A deterministic fluid model for production and energy mode control of a single machine

IF 9.8 1区 工程技术 Q1 ENGINEERING, INDUSTRIAL International Journal of Production Economics Pub Date : 2024-09-30 DOI:10.1016/j.ijpe.2024.109418
Barış Tan , Oktay Karabağ
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Abstract

Improving machines’ energy efficiency through dynamic energy mode control to meet demand requirements with minimal energy consumption is a promising approach. This study considers a machine operating in working, idle, off, and warmup energy modes with different energy consumption in each mode. A deterministic fluid model is developed to analyze an energy mode control policy that determines when to keep the machine working, off or idle, and switch to other modes based on the inventory/backlog level to minimize the total energy, inventory, and backlog costs. This approach facilitates the derivation of closed-form expressions for the optimal thresholds and the associated costs. This modeling approach allows us to prove that a policy that operates the machine between the working and off modes or the working and idle modes is always better than a hybrid policy that operates the machine in working, off, and idle modes simultaneously. We use the solution of the deterministic fluid model to propose an approximate policy for machines with stochastic production, warmup, and demand processes. We compare the results of the proposed approximation method with the optimal solution of a stochastic system where the production and warmup times are exponential and the demand inter-arrival times have Erlang distribution. The optimal solution for the stochastic system is determined by solving a Markovian Decision Process (MDP). Our numerical experiments show that the proposed approximation method predicts the optimal policy type for the stochastic case with a 89.3% accuracy, and the average error between the optimal cost and the cost obtained with the approximation method is 1.37% for 729 different cases tested. Furthermore, the computational efficiency of the proposed approximation is around 250 times better than the effort to determine the optimal policy using an MDP approach. We propose this approximation method where the control parameters are given in closed form as an easy-to-implement and effective policy to control energy modes to minimize the total energy, inventory, and backlog costs. Furthermore, we present the deterministic fluid modeling approach as a versatile approach to analyze energy mode control problems.
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用于单机生产和能源模式控制的确定性流体模型
通过动态能源模式控制提高机器能效,以最小的能耗满足需求,是一种很有前景的方法。本研究考虑了机器在工作、空闲、关闭和预热能源模式下的运行情况,每种模式下的能耗各不相同。本研究开发了一个确定性流体模型,用于分析能源模式控制策略,该策略可根据库存/积压水平决定何时保持机器工作、关闭或空闲,以及何时切换到其他模式,从而最大限度地降低总能耗、库存和积压成本。这种方法有助于推导出最佳阈值和相关成本的闭式表达式。通过这种建模方法,我们可以证明,在工作模式和关机模式之间或在工作模式和闲置模式之间运行机器的策略,总是优于同时在工作模式、关机模式和闲置模式下运行机器的混合策略。我们利用确定性流体模型的解法,为具有随机生产、预热和需求过程的机器提出了一种近似策略。我们将所提近似方法的结果与生产和预热时间为指数分布、需求到达时间为厄朗分布的随机系统的最优解进行了比较。随机系统的最优解是通过求解马尔可夫决策过程(MDP)确定的。我们的数值实验表明,所提出的近似方法预测随机情况下的最优策略类型的准确率为 89.3%,在 729 个不同的测试案例中,最优成本与用近似方法得到的成本之间的平均误差为 1.37%。此外,与使用 MDP 方法确定最优策略相比,所提近似方法的计算效率提高了约 250 倍。我们提出的这种近似方法以封闭形式给出了控制参数,是一种易于实施且有效的能源模式控制策略,可最大限度地降低总能源、库存和积压成本。此外,我们还提出了确定性流体建模方法,作为分析能源模式控制问题的通用方法。
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来源期刊
International Journal of Production Economics
International Journal of Production Economics 管理科学-工程:工业
CiteScore
21.40
自引率
7.50%
发文量
266
审稿时长
52 days
期刊介绍: The International Journal of Production Economics focuses on the interface between engineering and management. It covers all aspects of manufacturing and process industries, as well as production in general. The journal is interdisciplinary, considering activities throughout the product life cycle and material flow cycle. It aims to disseminate knowledge for improving industrial practice and strengthening the theoretical base for decision making. The journal serves as a forum for exchanging ideas and presenting new developments in theory and application, combining academic standards with practical value for industrial applications.
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