Optimal transportation and business cycles in an integrated production-inventory model with a discrete credit period

•Two integrated production inventory models.•Discrete credit period offered depending on the purchase quantity.•Optimal transportation cycles and optimal business cycles.•Free transportation cost offered.

This paper considers the impact of discrete trade-credit policy depending on the purchased quantity of raw-materials on an integrated multi-cycle production inventory system of a raw-material supplier and a manufacturer in some business cycles during finite time horizon. The manufacturer collects raw-materials with offer of free transportation cost in some transportation cycles. Our objective is to get the optimal number of transportation and business cycles in two models with three cases depending on different position of the credit period with respect to production period and cycle length. Some numerical examples have been illustrated along with sensitivity analysis and managerial insights.