Non-profit resource allocation and service scheduling with cross-subsidization and uncertain resource consumptions - Lu, Mengshi; Nakao, Hideaki; Shen, Siqian; Zhao, Lin (Omega (Oxford), 2021)
•We formulate a chance-constrained model and three safe approximations for allocating for-profit and non-profit service in different resources.•We formulate an integrated resource allocation and service scheduling model for the above problem.•We conduct numerical studies on instances of for-profit and non-profit surgery planning to compare different models and approaches.•We analyze the impact of varying parameters and cross-subsidization on nonprofit operations. We consider a mixture of for-profit and non-profit requests that share multiple resources at random consumption rates. The revenue from fulfilling for-profit requests is used to cross-subsidize the cost of non-profit operations, and we aim to maximize the number of completed non-profit service requests. We consider two problems that respectively optimize resource allocation and service schedules, and employ chance constraints to restrict the probability of undesired outcomes such as resource over-utilization and service delay. For the allocation model, we propose three approximations of the chance-constrained program, and derive their variants to allow variable resource capacities. For the scheduling model, we derive a mixed-integer linear programming reformulation and develop a two-phase algorithm that separately decides allocation decisions and the start time of each service request. We conduct numerical studies on randomly generated instances of non-profit surgery planning to demonstrate the computational results of different models, and the impact of varying parameters and cross-subsidization on non-profit operations.