Optimal production rate and production stopping time for perishable seasonal products with ramp-type time-dependent demand (Q606591)

This paper develops a production-inventory model for perishable seasonal products, where the demand function is time-dependent and of ramp-type, in particular, it is of increasing-steady-decreasing type. It is assumed that the length of the season is fixed and that inventory deteriorates at a uniform rate. In addition, a specific fraction of the produced items is defective and not re-worked, and shortages are not allowed. For this problem, the optimal production rate and the production stopping time are determined. It is proved that, when the production rate is demand dependent, production must be stopped in the final phase of demand to earn a maximum profit. Moreover, it is shown that, if the production is stopped in earlier time phases of demand, the production rate increases to satisfy the demand for the time horizon. A numerical example is presented to illustrate the analytical findings.