# The capital cost of holding inventory - A real options approach

Abstract: This thesis is based on three scientific papers dealing with costs and financial risks associated with keeping stock. Reasonable cost parameters are important to implement an effective inventory control system, which in turn is one of the key activities in logistics management. All three papers consider a single-level inventory system. Single-period, multi-period as well as continuous review systems are investigated. The models are analyzed in a real options framework. Stochastic demand is treated in Paper A and C, stochastic purchase price per unit in Papers A and B and stochastic set-up cost in Appendix 4. The parameters are varied one at a time and they are assumed to follow stochastic processes normally used in financial literature. Both the lognormal Wiener process and the Ornstein-Uhlenbeck process are used. The optimal policy is derived through a backward-pass dynamic programming approach. The expected net present value of the inventory costs associated with the optimal policy is then used to evaluate the cost efficiency of policies based on simple adjustments of well-known heuristics, such as the EOQ-formula. The thesis shows that the financial risk associated with a stochastic set-up cost typically can be neglected when the inventory control parameters are determined. This holds for stochastic demand, too, although a minor improvement could be achieved by a simple adjustment of the order point. It is also shown that autocorrelated demand has very little effect on the optimal inventory policy. The systematic risk of the unit purchase price has a significant effect on the optimal inventory control parameters. It is shown that an excellent approximation is attained if the expected rate of relative decrease in risk adjusted purchase price, i.e., the risk premium, is added to the capital cost rate. The results show that if this rate varies over time, a good policy is to use the average price change over a period of about 1/3 to 2/3 of the order cycle when estimating the risk premium. It can be concluded that one can obtain a close to optimal inventory control system by using well-known heuristics with just minor adjustments of the capital holding cost.

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