Optimal production rate and production stopping time for perishable seasonal products with ramp-type time-dependent demand

Determination of optimal production rate and production stopping time for perishable seasonal product, which experiences increasing-steady-decreasing type time dependent demand over the sales season, is essential because the product becomes obsolete or its usefulness decreases at the end of the season. In this paper, we develop an inventory model to address this issue by assuming that the demand is a time-dependent ramp-type function and on hand inventory deteriorates at a uniform rate. Length of the season is fixed and production rate depends on demand rate. A small fraction of produced items is defective and is not reworked. Shortages are not allowed. The profit function is formulated and its' concavity is verified. Some interesting results about production rate and production stopping time are derived analytically for better coordination between excessive stock and shortages. A numerical example is presented and sensitivity analysis of the model is carried out.