An inventory system using preservation technology investment for ameliorating and deteriorating items with ramp-type demand dependent on price and time and partial backlogging

This article describes an inventory model developed for ameliorating items considering ramp type demand dependent on price and time with partially backlogged shortages. Ameliorating items such as livestock are raised in the farm when their size and quantity are small. The quantity and size of these items increase due to their high growth rate. However, their quantity may decrease due to certain diseases or death. Amelioration rate is described by Weibull distribution. Preservation technology is adopted to reduce the deterioration effect. Ramp type demand results in two possible cases, for which two different models were developed. Our goal is to estimate optimal preservation technology cost, selling price and the time at which maximum inventory and shortage occurs while total cost is minimised. Some numerical examples for two different cases are solved. Impact of the parameters on optimal solution is analysed through sensitivity analysis while the results obtained are discussed accordingly.