Abstract: For the suppliers' order quantity allocation problem of multi-products, we propose a optimization algorithm combined with penalty function. In order to reduce the loss caused by supply disruption, by considering the reliability of supplier chain, this paper establishes multi-constrained programming model for maximizing the expected profit of purchasers. By using the penalty function, the multi-constraints optimization problem is transformed into an unconstrained optimization problem when dealing with the multi-constraints of the model. When solving the model, in order to enlarge the searching space of particles and keep the diversity of particles, we propose a hybridized algorithm of frog leaping and particle swarm, by combining the grouping theory of shuffled frog leaping algorithm with the fast convergence of particle swarm optimization algorithm. Experimental results show that the proposed algorithm has better performance compared with the independent particle swarm optimization algorithm in terms of speed and accuracy of optimization.

Key words: Order quantity allocation, Reliability, Expected profit, Penalty function, Particle swarm optimization algorithm

摘要： 针对多产品的供应商订购量分配问题,提出一种结合罚函数的优化算法。为减小由供应中断带来的损失，考虑供应链可靠性，构建以采购商期望利润最大化为目标的多约束规划模型。在处理模型中的多约束条件时，借助罚函数法将多约束优化问题转变为无约束优化问题。模型求解时，为扩大粒子的寻优空间并保持粒子的多样性，将混合蛙跳算法的分组思想与粒子群优化算法的快速收敛性结合，提出基于蛙跳粒子群的优化算法。算例实验结果表明，所提算法与独立粒子群算法的求解结果相比，本算法在寻优速度和精度方面均具有更好的性能。

关键词: 订购量分配, 可靠性, 期望利润, 罚函数, 粒子群优化算法