Assume a retailer–supplier system, where a single item and order-up-to S inventory policy are considered.
To simplify the model, excess inventory can be returned without cost, and excess demand is backlogged.
The timing of events during a replenishment period is as follows: at the beginning of each period t, the retailer
order a single item of quantity qt from the supplier. There is a lead time of L periods between ordering and
receiving the goods. After that, the goods ordered L periods ago arrived. Finally, demand is realized and the
available stock is used to meet the demand. A serially correlated demand process is assumed to follow the AR
(1) model, and it is similar to Lee et al. [17] and Hayakawa [24]