Coordination of a three-level supply chain with variable demand and order size dependent trade credit in healthcare industries

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In a traditional inventory model, the customer who purchases the goods is expected to pay the seller immediately. However, in many practical situations, the seller will give the customer a reasonable postpone period when the customer’s request amount surpasses a given limit. Now-a-days, the time-dependent demand plays a vital role in the healthcare industries. This paper, we generalized an order linked trade credit approach in three-level supply chain system, including the pharmaceutical manufacturer, the wholesaler and, the hospitals are involved. The pharmaceutical manufacturer gives a permissible delay period to the wholesaler and, the wholesaler likewise gives an order linked trade credit policy on the hospital. This entire investigation is examined in a pharmaceutical stock model for time-dependent production and time-dependent demand of healthcare industries. We outline the pharmaceutical model of three-level supply chain system with cost minimization to decide the optimal cycle time. Further, we decide the optimal cycle time, optimal order quantity and optimal payment time. The model is solved analytically by minimizing the total annual inventory cost of the centralized supply chain model. To delineate the pharmaceutical inventory models the numerical examples are provided. The sensitivity analysis is carried out for parameters and, the managerial implications are also obtained.