Optimizing hospital drug procurement with rebate contracts

Contracts are prevalent in the Australian pharmaceutical industry and create a new challenge for public hospitals in terms of their procurement activities. Under a standard rebate contract, a manufacturer offers a rebate reward conditional on hospitals purchasing a minimum volume (i.e., the rebate threshold or target) of a specified drug. Additionally, a generic version of the specified drug is also available but does not qualify for any rebate reward. To assist hospitals in choosing between a generic brand and a rebate brand, we develop a periodic-review dynamic programming (DP) model to minimize the total expected procurement cost. The rebate threshold creates a discontinuous and piecewise linear boundary condition in the DP model, causing the objective function to become ill-behaved and making the exact characterization of the optimal policy difficult. We therefore propose three easy-to-use heuristic policies: quota met before switching, constant threshold, and dynamic heuristic policies. Through simulation, we evaluate the performance of these heuristics and identify that which emerges as the best performer. Finally, we discuss three extensions that allow for simultaneous procurement, multiple products and demand realization after decision making.