A new discrete-time queueing model to optimize cargo dispatch for a warehouse

This paper develops a new discrete-time queueing model with a workload-controlled D-policy for a cargo loading process in a warehouse, where a packed cargo is considered a customer and the handling equipment a server. Applying an intuitive and primary probabilistic analysis method, we obtain the z-transform expressions for the probability distribution of the number of packed cargoes at any epoch  \(n^+\) $n^{+}$  under any initial state. Then, some significant steady-state queueing performance measures, such as the explicit recursive formulas for the steady-state distribution of the number of packed cargoes at different epochs  \(n^+\) $n^{+}$ ,  \(n^-\) $n^{-}$  and n, the expected number of packed cargoes, and the mean waiting time, are derived. In addition, computational experiments are implemented to explore the effect of parameters on system performance indicators and the rationalization design of warehouse capacity. Finally, considering transportation expense as part of the fixed cost of the system, we discuss the minimum cost problems of the system. Without (with) average queue waiting time constraints, optimal loading policies that minimize the long-run expected cost rate are numerically determined.