Abstract
The main purpose of this paper wants to investigate the optimal retailer's lot-sizing policy with
two warehouses under partially permissible delay in payments within the economic order quantity (EOQ) framework. In this paper,
we want to extend that fully permissible delay in payments to the supplier would offer the retailer
partially permissible delay in payments. That is, the retailer must make a partial payment to the supplier
when the order is received. Then the retailer must pay off the remaining balance at the end of the
permissible delay period. In addition, we want to add the assumption that the retailer's storage
space is limited. That is, the retailer will rent the warehouse to store these exceeding items when
the order quantity is larger than retailer's storage space. Under these conditions,
we model the retailer's inventory system as a cost minimization problem to determine the retailer's
optimal cycle time and optimal order quantity. Three theorems are developed to efficiently determine
the optimal replenishment policy for the retailer. Finally, numerical examples are given to
illustrate these theorems and obtained a lot of managerial insights.