Analysis of order-up-to-S inventory policies under cash flow market value minimization

An appropriate appraisal of inventory policies, taking into account not only expected cost/profit effects but also impacts on the risk position of the firm, can be performed by assessing the policy-induced stochastic cash flows by means of financial valuation models like the CAPM. Up to now, in the context of inventory theory this has only been done for the ordinary one-period newsboy problem. In this paper an extension of a multi-period framework of a periodic order-up-to-S policy is presented resulting in a situation where an infinite annuity stream of cash flows has to be valued. Optimality conditions for the reorder level S are derived for both the back-order and the lost-sales case. It is analyzed how costs and price parameters as well as capital market data and demand risk (in terms of correlation between demand and market return) influence the reorder level. In addition, it is shown how risk adaptation of the cost of capital has to be performed. At last, an extension of these considerations to a (S,T) policy with variable reorder cycle T is presented.