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Production and work force assignment problem: A bi-level programming approach

机译：生产和劳动力分配问题：双层编程方法

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摘要

A home supplies manufacturer manufactures many products and each requires workers with different skills. The manufacturer invites a contracting company to supply workers with different skills for each phase of the production process. The problem becomes a production and work force assignment problem, which can be considered as a bi-level programming problem. The supplier, as the upper decision maker, aims to achieve the objective of maximizing gross revenue by making decisions concerning production levels. The contracting company, as the lower-level decision maker, regards the target to be maximizing profit by making decisions concerning the number of assigned workers. There are uncertainties during the production process and therefore the problem has random fuzzy coefficients. To deal with the uncertainties, a general linear bi-level model with random fuzzy variables is introduced and several properties and crisp equivalents are proposed. Then an interactive programming method is applied to deal with the derived expected bi-level programming problem; after several iterations, the interactive solutions converge to the optimal one. Lastly, a numerical example is also presented to demonstrate the proposed optimization methods.
机译：一家家庭用品制造商生产许多产品，每个产品都需要具有不同技能的工人。制造商邀请承包公司在生产过程的每个阶段为工人提供不同的技能。该问题成为生产和劳动力分配问题，可以认为是双层编程问题。供应商作为最高决策者，旨在通过做出有关生产水平的决策来实现使总收入最大化的目标。订约公司作为下级决策者，认为目标是通过制定与分配的工人数量有关的决策来实现利润最大化。生产过程中存在不确定性，因此该问题具有随机的模糊系数。为了解决不确定性，引入了带有随机模糊变量的一般线性双层模型，并提出了一些性质和清晰的等价物。然后采用交互式编程方法处理导出的期望双层编程问题。经过几次迭代后，交互式解决方案收敛到最佳解决方案。最后，通过数值算例说明了所提出的优化方法。

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