Gutiérrez Michael
Department of Business and Economics, Neu-Ulm University of Applied Sciences (HNU), Wileystr. 1, 89231 Neu-Ulm, Germany.
Heliyon. 2021 Feb 20;7(2):e06096. doi: 10.1016/j.heliyon.2021.e06096. eCollection 2021 Feb.
The purpose of multi-level contribution margin accounting in cost accounting is to analyze the profitability of products and organizational entities with appropriate allocation of fixed costs and to provide relevant information for short-term, medium- and longer-term decisions. However, the conventional framework of multi-level contribution margin accounting does not usually incorporate a mathematical optimization method that simultaneously integrates variable and fixed costs to determine the best possible product mix within hierarchically structured organizations. This may be surprising in that operations research provides an optimization model in the form of the fixed-charge problem (FCP) that takes into account not only variable costs but also fixed costs of the activities to be planned. This paper links the two approaches by expanding the FCP to a multi-level fixed-charge problem (MLFCP), which maps the hierarchical decomposition of fixed costs in accordance with multi-level contribution margin accounting. In this way, previously hidden optimization potentials can be made visible within the framework of multi-level contribution margin accounting. Applying the linkage to a case study illustrates that the original assessment of profitability gained on the sole basis of a multi-level contribution margin calculation might turn out to be inappropriate or even inverted as soon as mathematical optimization is utilized: products, divisions, and other reference objects for fixed cost allocation, which at first glance seem to be profitable (or unprofitable) might be revealed as actually unprofitable (or profitable), when the multi-level contribution margin calculation is linked to the MLFCP. Furthermore, the proposed concept facilitates assessment of the costs of an increasing variant diversity, which also demonstrates that common rules on how to interpret a multi-level contribution margin calculation may have to be revised in some cases from the viewpoint of optimization. Finally, the impact of changes in the fixed cost structure and other parameters is tested via sensitivity analyses and stochastic optimization.
成本会计中多级边际贡献会计的目的是通过合理分配固定成本来分析产品和组织实体的盈利能力，并为短期、中期和长期决策提供相关信息。然而，传统的多级边际贡献会计框架通常不包含一种数学优化方法，该方法能同时整合可变成本和固定成本，以在层次结构组织中确定最佳的产品组合。这可能令人惊讶，因为运筹学提供了一种固定费用问题（FCP）形式的优化模型，该模型不仅考虑可变成本，还考虑计划活动的固定成本。本文通过将FCP扩展为多级固定费用问题（MLFCP）来连接这两种方法，MLFCP根据多级边际贡献会计对固定成本的层次分解进行映射。通过这种方式，可以在多级边际贡献会计框架内发现以前隐藏的优化潜力。将这种联系应用于案例研究表明，一旦使用数学优化，仅基于多级边际贡献计算得出的原始盈利能力评估可能会变得不合适甚至颠倒：乍一看似乎盈利（或不盈利）的产品、部门和其他固定成本分配参考对象，在将多级边际贡献计算与MLFCP联系起来时，可能会被揭示为实际上不盈利（或盈利）。此外，所提出的概念有助于评估不断增加的产品多样性成本，这也表明，从优化的角度来看，在某些情况下可能需要修订关于如何解释多级边际贡献计算的通用规则。最后，通过敏感性分析和随机优化测试固定成本结构和其他参数变化的影响。
