The Optimization of a Virtual Dual Production-Inventory System under Dynamic Supply Disruption Risk

Major events such as the COVID-19 pandemic, Olympic Games, and G20 Summit bring about supplier disruption risks and challenges to supply chain management. To help deal with these risks, a virtual dual-sourcing production-inventory system can be deployed. In this paper, we study such a system which consists of a raw material supplier, a manufacturer, and a virtual dual-sourcing contingency supplier. The manufacturer needs to determine the production, procurement, and inventory plan of raw materials. When its supplier is interrupted, the manufacturer may need to adjust the production and inventory plan and work with the contingency supplier. We develop a system dynamics method to simulate the operations in this production-inventory system to identify the approximately optimal order-up-to-level inventory policies. We find that the virtual dual production-inventory strategy can be the optimal contingency policy to deal with supplier dynamic disruption risks. Furthermore, for disruption risk with low frequency and long duration, the manufacturer should increase the safety inventory level before the disruption. Otherwise, it should increase the safety inventory level in every cycle.

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Optimal Maintenance of a Production-inventory System With Continuous Repair Times and Idle Periods

International Journal of Applied Mathematics and Informatics ◽

10.46300/91014.2020.14.5 ◽

2020 ◽

Vol Volume 14 ◽

Keyword(s):

Preventive Maintenance ◽

Average Cost ◽

Inventory System ◽

Control Limit ◽

Raw Material ◽

Production Unit ◽

Numerical Examples ◽

Long Run ◽

Production Inventory ◽

Production Inventory System

In this paper two similar models for the maintenance of a production-inventory system are considered. In both models, an input generating installation supplies a buffer with a raw material and a production unit pulls the raw material from the buffer. The installation in the first model and the production unit in the second model deteriorate stochastically over time and the problem of their optimal preventive maintenance is considered. In the first model, it is assumed that the installation, after the completion of its maintenance, remains idle until the buffer is evacuated, while in the second model, it is assumed that the production unit, after the completion of its maintenance, remains idle until the buffer is filled up. The preventive and corrective repair times of the installation in the first model and the preventive and corrective repair times of the production unit in the second model are continuous random variables with known probability density functions. Under a suitable cost structure, semi-Markov decision processes are considered for both models in order to find a policy that minimizes the long-run expected average cost per unit time. A great number of numerical examples provide strong evidence that, for each fixed buffer content, the average-cost optimal policy is of control-limit type in both models, i.e. it prescribes a preventive maintenance of the installation in the first model and a preventive maintenance of the production unit in the second model if and only if their degree of deterioration is greater than or equal to a critical level. Using the usual regenerative argument, the average cost of the optimal control-limit policy is computed exactly in both models. Four numerical examples are also presented in which the preventive and corrective repair times follow the Exponential, the Weibull, the Gamma and the Log-Normal distribution, respectively.

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