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An approximation-based approach for fuzzy multi-period production planning problem with credibility objective

机译：具有可信度目标的模糊多周期生产计划问题的基于近似方法

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This paper develops a fuzzy multi-period production planning and sourcing problem with credibility objective, in which a manufacturer has a number of plants or subcontractors. According to the credibility service levels set by customers in advance, the manufacturer has to satisfy different product demands. In the proposed production problem, production cost, inventory cost and product demands are uncertain and characterized by fuzzy variables. The problem is to determine when and how many products are manufactured so as to maximize the credibility of the fuzzy costs not exceeding a given allowable invested capital, and this credibility can be regarded as the investment risk criteria in fuzzy decision systems. In the case when the fuzzy parameters are mutually independent gamma distributions, we can turn the service level constraints into their equivalent deterministic forms. However, in this situation the exact analytical expression for the credibility objective is unavailable, thus conventional optimization algorithms cannot be used to solve our production planning problems. To overcome this obstacle, we adopt an approximation scheme to compute the credibility objective, and deal with the convergence about the computational method. Furthermore, we develop two heuristic solution methods. The first is a combination of the approximation method and a particle swarm optimization (PSO) algorithm, and the second is a hybrid algorithm by integrating the approximation method, a neural network (NN), and the PSO algorithm. Finally, we consider one 6-product source, 6-period production planning problem, and compare the effectiveness of two algorithms via numerical experiments.
机译：本文提出了一个具有可信度目标的模糊多周期生产计划和采购问题，其中制造商拥有许多工厂或分包商。根据客户预先设定的信誉服务水平，制造商必须满足不同的产品需求。在提出的生产问题中，生产成本，库存成本和产品需求是不确定的，并且具有模糊变量的特征。问题是确定何时制造多少产品，以使模糊成本的可信度最大化，而不超过给定的允许投资资本，并且这种可信度可以视为模糊决策系统中的投资风险标准。在模糊参数是相互独立的伽玛分布的情况下，我们可以将服务水平约束转换为它们的等效确定性形式。但是，在这种情况下，无法获得用于可信度目标的确切分析表达式，因此常规的优化算法无法用于解决我们的生产计划问题。为了克服这一障碍，我们采用一种近似方案来计算可信度目标，并对计算方法的收敛性进行处理。此外，我们开发了两种启发式求解方法。第一种是近似方法和粒子群优化（PSO）算法的组合，第二种是将近似方法，神经网络（NN）和PSO算法集成在一起的混合算法。最后，我们考虑一个6产品来源，6周期生产计划问题，并通过数值实验比较两种算法的有效性。

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