An EOQ model for rebate value and selling-price-dependent demand rate with shortages

In this paper, we develop a deterministic purchasing inventory model for a single item over an infinite horizon. In addition, shortages are allowed and the unsatisfied demand is partially backlogged. The model is studied under the replenishment policy, shortages followed by inventory. The backlogging rate is any non-increasing function of the waiting time up to the next replenishment. The objective of this model is to maximise the Total Profit (TP), which includes sales revenue, purchase cost, the set-up cost, holding cost, rebate redemption cost, shortage cost and opportunity cost due to lost sales. Here, demand varies with price and rebate value. The existence and uniqueness of the proposed systems are examined. Finally, numerical examples are presented to determine the developed model and the solution procedure. Sensitivity analysis of the optimal solution with respect to major parameters is carried out. We propose a solution procedure to find the solution and obtain some managerial results by using sensitivity analysis.