A lot sizing model with advance payment and planned backordering

Abstract

One of the assumptions in the classic economic order quantity model is that the buyer pays the purchasing cost for an order immediately after receiving the goods. In the real world, the vendors sometimes offer the buyers to pay all or a proportion of the purchasing cost after receiving the items to encourage them to increase their orders (i.e., delayed payment). Furthermore, in some cases, the powerful vendors may ask the buyers to prepay the entire, or a fraction of the purchasing cost before the delivery to mitigate the risk of cancellation or procuring the primary parts (i.e., advance payment). Advance payment is widely used by firms, but its effects on customer’s inventory decisions are seldom discussed. In this paper, we investigate the customer’s inventory policy by considering two different conditions: (a) full prepayment with shortage, (b) partial prepayment–partial delayed payment with shortage. We discuss the effect of parameters such as price discount linked to prepayment and length of prepayment on optimal periods of inventory and shortage quantity. The conclusions shows that the length of the advance payment period does not influence the inventory cycle, but that parameters such as discount factor linked to advance payment and delayed payment period affect the optimal inventory cycle in all cases. Numerical examples and a sensitivity analysis are presented to demonstrate the performance of the model and the results.