  Motivated by the operational problems in click and collect systems, such as
curbside pickup programs, we study a joint admission control and capacity
allocation problem. We consider a system where arriving customers have
preferred service delivery times and gauge the service quality based on the
service provider's ability to complete the service as close as possible to the
preferred time. Customers can be of different priority classes, and their
priority may increase as they wait longer in the queue. The service provider
can reject customers upon their arrival if the system is overloaded or
outsource the service (alternatively work overtime) when the capacity is not
enough. The service provider's goal is to find the minimum-cost admission and
capacity allocation policy to dynamically decide when to serve and whom to
serve. We model this problem as a Markov Decision Process. Our structural
results partially characterize a set of suboptimal solutions, and we develop
solution methods using these results. We also develop a problem-specific
approximation method that is based on state aggregation to overcome the
computational challenges. We present extensive computational results and
discuss the impact of problem parameters on the optimal policy.
