Solving task scheduling problem in cross docking by modified differential evolution algorithm

Abstract

This research focus on internal operational management in a cross docking terminal as an internal task scheduling problem. Based on a literature review, studies pertaining to internal task scheduling in cross docking are scarce. Therefore, this research aims to fill the research gap in the cross docking platform by focusing on an internal task scheduling problem and considered resource allocations in cross docking. Novel mathematical models of deterministic and stochastic internal task scheduling in cross docking were proposed for minimizing 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. However, the internal task scheduling problem in cross docking is NP-hard. Therefore, metaheuristic approaches were considered for addressing complexities in real-world practices. For solving deterministic internal task scheduling problem, a novel self-learning differential evolution (SLDE) algorithm for addressing large-scale internal tasks scheduling problems in cross docking was proposed. The proposed SLDE aims to increase the search capability of its original differential evolution (DE). The key concept of SLDE is to allow a DE population to learn the capabilities of different search strategies and automatically adjust itself to potential search strategies. The performance of the proposed algorithms was evaluated on a set of generated data based on a real case scenario of a real word problem; subsequently, the performance results are compared with results obtained from GA, PSO and DE. Numerical results demonstrate that the proposed SLDE outperforms other algorithms in terms of solution quality and convergence behavior by providing superior solutions using fewer function evaluations. Subsequently, modified SLDE algorithms (MSLDE1 and MSLDE2) were proposed for solving stochastic internal task scheduling problem. Additional terminate conditions were added to MSLDE1 and MSLDE2 to improve computational time. Besides, a different technique to prioritize the strategy was applied to MSLDE2 to improve solution quality. The performance of the proposed algorithms was evaluated on a set of generated data based on a real case scenario of a real word problem. Numerical results showed that SLDE, MSLDE1 and MSLDE2 outperforms other algorithms in terms of solution quality and convergence behavior. Moreover, MSLDE1 and MSLDE2 outperforms the other algorithms in term computational time. In addition, facility cost in term transferring equipment number was analyzed based on trade-off features between cost and total tardiness. Thus, solutions obtained from the cost analysis provide the decision maker with good insights into possible alternative for the final decision on investment of facility in cross docking. According to computational experiment results, GA indicated the lowest performance due to low population diversity. PSO and DE yielded better performance than GA, however, the diversification of PSO is less than DE thus DE has better performance than PSO. The proposed modified DE algorithms indicated the highest performance according to the exploration ability was enhanced. It is noteworthy that this results were form solving large-scale internal task scheduling problems on specific key parameters of each algorithm only. The results could be changed if we solve other problems or consider the difference range of key parameter setting.