A queueing control model for retail services having back room operations and cross-trained workers

Many retail service facilities have both front room and back room operations. The front room deals with serving customers, perhaps from a queue. The back room focuses typically on restocking of shelves and sorting and/or processing of paperwork. We model such a facility having workers who are cross-trained to do both jobs. We assume that back room work is interruptible. A manager can bring a worker from the back room to the front room when the customer checkout queue becomes “too long”. A reverse assignment occurs when the number of customers is sufficiently small. We assume that the retail facility contains two customer-counting technologies. The first counts the number of shoppers in the store who are not already in checkout queues and the second counts the number of customers at checkout. The goal is to find the minimum number of workers to staff the facility subject to two performance constraints. The mean queue delay in the front room must be less than a pre-specified value, and the time-average number of workers in the back room must be greater than a pre-specified value. Once the minimum complement of workers is found, a secondary goal is to minimize mean queueing delay subject to retaining back room feasibility. The system is a continuous time Markov process having a three-dimensional state space. The (heuristic) optimization process includes state-dependent rules for switching workers between rooms.