Stochastic internal task scheduling in cross docking using chance-constrained programming

Abstract

ABSTRACT A novel mathematical model of stochastic internal task scheduling in cross docking is proposed herein for minimizing the total tardiness of customer orders. The model aims to simultaneously assign internal cross-dock working teams and transportation equipment to obtain the optimal internal task schedule in a single unloading activity. Stochastic parameters are considered to yield a more realistic problem. In this problem, the processing times of breaking down incoming containers and building up customer orders, and the due dates of customer orders are assumed as random variables subjected to normal and uniform distributions, respectively. The problem was formulated using chance-constrained programming to minimize the total tardiness. An experiment was performed for comparing solutions between stochastic and deterministic scheduling environments. Computational experiment using a LINGO optimization solver showed that the total tardiness obtained from the stochastic model with chance-constraint programming was higher than that from the deterministic model because of uncertainties in terms of processing times and due dates. However, the internal task scheduling problem in cross docking is NP-hard. The exact method provides an optimal solution within a reasonable time for small problems. Therefore, future research should consider metaheuristic approaches to addressing complexities in real-world practices.