Joint inventory and rationing decisions in reward-based crowdfunding

We study an entrepreneur's joint inventory and rationing decision if the required capital for a venture is raised in a reward-based crowdfunding campaign. The entrepreneur sets a financing target first, and then decides the rationing policy and inventory if the campaign succeeds. We investigate the whole event with a backward induction. Maximizing the profit in our inventory model, we first obtain the optimal order quantities under each rationing policy and find that surplus funding is critical for the inventory decision. Under both policies, we find that additional borrowing yields a suboptimal order quantity, that the optimal order quantity can be reached without borrowing on a working capital line, and that the entrepreneur will expense all available funds for ordering products without borrowing. Then, we compare rationing policies and analyse the optimal financing target. The results show that, compared to the "funders first" policy, the "regular consumers first" policy is more profitable and yields lower inventory. Meanwhile, we find the optimal financing target is the lower bound in the feasible zone of the funding amount, and the "funders first" policy is more likely to yield a greater financing target. Finally, we conduct numerical examples to verify these results.