Due to the disadvantages of economic scale and industry status, the purchase order of a small and medium enterprise (SME) cannot often reach the minimum order quantity set by a strong supplier, and it is difficult for an SME to make vertical purchase cooperation with strong suppliers. Therefore, a joint procurement model is proposed in the horizontal cooperation among SMEs. The model considers multiple objective and multiple realistic constraints. To solve the proposed multi-objective model, the improved genetic algorithm is designed to determine the optimal purchased quantity in SMEs. Finally, a numerical experiment is conducted to validate the feasibility of the proposed model and algorithm. As the results illustrated, the joint procurement model and the improved genetic algorithm are efficient for SMEs under the weak procurement environment. The gaps among the optimal Pareto solutions are relatively small in contrast to the initial solution. Besides, a sensitivity analysis is also performed to prove that the algorithm is effectively solving the real-world joint procurement problem.

由于经济规模和行业地位的不利，中小企业的采购订单往往无法达到强大供应商设定的最小订购数量，而中小企业很难与强大的供应商进行纵向采购合作。供应商。因此，在中小企业之间的横向合作中提出了联合采购模式。该模型考虑了多个目标约束和多个现实约束。为了解决所提出的多目标模型，设计了改进的遗传算法来确定中小企业的最优采购量。最后，进行了数值实验，验证了所提模型和算法的可行性。结果表明，联合采购模型和改进的遗传算法对于弱采购环境下的中小企业是有效的。与初始解决方案相比，最优Pareto解决方案之间的差距相对较小。此外，还进行了敏感性分析，以证明该算法有效地解决了现实世界中的联合采购问题。