A group purchasing Organisation (GPO) is an entity which aggregates the purchasing volume of health care providers to save costs by getting quantity discounts from manufacturers and distributors. This paper investigates a health care supply chain consisting of a for-profit GPO, a number of suppliers presenting different types of products with limited capacities, and several health service providers requiring various kinds of products with different quantity. Health care providers can either join the GPO by paying a membership fee and buy the products needed at the GPO prices negotiated with the suppliers or negotiate (themselves) directly with the suppliers. The GPO negotiates with suppliers on products’ prices for the health care providers. Furthermore, the GPO takes a contract administration fee from the supplier, i.e., a percentage of all monetary value of the purchased products through the GPO contract. Each supplier offers a quantity discount schedule for each of its products. All prevalent challenges to the GPO performance are taken into consideration, and then the supply chain is formulated as a mixed integer non-linear programming model. A global optimisation framework is employed to find the optimal solution. A case study and sensitivity analyses are conducted to extract some managerial insights. Our investigations confirm that GPOs play a strategic role in the purchasing process, and also it is turned out that they behave in a way which results in satisfying all members of the supply chain.