  In this paper, 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 (PSO) algorithm with a heuristic algorithm based on
A search is proposed. The heuristic A algorithm is embedded to solve the
mixed-integer nonlinear programming (MINLP) sub-problems for each supplier
according to the received variable values determined by PSO system particles
(buyer's request for quotations (RFQs)). The computational analyses have shown
that the proposed hybrid algorithm called PSO-A outperforms PSO-SA and
PSO-Greedy algorithms.
