Financial flows are one of the three majors in a Supply Chain (SC). Ignoring financial flows, regardless of the quality of freight transport and information, could lead the organization to a state of bankruptcy, which is a situation directly resulting from a lack of control over financial inputs/outputs. This study proposes a multi-product mathematical model, which makes it possible to choose among suppliers, manufacturing sites, distribution centres, retailers, and transportation vehicles. The purpose of the model is to integrate physical and material dimensions to maximize net corporate profits through inbound and outbound financial flows; it involves payment mechanisms between the financial and physical flows through maximizing the cash flows of manufacturing sites and suppliers, as two conflicting objectives that must consider the reciprocal effects of their decisions. These objectives are calculated by subtracting costs from the revenue; this process, of course, will ultimately result in an optimization of the organization’s financial flow. To solve the proposed mathematical model, the study relies on two algorithms, namely Particle Swarm Optimization (PSO) and Imperialist Competition Algorithm (ICA). The sample under investigation is solved separately using the three algorithms, and results are then compared. The observations of the study reveal the better performance of PSO.

中文翻译：

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基于输入输出网络流的金融供应链分支和切割/元启发式优化：调查伊朗矫形鞋

资金流是供应链 (SC) 中的三大支柱之一。无论货物运输和信息的质量如何，忽视资金流都可能导致组织破产，这是由于缺乏对财务投入/产出的控制而直接导致的情况。本研究提出了一个多产品数学模型，可以在供应商、制造场所、配送中心、零售商和运输车辆之间进行选择。该模型的目的是整合实体和物质维度，通过流入和流出的资金流来最大化企业的净利润；它涉及通过最大化制造场所和供应商的现金流量来实现财务流和实物流之间的支付机制，作为两个相互冲突的目标，必须考虑其决策的相互影响。这些目标是通过从收入中减去成本来计算的；当然，这个过程最终会导致组织财务流动的优化。为了解决所提出的数学模型，该研究依赖于两种算法，即粒子群优化 (PSO) 和帝国主义竞争算法 (ICA)。使用三种算法分别求解所研究的样本，然后比较结果。该研究的观察结果表明 PSO 的性能更好。该研究依赖于两种算法，即粒子群优化 (PSO) 和帝国主义竞争算法 (ICA)。使用三种算法分别求解所研究的样本，然后比较结果。该研究的观察结果表明 PSO 的性能更好。该研究依赖于两种算法，即粒子群优化 (PSO) 和帝国主义竞争算法 (ICA)。使用三种算法分别求解所研究的样本，然后比较结果。该研究的观察结果表明 PSO 的性能更好。