Optimality of cycle time and inventory decisions in a coordinated and non-coordinated three-echelon supply chain under exponential price dependent demand

To remain competitive in the prevailing stiff business competition, coordination among the entities of the supply chain is becoming mandatory. The people in the supply chain have to integrate their business decisions beyond the organisation's boundary. This paper develops a mathematical model for a coordinated and non‐coordinated three‐echelon supply chain under exponential price‐dependent demand. The model is developed with the consideration of ordering/setup, carrying and transportation costs. The objective of this work is to demonstrate the optimality of inventory replenishment decisions, shipment frequencies and the annual total variable costs, with and without coordination. A numerical illustration is presented to determine the optimal values of the objective function and decision variables. Further, the sensitivity analysis is carried out to study the influence of the model parameters on the optimality of decision variables and the objective function.