Production-inventory model with preservation technology investment under the effect of learning and shortages

The social and environmental changes make the preservation technologies very important for those organizations which deal with deteriorating items. To study the effect of preservation technologies we have established a inventory model with preservation technology investment for the deteriorating items. The rate of production is directly related to the demand which is depends on time. The partially backlogged shortages are permitted with exponential backlogging rate under the learning effect on set-up and production costs. Objective of present study is to find optimum value of total cost in two different cases. First one is when model ends with shortages and second one is when model starts with the shortages. At the end of this article a numerical example and sensitivity analysis is discussed. The calculation part is done with the help of mathematical software Mathematica7.