Two-warehouse inventory model of deteriorating items with three-component demand rate and time-proportional backlogging rate in fuzzy environment

A finite time horizon inventory problem for a deteriorating item having two separate warehouses, one with an own warehouse (OW) of finite dimension and the other with a rented warehouse (RW), is developed in fuzzy environment. Due to different preserving facilities and storage environment, inventory holding cost is considered to be different in different warehouses. The demand rate of item depends on the selling price and is displayed stocked level in own warehouse. Shortages are allowed and backlogged them partially, which depends on the duration of stock out. The stocks of RW are transported to OW in continuous release pattern. Due to impreciseness in nature, total revenue and shortage cost are assumed to be imprecise in nature too. By using the fuzzy goal programming method, multi-objective problem is converted into single objective function. The model is illustrated numerically and the results are presented in tabular form.