Multi-item inventory model of breakable items with stock-dependent demand under stock and time dependent breakability rate

Items made of glass, ceramic, etc. are normally stored in stacks and get damaged during the storage due to the accumulated stress of heaped stock. These items are known as breakable items. Here a multi-item inventory model of breakable items is developed, where demands of the items are stock dependent, breakability rates increase linearly with stock and nonlinearly with time. Due to non-linearity and complexity of the problem, the model is solved numerically and final decisions are made using Genetic Algorithm (GA). In a particular case, model is solved analytically as well as numerically and results are compared. Models are developed with both crisp and uncertain inventory costs. For uncertain inventory costs both fuzzy and stochastic parameters are considered. A chance constrained approach is followed to deal with simultaneous presence of stochastic and fuzzy parameters. Different numerical examples are used to illustrate the problem for different cases.