This paper studied the problem of determining the optimal inventory level to meet the customer service target level in a situation where the customer demand for each branch of a nationwide retailer is uncertain. To this end, ISR (In-Stock Ratio) was defined as a key management indicator (KPI) that can be used from the perspective of a nationwide retailer such as Samsung, LG, or Apple that sells goods at branches nationwide. An optimization model was established to allow the retailer to minimize the total amount of inventory held at each branch while meeting the customer service target level defined as the average ISR. This paper proves that there is always an optimal solution in the model and expresses the optimal solution in a generalized form using the Karush-Kuhn-Tucker condition regardless of the shape of the probability distribution of customer demand. In addition, this paper studied the case where customer demand follows a specific probability distribution such as a normal distribution, and an expression representing the optimal inventory level for this case was derived.

1. Introduction
2. Mathematical Model
3. Calculation of Optimal Inventory Level
4. Conclusion
Acknowledgement
References

• Hyoungtae Kim(Corporate Management Major, Department of Convergence Management, Woosong University) | 김형태 (우송대학교 융합경영학부 경영학전공) Corresponding author