Dynamic Model for Planning and Business Optimization


The growing internationalization of markets, backed by the free movement of capital flows, has redefined the past quarter century’s business strategies and tends to continue driving economic and financial integration throughout this century. In this context, firms that aim to stand out in such markets should use the essence of the theoretical apparatus to allocate scarce resources efficiently. This means seeking the best possible benefits to offset the constraints that are inherent to the nature of the business environment. In this turbulent and competitive world, there is an increasing need to devise planning models to address the multiple issues that affect competitiveness, such as: planned rate of return, price adjustment, technological obsolescence, optimal investment path, among others. In an effort to contribute to solutions for this need, this paper proposes a dynamic model based on the Hamiltonian approach that combines the Cobb Douglas function and Pontryagin conditions. The model also suggests valuable improvements for company operations.

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S. David, C. Oliveira and D. Quintino, "Dynamic Model for Planning and Business Optimization," Modern Economy, Vol. 3 No. 4, 2012, pp. 384-391. doi: 10.4236/me.2012.34049.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] S. Nickell, “Uncertainty and Lags in the Investment Decisions of Firms,” The Review of Economic Studies, Vol. 44, No. 2, 1977, pp. 249-263. doi:10.2307/2297065
[2] J. Matulka and R. Neck, “Optcon: An Algorithm for the Optimal Control of Nonlinear Stochastic Models,” Annals of Operations Research, Vol. 37, No. 1, 1992, pp. 375-401. doi:10.1007/BF02071066
[3] B. Robinson and C. Lakhani, “Dynamic Price Models for New-Product Planning,” Management Science, Vol. 21, No. 10, 1975, pp. 1113-1122. doi:10.1287/mnsc.21.10.1113
[4] M. Alghalith, “General Closed-Form Solutions to the Dynamic Optimization Problem in Incomplete Markets,” Applied Mathematics, Vol. 2, No. 4, 2011, pp. 433-435. doi:10.4236/am.2011.24054
[5] R. Chaves and J. L. Monzón, “Beyond the Crisis: The Social Economy, Prop of a New Model of Sustainable Economic Development,” Service Business, Vol. 6, No. 1, 2012, pp. 5-26. doi:10.1007/s11628-011-0125-7
[6] J. C. Eckalbar, “Closed-Form Solutions to Bundling Problems,” Journal of Economics & Management Strategy, Vol. 19, No. 2, 2010, pp. 513-544. doi:10.1111/j.1530-9134.2010.00260.x
[7] J. Claro, et al., “Integrated Method for Assessing and Planning Uncertain Technology Investments,” International Journal of Engineering Management and Economics, Vol. 1, No. 1, 2010, pp. 3-30.
[8] S. C. Graves, et al., “A Dynamic Model for Requirements Planning with Application to Supply Chain Optimization,” Operations Research, Vol. 46, No. 3, 1998, pp. S35-S49. doi:10.1287/opre.46.3.S35
[9] E. G. Davis, “A Dynamic Model of the Regulated Firm with a Price Adjustment Mechanism,” The Bell Journal of Economics and Management Science, Vol. 4, No. 1, 1972, pp. 270-282. doi:10.2307/3003148
[10] S. D. Lewis, “Adjustment Time and Optimal Control of Neoclassical Monetary Growth Models,” Optimal Control Applications and Methods, Vol. 2, No. 3, 1981, pp. 251- 267. doi:10.1002/oca.4660020305
[11] L. E. Ohanian, E. C. Prescott and N. L. Stokey, “Introduction to Dynamic General Equilibrium,” Journal of Economic Theory, Vol. 144, No. 6, 2009, pp. 2235-2246. doi:10.1016/j.jet.2009.09.001
[12] R. Davidson and R. Harris, “Non-Convexities in Continuous-Time Investment Theory,” Review of Economic Stu- dies, Vol. 48, No. 2, 1981, pp. 235-253. doi:10.2307/2296882
[13] E. Silberberg, “The Structure of Economics: A Mathematical Analysis,” 2nd Edition, McGraw Hill, Boston, 1990.
[14] H. Goldstein, C. P. Poole and J. Safko, “Classical Mechanics,” 3rd Edition, Addison Wesley, Boston, 2001.
[15] S. Katayama, “Optimal Investment Policy of the Regulated Firm,” Journal of Economic Dynamics and Control, Vol. 13, No. 4, 1989, pp. 532-552. doi:10.1016/0165-1889(89)90002-X
[16] E. P. López, et al., “A Model Predictive Control Strategy for supply Chain Optimization,” Computers & Chemical Engineering, Vol. 27, No. 8-9, 2003, pp. 1201-1218. doi:10.1016/S0098-1354(03)00047-4
[17] L. K. Vanston and R. L. Hodges, “Depreciation Lives for Telecommunications Equipment,” Technology Futures, Inc., Austin, 1996.
[18] S. L. Barreca, “Comparison of Economic Life Techniques,” Technology Futures, Inc., Austin, 1999.
[19] L. C. Won, “On the Policy Implications of Endogenous Technological Progress,” The Economic Journal, Vol. 111, No. 471, 2001, pp. 164-179. doi:10.1111/1468-0297.00626
[20] H. Aoyama, et al., “Fluctuation of Firm Size in the Long- Run and Bimodal Distribution,” Advances in Operations Research, 2011, pp. 1-21. doi:10.1155/2011/269239
[21] R. Dorfman, “An Economic Interpretation of Optimal Control Theory,” American Economic Review, Vol. 59, No. 5, 1969, pp. 817-831.
[22] L. G. Epstein, “The Le Chatelier Principle in Optimal Control Problems,” Journal of Economic Theory, Vol. 19, No. 1, 1978, pp. 103-122. doi:10.1016/0022-0531(78)90058-3

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