An effective and efficient differential evolution algorithm for the integrated stochastic joint replenishment and delivery model

As an important managerial problem, the practical joint replenishment and delivery (JRD) model under stochastic demand can be regarded as the combination of a joint replenishment problem and traveling salesman problem, either one is an NP-hard problem. However, due to the JRD’s difficult mathematical properties, high quality solutions for the problem have eluded researchers. This paper firstly proposes an effective and efficient hybrid differential evolution algorithm (HDE) based on the differential evolution algorithm (DE) and genetic algorithm (GA) that can solve this NP-hard problem in a robust and precise way. After determining the appropriate parameters of the HDE by parameters tuning test, the effectiveness and efficiency of the HDE are verified by benchmark functions and numerical examples. We compare the HDE with the available best approach and find that the HDE can always obtain the slightly lower total costs under some situations. Compared with another popular evolutionary algorithm, results of numerical examples also show HDE is faster than GA and the convergence rate of HDE is higher than GA. HDE is a strong candidate for the JRD under stochastic demand.