A memo on stock model with partial backlogging under delay in payments

In this paper, we presents an inventory problem where initially, a retailer purchases Q(=P+R) units and after fulfilling the backlogged quantities, there is a P unit of the on-hand inventory. It continuously declines to meet the customer’s demand, which depends on the on-hand inventory level up to the time t = t1. After that the inventory level declines by constant demand up to t = t2. Thereafter, shortage occurs and it accumulates at the rate ?(T-t) till t = T when the next batch arrives. This whole cycle repeats itself after the cycle length T. The proposed model of this paper is investigated under various conditions and the implementation of the proposed model is presented through some numerical examples.