# On Determination of Inventory Cost Parameters

Abstract: Efficient inventory control depends on correct values of inventory cost parameters, such as holding costs, shortage/stockout costs and ordering/setup costs. However, there exists surprisingly little research concerning the size of these parameters or how they should be determined. This thesis is devoted to increasing our knowledge of these matters. The research is presented in the form of five scientific papers, A-D, preceded by a summarizing introduction. The introduction also contains a review of how cost parameters are determined today, and an extended discussion pertaining to the capital cost of holding inventory ? how it ought to be determined and the reasonable values for this cost. Methodologically, the research belongs to the field of applied mathematical modeling and operations research. Papers A, B and D draw from results in financial theory, and in these papers three sources of financial risk associated with holding inventory are investigated, namely stochastic demand (in A and D), stochastic per unit replenishment cost (in A and B) and stochastic ordering cost (in A). Paper C presents a more accurate method for determining the holding cost by employing an Activity Based Costing approach. In Paper E we focus on a two-level distribution system and investigate how the different system parameters influence the induced shortage/stockout cost at the higher echelon that is used to coordinate the system. The conclusions of Papers A, B and D are that the financial risks associated with stochastic demand and setup cost have little influence on the optimal policy, and thus on the inventory cost parameters. In the case of stochastic demand, a minor improvement could be obtained by adjusting the order point. On the other hand, the financial risk associated with stochastic per unit replenishment cost does have a large influence on the optimal policy. We demonstrate that a good estimate of the optimal policy can be obtained through traditional heuristics if the capital cost of holding inventory is computed as the current replenishment cost times a capital cost rate that is the sum of the risk free interest rate and the rate at which the risk adjusted replenishment cost is expected to decrease. The size of the capital cost rate is discussed in Section 7 in the introduction. Empirical data indicate that on average it is fairly low, around 2.5%, and that it can be negative. These results contradict the common hypothesis that the capital cost makes up the main part of the holding cost. The method for determining the holding cost presented in Paper C does not rely on the assumption that the capital cost constitutes the main part of the holding cost. Numerical tests show that substantial cost savings can be made (>20%) when using this method as compared to a more traditional method where the holding cost is computed as a percentage of the product value. The contributions of Paper E include insights into how the induced shortage/stockout cost is influenced by the system parameters. It also contains the determination of simple closed form estimates for this cost. Having a good simple estimate offers a practical means to achieve coordinated control in decentralized systems.

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