Retailer’s optimal credit period and cycle time in a supply chain for deteriorating items with up-stream and down-stream trade credits


Department of Mathematics, Sitananda College, P.O. & P.S.-Nandigram, Dist.-Purba Medinipur, Nandigram, 721631, West Bengal, India


In practice, the supplier often offers the retailers
a trade credit period M and the retailer in turn provides
a trade credit period N to her/his customer to stimulate
sales and reduce inventory. From the retailer’s perspective,
granting trade credit not only increases sales and revenue
but also increases opportunity cost (i.e., the capital opportunity
loss during credit period) and default risk (i.e.,
the percentage that the customer will not be able to pay off
his/her debt obligations). Hence, how to determine credit
period is increasingly recognized as an important strategy
to increase retailer’s profitability. Also, the selling items
such as fruits, fresh fishes, gasoline, photographic films,
pharmaceuticals and volatile liquids deteriorate continuously
due to evaporation, obsolescence and spoilage. In
this paper, we propose an economic order quantity model
for the retailer where (1) the supplier provides an up-stream
trade credit and the retailer also offers a down-stream trade
credit, (2) the retailer’s down-stream trade credit to the
buyer not only increases sales and revenue but also opportunity
cost and default risk, and (3) the selling items are
perishable. Under these conditions, we model the retailer’s
inventory system as a profit maximization problem to determine
the retailer’s optimal replenishment decisions under
the supply chain management. We then show that the
retailer’s optimal credit period and cycle time not only
exist but also are unique. We deduce some previously
published results of other researchers as special cases.
Finally, we use some numerical examples to illustrate the
theoretical results.