Deterministic inventory model with two levels of storage, a linear trend in demand and a fixed time horizon
A deterministic inventory model is developed for a single item having two separate storage facilities (owned and rented warehouses) due to limited capacity of the existing storage (owned warehouse) with linearly time-dependent demand (increasing) over a fixed finite time horizon. The model is formulated by assuming that the rate of replenishment is infinite and the successive replenishment cycle lengths are in arithmetic progression. Shortages are allowed and fully backlogged. As a particular case, the results for the model without shortages are derived. Results are illustrated with two numerical examples. Throughout the world, the production of food grains is periodical. Normally, in countries where state control is less, the demand of essential food grains is lowest at the time of harvest and goes up to the highest level just before the next harvest. This phenomenon is very common in developing third world countries where most of the people are landless or marginal farmers. At the time of harvest, they share some grain/product with landowners and as soon as the small inventory is exhausted, they are forced to buy food grains from the open market. As a result, demand for food grains increases with time in a period along with the number of the people whose initial stock of food grains gets exhausted. In this paper, a two-storage inventory model with time-dependent demand and fixed time horizon is developed and solved by a mathematical programme based on gradient method. This methodology of model development and its solution are quite general and it can be applied to inventory models of any product whose production is periodical and demand increases linearly with time.
finite time horizon inventory management two storage deterioration