Developing a Mathematical Negotiation Mechanism for a Distributed Procurement Problem and a Hybrid Algorithm for its Solution
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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.
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