An optimization problem is formulated in this study to optimize the total investment in education, apprenticeship, and financial incentive to address the skilled labor shortages in the construction industry. Three separate mathematical models, namely linear programming (LP) models, fuzzy mathematical models, and structural equation models are compared for their accuracy, robustness, and ease of application in solving the optimization problem. LP models are found to be the best fit for solving the optimization problem. Relevant data on construction budget and investment preferences in education, apprenticeship, and financial incentive are obtained through a survey questionnaire from construction firms engaged in commercial and residential construction. The survey response suggests that more apprentices lean toward electrical and plumbing over carpentry due to the higher pay scale in both trade fields, thus reducing the skilled labor shortage in both areas when compared to carpentry. The optimization results indicate that apprenticeship and financial incentives play a significant role in reducing short-term labor shortages. Education, on the other hand, plays a significant role in reducing the labor shortage in the long run. A sensitivity analysis shows different optimal investments for the optimal allocation of labor shortages to be overcome by investments in education, apprenticeship, and financial incentives. A more robust analysis using additional data can be performed in future works to further investigate the relative effectiveness of investments in education, apprenticeship, and financial incentives in reducing skilled labor shortage.

本研究提出了一个优化问题，以优化教育、学徒和财政激励方面的总投资，以解决建筑行业熟练劳动力的短缺问题。比较了三种独立的数学模型，即线性规划 (LP) 模型、模糊数学模型和结构方程模型在解决优化问题时的准确性、鲁棒性和易用性。LP 模型被发现最适合解决优化问题。通过对从事商业和住宅建筑的建筑公司进行调查问卷，获得了建筑预算和教育、学徒培训和财务激励方面的投资偏好的相关数据。调查结果表明，由于这两个行业的薪资水平较高，更多的学徒倾向于电气和管道工程，而不是木工，因此与木工相比，这减少了这两个领域熟练劳动力的短缺。优化结果表明，学徒制和经济激励在减少短期劳动力短缺方面发挥着重要作用。另一方面，从长远来看，教育在减少劳动力短缺方面发挥着重要作用。敏感性分析显示了通过教育、学徒和财政激励投资来克服劳动力短缺最优配置的不同最佳投资。在未来的工作中可以使用额外的数据进行更稳健的分析，以进一步调查教育、学徒和财政激励方面的投资在减少熟练劳动力短缺方面的相对有效性。