Queueing Systems with Preferred Service Delivery Times and Multiple Customer Classes

TL;DR

This paper models a complex queueing system with customer preferences and priorities, proposing a Markov Decision Process approach to optimize admission and capacity decisions in click-and-collect contexts.

Contribution

It introduces a novel joint admission control and capacity allocation model considering customer preferences and priority dynamics, with solution methods and approximations.

Findings

Structural results for suboptimal policies

Development of a state aggregation approximation method

Extensive computational analysis of policy impacts

Abstract

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.