An inventory model for ameliorating and deteriorating items with stock and price dependent demand and time dependent holding cost with preservation technology investment (Q2073503)

Summary: An inventory model is developed for ameliorating and deteriorating items considering stock and price dependent demand with completely backlogged shortages. Fast growing animals such as chicken, duck, etc. when are small in size and stock are purchased and raised in the farm. Stock and value of these items increases because of their high growth rate while stock may reduce due to death or other factors. Amelioration rate is assumed to follow Weibull distribution. Deterioration rate is considered to be constant and is controlled through an investment in preservation technology. The objective is to minimise the total cost per unit time and determine optimal selling price, preservation technology investment, time of occurrence of maximum inventory and shortage. To illustrate our model, some numerical examples are solved using an algorithm while convexity is shown graphically. Sensitivity analysis is performed to study the impact of variation of the parameters on optimal solution.