Stochastic programming approach to capital budgeting in the decentralized firm

Abstract

This thesis is concerned with the development of a stochastic programming model that can be applied to the optimal budget allocation under risk in the investments of decentralized firms. In view of firm structures, division-wise decentralization has been activated to accomplish many managerial objectives such as economies of scale through the decentralized decision-making, continuous technological learning processes, communication cost reduction, psychological motivation promotion, preferable time-sensitivity of decision-making, etc.. These days, capital budgeting problems are mainly treated in the decentralized systems under certainty. However, many investment decisions in firms have to be made under risk due to their stochastic environments. In this work, we consider stochastic programming approaches for the analysis of the decentralized budgeting systems with stochastic returns such as normal, multivariate-normal, exponential, and uniform variates. In case of the normal variates of investment returns, the corresponding stochastic programming systems were shown to be transformed into quadratic programming systems. Then, Hass`` decomposition algorithm and Kataoka``s Iteration Method were applied to solve for the optimal fraction of division-wise projects. Likewise, it was shown that these methods can be also applied to the stochastic programming systems associated with the multivariate-normal variates of investment returns. However, for the exponential and uniform variates of investment returns, the corresponding stochastic programming systems were transformed into a deterministic nonlinear mathematical programming system, which is too difficult to be decomposed. In conclusion, since the optimal budget allocation associated with the optimal fraction of division-wise projects can be directed to the maximum expected net present value of the whole firm investment returns, the application of these stochastic analyses is greatly anticipated in decentralized-firm in...