2013/09/19 by Bryan Johnston, Johnston, Bryan
Business, Management and Accounting · Decision Sciences · Mathematics · #Advanced Queuing Theory Analysis #Advanced Statistical Process Monitoring #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Supply Chain and Inventory Management #math.OC #math.PR
paper · pdf · doi:10.48550/arxiv.1309.4835
Fixed typos. Changed to two column layout. Rephrased introduction
openalex publication_date 2013/09/19 · arxiv created 2013/09/30 · arxiv updated 2013/10/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We demonstrate that the fraction of sales lost for the (r, q) system under consideration can be conveniently bounded in a manner suitable for quick, back-of-the-envelope estimates. We assume that customer demand arises from a Poisson process with one unit demanded at a time, that all demand occurring during a stockout is lost, and that lead time is constant. In addition, we allow the situation where multiple replenishment orders may be simultaneously outstanding. We show that the difference between the upper and lower bounds on the the fraction of sales lost appears likely to be no more than 6:5% (0:065), and is typically significantly better than that. In particular, the bounds appear to be very useful when the reorder point is relatively high or when the mean lead time demand is significantly different from the reorder point. In addition, we relate the common performance measures for the system, and so enable bounding the total operating costs.