Considering the players' bargaining power, designing a bi-level programming model is suitable to reflect the hierarchical nature of the decision-making process. In this paper, typical negotiation components perfectly match with the mathematical model and its solution procedure. For this purpose, a mathematical negotiation mechanism is designed to minimize the negotiators' costs in a distributed procurement problem at two echelons of an automotive supply chain. The buyer's costs are procurement cost and shortage penalty in a one-period contract. On the other hand, the suppliers intend to solve a multi-period, multi-product production planning to minimize their costs. Such a mechanism provides an alignment among suppliers' production planning and order allocation, also supports the partnership with the valued suppliers by taking suppliers' capacities into account. Such a circumstance has been modeled via bi-level programming, in which the buyer acts as a leader, and the suppliers individually appear as followers in the lower level. To solve this nonlinear bi-level programming model, a hybrid algorithm by combining the particle swarm optimization algorithm with a heuristic algorithm based on A search is proposed. In this algorithm, a heuristic algorithm based on A search is embedded to solve the mixed-integer nonlinear programming sub-problems for each supplier according to the received variable values determined by PSO system particles.

中文翻译：

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开发分布式采购问题的数学协商机制及其解决方案的混合算法

考虑到参与者的议价能力，设计一个双层规划模型适合反映决策过程的层次性。在本文中，典型的谈判组件与数学模型及其求解过程完美匹配。为此，设计了一种数学谈判机制，以在汽车供应链的两个梯队的分布式采购问题中最小化谈判者的成本。买方的成本为一期合同中的采购成本和短缺罚金。另一方面，供应商打算解决一个多期、多产品的生产计划，以最大限度地降低成本。这种机制使供应商的生产计划和订单分配保持一致，还通过考虑供应商的能力来支持与重要供应商的伙伴关系。这种情况已通过双层规划建模，其中买方充当领导者，供应商单独作为较低级别的追随者出现。针对这种非线性双层规划模型，提出了一种将粒子群优化算法与基于A搜索的启发式算法相结合的混合算法。该算法中嵌入了基于A搜索的启发式算法，根据接收到的PSO系统粒子确定的变量值，求解每个供应商的混合整数非线性规划子问题。供应商单独显示为较低级别的追随者。针对这种非线性双层规划模型，提出了一种将粒子群优化算法与基于A搜索的启发式算法相结合的混合算法。该算法中嵌入了基于A搜索的启发式算法，根据接收到的PSO系统粒子确定的变量值，求解每个供应商的混合整数非线性规划子问题。供应商单独显示为较低级别的追随者。针对这种非线性双层规划模型，提出了一种将粒子群优化算法与基于A搜索的启发式算法相结合的混合算法。该算法中嵌入了基于A搜索的启发式算法，根据接收到的PSO系统粒子确定的变量值，求解每个供应商的混合整数非线性规划子问题。