This paper considers an economic order quantity (EOQ) inventory model for items with imperfect quality and shortage backordering under several styles of managerial leadership via lock fuzzy game theoretic approach. The decision maker (DM) controls several cost components by playing as Player 1 on the one side and the consumers who may accept/reject those items (unwilling to buy those commodities) stands as Player 2 on the other side. First of all, we develop a profit maximization backlogging EOQ model where the imperfect items are screened out batchwise. Because of the fuzzy flexibility of the model parameters we also develop a fuzzy mathematical model by considering the demand, all cost parameters, and other input parameters of the inventory system as triangular lock fuzzy numbers. Then we develop a 3 × 3 matrix game by applying a five‐stage leadership theory employing several key vectors in the model itself. The problem has been solved for crisp, general fuzzy models of several leadership styles also. Numerical results show that for a cooperative game, inventory profit function reaches its maximum rather than the noncooperative game by the use of proper keys. Finally, comparative study, sensitivity analysis, and graphical illustrations are made to justify the new approach.

中文翻译：

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模糊锁领导博弈方法下带延期交货的不完美质量EOQ模型的求解

本文通过锁定模糊博弈理论方法考虑了几种管理领导风格下质量不完美和缺货缺货的商品的经济订货量（EOQ）库存模型。决策者 (DM) 一方面通过扮演参与者 1 来控制多个成本组成部分，而可能接受/拒绝这些物品（不愿购买这些商品）的消费者则充当参与者 2。首先，我们开发了一个利润最大化积压 EOQ 模型，其中不完美的项目被分批筛选出来。由于模型参数的模糊灵活性，我们还通过将需求、所有成本参数和库存系统的其他输入参数考虑为三角锁模糊数来开发模糊数学模型。然后我们通过应用五阶段领导理论在模型本身中使用几个关键向量来开发一个 3 × 3 矩阵博弈。对于几种领导风格的清晰、通用的模糊模型，该问题也已得到解决。数值结果表明，对于合作博弈，库存利润函数通过使用适当的密钥而不是非合作博弈达到最大值。最后，通过比较研究、敏感性分析和图形说明来证明新方法的合理性。