θTTθT

From Fig. 5, we can fi nd that dpT is increasing in θ when 0.068θ ≤ . When 0.068θ > , since the deterioration rate is so high that the manufacturer cannot satisfy the demand by self-producing. He has to buy products from spot markets in order to avoid shortage. From Fig. 7 and Fig.8, we can see that rT is decreasing in θ and rQ is increasing in θ when

Conclusions In this paper, we propose a production-inventory model for a deteriorating item with production disruptions. Here, we analyze this inventory system under different situations. We have showed that our method helps the manufacturer reduce the loss caused by production disruptions. In this study, the proposed model considers the deterioration rate as constant. In real life, we may consider the deterioration rate as a function of time, stock, and so on. This will be done in our future research.