Single-vendor single-buyer inventory model with discrete delivery order, random machine unavailability time and lost sales

Integrated single-vendor single-buyer inventory model with multiple deliveries has proved to result in less inventory cost. However, many researchers assumed that the production run is perfect and there is no production delay. In reality, production delay is prevalent due to random machine unavailability and shortages. This study considers lost sales, and two kinds of machine unavailability distributions - uniformly and exponentially distributed. A classical optimization technique is used to derive an optimal solution and a numerical example is provided to illustrate the theory. The results show that delivery frequency has significant effect on the optimal total cost, and a higher lost sales cost will result in a higher delivery frequency.