Service Level Constrained Distribution-Free Newsvendor Problem with Balking Penalty

This study extends the newsvendor model to address customer balking and its penalty under service-level constraints. The model designed in this study determines the optimal order quantity to derive the maximum expected profit when a customer is reluctant to buy a product and the available inventory falls below a certain threshold. In addition, the service level is introduced into the procedure to determine the optimal order quantity, thus facilitating the process. Under these circumstances, we also propose a corresponding distribution-free model to determine tight lower bounds on expected profits under the worst-case scenario. To quantitatively evaluate our model's performance, we compared profits based on the presence or absence of demand distribution, and demonstrated the effect of varying balking penalty costs and probabilities. Introducing a practical service level that can be used as a trade-off tool to help determine reasonable estimates and profitable decisions is beneficial when determining order quantity by comparing goodwill and holding costs.