A hybrid binomial inverse hypergeometric probability distribution: Theory and applications

In this paper, we define a novel probability distribution triggered by a due date setting problem from a multi-item single level production system. As a result, we derive a recurrence relation for the underlying distribution function and, finally, we also infer the novel discrete distribution function. We underpin our analytical findings by numerical results when computing the distribution function, the expected value as well as the variance. In order to apply and translate our apparatus to other problems, we come up with an application when determining due dates for a production system with sequence-dependent setup costs.