv. Mod. Opt., 2008, 10(1), 25–37.

  • Bansal, K. K., Inventory model for deteriorating items with the effect of inflation. Int. J. Appl. Innov. Eng. Manage., 2013, 2(5), 143–150.

  • Gite, S., An EOQ model for deteriorating items with quadratic time dependent demand rate under permissible delay in payment. Tc, 2013, 3(3), 2–2.

  • Sharma, V. and Chaudhary, R., An inventory model for deteriorating items with Weibull deterioration with time dependent demand and shortages. Res. J. Manage. Sci., 2013, 2(3), 28–30.

  • Mishra, S. S. and Singh, P. K., A computational approach to EOQ model with power-form stock-dependent demand and cubic deterioration. Am. J. Opera. Res., 2011, 1(1), 5–13.

  • Misra, U. K., Sahu, S. K., Bhaula, B. and Raju, L. K., An inventory model for weibull deteriorating items with permissible delay in payments under inflation. Int. J. Res. Rev. Appl. Sci., 2011, 6(1), 10–17.

  • Kundu, S. and Chakrabarti, T., An EOQ model for deteriorating items with fuzzy demand and fuzzy partial backlogging. IOSR J. Math., 2012, 2(3), 13–20.

  • Singh, T. and Sahu, S. K., An inventory model for deteriorating items with different constant demand rates. Af. J. Math. Comp. Sci. Res., 2012, 5(9), 158–168.

  • Sharma, A. K., Sharma, M. and Ramani, N., An inventory model with weibull distribution deteriorating item power pattern demand with shortage and time dependent holding cost. Am. J. Appl. Math. Math. Sci., 2012, 1(1-2), 17–22.

  • Patel, S. S. and Patel, R., An inventory model for weibull deteriorating items with linear demand, shortages under permissible delay in payments and inflation. Int. J. Math. Stat. Inven., 2013, 1(1), 22–30.

  • Kumar, S. and Rajput, U. S., An EOQ model for weibull deteriorating items with price dependent demand. IOSR J. Math., 2013, 6(6), 63–68.

  • Zhao, L., An inventory model under trapezoidal-type demand, Weibull-distributed deterioration and partial backlogging. J. Appl. Math., 2014, 1–10.

  • Rao, S. V., Rao, K. S. and Subbaiah, K. V., Production inventory model for deteriorating items with on-hand inventory and time dependent demand. Jordan J. Mech. Indust. Eng., 2010, 4(6), 739–756.

  • Kawale, S. and Bansode, P., An EPQ model using weibull deterioration for deterioration item with time varying holding cost. Int. J. Sci., Eng. Tech. Res., 2012, 1(4), 29–33.

  • Pal, S., Mahapatra, G. S. and Samanta, G. P., A production inventory model for deteriorating item with ramp type demand allowing inflation and shortages under fuzziness. Econ. Model., 2015, 46, 334–345.

  • Das, B. C., Das, B. and Mondal, S. K, An integrated production inventory model under interactive fuzzy credit period for deteriorating item with several markets. Appl. Soft Comput., 2015, 28, 453–465.

  • Benhadid, Y., Tadj, L. and Bounkhel, M., Optimal control of production inventory systems with deteriorating items and dynamic costs. Appl. Math. E-Notes, 2008, 8, 194–202.

  • Emamverdi, G. A., Karimi, M. S. and Shafiee, M., Application of optimal control theory to adjust the production rate of deteriorating inventory system (Case study: Dineh Iran Co.). Middle-East J. Sci. Res., 2011, 10(4), 526–531.

  • Zanoni, S. and Zavanella, L., Model and analysis of integrated production–inventory system: the case of steel production. Inter. J. Prod. Econ., 2005, 93, 197–205.

  • Moengin, P. and Fitriana, R., Model of integrated productioninventorydistribution system: the case of billet steel manufacturing. In Proceedings of the World Congress on Engineering, London, UK, 2015, vol. II.

  • Lee, A. H. and Kang, H. Y., A mixed 0–1 integer programming for inventory model: a case study of TFT-LCD manufacturing company in Taiwan. Kybernetes, 2008, 37(1), 66–82.

  • Kefeli, A., Uzsoy, R., Fathi, Y. and Kay, M., Using a mathematical programming model to examine the marginal price of capacitated resources. Int. J. Prod. Econ., 2011, 131(1), 383–391.

  • Grimmett, D., Multi-period production planning with inventory, interest rate, and backorder considerations. IRJGBD, 2012, 1(1), 1–8.

  • Veselovska, L., A linear programming model of integrating flexibility measures into production processes with cost minimization. J. Small Bus. Entrepren. Dev., 2014, 2(1), 67–82.

  • Talapatra, S., Saha, M. and Islam, M. A., Aggregate planning problem solving using linear programming method. Am. Acad. Scholar. Res. J., 2015, 7(1), 20–28.

  • Sethi, S. P. and Thompson, G. L., Optimal Control Theory Application to Management Science and Economics, Springer, USA, 2000, 2nd edn.


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  • A Comparison between Linear Programming Model and Optimal Control Model of Production-Inventory System

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Authors

Ali Khaleel Dhaiban
Apparatus of Supervision and Scientific Evaluation, Ministry of Higher Education and Scientific Research, Iraq

Abstract


This study compares two models of the production- inventory system - optimal control and linear programming. We derived the optimality conditions of optimal control model and formulated the linear programming model. A new method to determine the theoretical solution of the boundary value problem has been suggested. Our numerical results suggest that control on the inventory level was realized at the end of the planning period, depending on the optimal control model, while in the linear programming model, it was realized from the beginning of the planning period. Also, the method to determine the theoretical solution of the boundary value problem has proven to be efficient.

Keywords


Boundary Value Problem, Deteriorating Items, Linear Programming, Optimal Control, Production–Inventory System.

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DOI: https://doi.org/10.18520/cs%2Fv112%2Fi09%2F1855-1863