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Motivated by the operational problems in click and collect systems, such ascurbside pickup programs, we study a joint admission control and capacityallocation problem. We consider a system where arriving customers havepreferred service delivery times and gauge the service quality based on theservice provider's ability to complete the service as close as possible to thepreferred time. Customers can be of different priority classes, and theirpriority may increase as they wait longer in the queue. The service providercan reject customers upon their arrival if the system is overloaded oroutsource the service (alternatively work overtime) when the capacity is notenough. The service provider's goal is to find the minimum-cost admission andcapacity allocation policy to dynamically decide when to serve and whom toserve. We model this problem as a Markov Decision Process. Our structuralresults partially characterize a set of suboptimal solutions, and we developsolution methods using these results. We also develop a problem-specificapproximation method that is based on state aggregation to overcome thecomputational challenges. We present extensive computational results anddiscuss the impact of problem parameters on the optimal policy.

Queueing Systems with Preferred Service Delivery Times and Multiple Customer Classes