scholarly journals Optimal Maintenance of a Production System with Intermediate Buffers

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Constantinos C. Karamatsoukis ◽  
Epaminondas G. Kyriakidis
Keyword(s):  
Optimal Policy ◽  
Production System ◽  
Preventive Maintenance ◽  
Critical Level ◽  
Cost Structure ◽  
Raw Material ◽  
Production Unit ◽  
Production Inventory ◽  
Optimal Maintenance ◽  
Production Inventory System

We consider a production-inventory system that consists of an input-generating installation, a production unit andLintermediate buffers. It is assumed that the installation transfers the raw material to buffer and the production unit pulls the raw material from buffer We consider the problem of the optimal preventive maintenance of the installation if the installation deteriorates stochastically with usage and the production unit is always in operative condition. We also consider the problem of the optimal preventive maintenance of the production unit if the production unit deteriorates stochastically with usage and the installation is always in operative condition. Under a suitable cost structure and for given contents of the buffers, it is proved that the average-cost optimal policy for the first (second) problem initiates a preventive maintenance of the installation (production unit) if and only if the degree of deterioration of the installation (production unit) exceeds some critical level. Numerical results are presented for both problems.

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

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.

OPTIMAL POLICY FOR A PRODUCTION–INVENTORY SYSTEM WITH SETUP COST AND AVERAGE COST CRITERION

2012 ◽  
Vol 26 (4) ◽  
pp. 457-481 ◽  
Author(s):  
Xiuli Chao ◽  
Yifan Xu ◽  
Baimei Yang
Keyword(s):  
Optimal Control ◽  
Optimal Policy ◽  
Production Capacity ◽  
Control Policy ◽  
Inventory System ◽  
Setup Cost ◽  
Inventory Theory ◽  
Cost Rate ◽  
Production Inventory ◽  
Production Inventory System

One of the most fundamental results in inventory theory is the optimality of (s, S) policy for inventory systems with setup cost. This result is established under a key assumption of infinite ordering/production capacity. Several studies have shown that, when the ordering/production capacity is finite, the optimal policy for the inventory system with setup cost is very complicated and indeed, only partial characterization for the optimal policy is possible. In this paper, we consider a continuous review production/inventory system with finite capacity and setup cost. The demand follows a Poisson process and a demand that cannot be satisfied upon arrival is backlogged. We show that the optimal control policy has a very simple structure when the holding/shortage cost rate is quasi-convex. We also develop efficient algorithms to compute the optimal control parameters.

Modeling condition-based maintenance and replacement strategies for an imperfect production-inventory system

2016 ◽  
Vol 232 (10) ◽  
pp. 1858-1871 ◽  
Author(s):  
Guoqing Cheng ◽  
Binghai Zhou ◽  
Faqun Qi ◽  
Ling Li
Keyword(s):  
Product Quality ◽  
Preventive Maintenance ◽  
Inventory System ◽  
Single Type ◽  
Maintenance Cost ◽  
Total Cost ◽  
Penalty Cost ◽  
Imperfect Production ◽  
Production Inventory ◽  
Production Inventory System

In this article, we consider an imperfect production-inventory system which produces a single type of product to meet the constant demand. The system deteriorates stochastically with usage and the deterioration process is modeled by a non-stationary gamma process. The production process is imperfect which means that the system produces some non-conforming items and the product quality depends on the degradation level of the production system. To prevent the system from deteriorating worse and improve the product quality, preventive maintenance is performed when the level of the system degradation reaches a certain threshold. However, the preventive maintenance is imperfect which cannot restore the system as good as new. Hence, the aging system will be replaced by a new one after some production cycles. The preventive maintenance cost, the replacement cost, the production cost, the inventory holding cost and the penalty cost of lost sales are considered in this article. The objective is to minimize the total cost per unit item which depends on two decision variables: the preventive maintenance threshold and the time at which the system is replaced. We derive the explicit expression of the total cost per unit item and the optimal joint policy can be obtained numerically. An illustrative example and sensitivity analysis are given to demonstrate the proposed model.

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