Intelligent algorithms for a new joint replenishment and synthetical delivery problem in a warehouse centralized supply chain

• We provide a new designed delivery process of JRD with vary number of customers.
• We propose procedures to deal with three cases in the new delivery process.
• Three algorithms, QEA, DE and QDE are redesigned to solve the new JRD model.
• Superiorities of DE and QDE are testified through the tests on different JRDs.

In this paper, a novel joint replenishment and synthetical delivery (JRD) model is proposed to improve the coordination of replenishment and delivery processes. Traditional, in a warehouse centralized supply chain, orders from online customers are usually delivered independently after multiple items have been jointly replenished. To decrease the outbound delivery cost, a new delivery strategy considering synthetical dispatched orders, orders and customers matching, and customer visiting sequence is proposed. Three new beta-heuristic algorithms, namely, quantum evolution algorithm (QEA), differential evolution algorithm (DE) and quantum differential evolution algorithm (QDE), are utilized to solve the proposed JRD. The most important parts of each algorithm (initialization, reproduction and mutation, and selection) are redesigned according to the structure of the decision variables. Numerical experiments are conducted to find the best parameter settings and potential searching abilities of each algorithm. Finally, experimental results show the superiorities of the proposed DE and QDE in terms of searching speed, accuracy, and robustness.