OBRUN algorithm for the capacity-constrained joint replenishment and delivery problem with trade credits

This study investigates the joint replenishment and delivery problem taking trade credits the delay in payment permitted by suppliers and capacity-constrained into consideration (CJRD-TC). The CJRD-TC aims to minimize the total system costs by finding a reasonable replenishment and delivery schedule policy. In this paper, an opposite-based RUNge Kutta optimization algorithm (OBRUN) is proposed to compare with other intelligent algorithms, including the differential evolution (DE), RUNge Kutta optimization algorithm (RUN), sine cosine algorithm (SCA), and adaptive differential evolution with optimal external archive (JADE). The proposed algorithm is tested on 14 optimization functions. The values of average, standard deviation, and the best are the lowest for 12 functions, which demonstrates OBRUN is superior to other algorithms. We also provide graphs of search history, 2D views of functions, trajectory curve, average fitness history, and convergence curve of OBRUN, the balance between exploration and exploitation over the course of iterations can be observed. The convergence curves of five algorithms are also depicted, which show OBRUN has a fast convergence rate and accuracy than other algorithms. We conduct numerical experiments, parameter tuning, and sensitivity analysis for each of the small-scale, medium-scale, and large-scale number of items. The OBRUN can always find better solutions with the lowest mean values and the best-found total cost results than other algorithms. Indicators of the average optimality gap and the optimality gap dominate by the value of zero. These computational results have demonstrated OBRUN is a suitable and effective candidate for managers to solve the practical CJRD-TC problems.