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This paper analyses and provides insights into the time buffer size of a capacity constrained resource (CCR) with multiple parallel processes in the context of the Theory of Constraints (TOC). We describe the CCR as a finite multi-server queue, where the appropriate capacity size (including the CCR’s time buffer and servers) would protect the CCR from becoming idle with a certain probability, denoted as the accepted idle rate. We then formulate a constrained optimization model, where the key decision variable is the capacity size, and the objective is to maximize the net profit, defined in the TOC as the difference of throughput and operating expenses. We also prove that the model has a unique optimal solution for the capacity size. For the in-depth understanding of the model’s optimal solutions, we conduct a sensitivity analysis of the optimal capacity size and net profit based on variations of the model parameters, i.e., accepted idle rate, arrival rate, processing (service) rate, and cost characteristics. This sensitivity analysis proves the existence of important thresholds for these model parameters, and we explain the behavior of the optimal capacity size and net profit depending on the values of these parameters above or below their respective thresholds. |
