A three-layer supply chain integrated production-inventory model under permissible delay in payments in uncertain environments

In this paper, an integrated production-inventory model is presented for a supplier, manufacturer, and retailer supply chain under conditionally permissible delay in payments in uncertain environments. The supplier produces the item at a certain rate, which is a decision variable, and purchases the item to the manufacturer. The manufacturer has also purchased and produced the item in a finite rate. The manufacturer sells the product to the retailer and also gives the delay in payment to the retailer. The retailer purchases the item from the manufacture to sell it to the customers. Ideal costs of supplier, manufacturer, and retailer have been taken into account. An integrated model has been developed and solved analytically in crisp and uncertain environments, and finally, corresponding individual profits are calculated numerically and graphically.