An optimal deterministic control policy of servers in front and back rooms with a variable number of switching points and switching costs

摘要

In this paper we consider a retail service facility with cross-trained workers who can perform operations in both the front room and back room.Workers are brought from the back room to the front room and vice versa depending on the number of customers in the system.A loss of productivity occurs when a worker returns to the back room.Two problems are studied.In the onrst problem,given the number of workers available,we determine an optimal deterministic switching policy so that the expected number of customers in queue is minimized subject to a constraint ensuring that there is a sufoncient workforce to fulonll the functions in the back room.In the second problem,the number of workers needed is minimized subject to an additional constraint requiring that the expected number of customers waiting in queue is bounded above by a given threshold value.Exact solution procedures are developed and illustrative numerical examples are presented.