Optimal lot-size decision for deteriorating items with price-sensitive demand, linearly time-dependent holding cost under all-units discount environment

Due to the competitive market dynamics and globalisation, it gradually becomes challenging for the manufacturers or suppliers to entice any potential customer and turn into actual one. In this connection, to attract the retailers' consideration, manufacturers or suppliers offer an order size dependent discount policy where the per unit purchase cost is measured as a descending step function of the amount of order quantity. A profit maximising inventory model is constructed for a deteriorating product where demand of the product is dependent on selling price, per unit carrying cost as linearly time varying and also proportional to the per unit purchase price under all-units discount environment. After examining the optimality of the decision variables a solution algorithm is suggested to achieve the optimal values of the selling price per unit and replenishment cycle length along with the optimal order size for optimising the net profit. Two computational experiments are executed along with observing the applicability of the proposed algorithm. Finally, a sensitivity analysis is performed for the model by changing the values of all parameters and hence a conclusion is made regarding the current study.