The authors extend the results of

*S. Kar, A. K. Bhunia* and

*M. Maiti* [Comput. Oper. Res. 28, 1315–1331 (2001;

Zbl 1024.90005)] for a deteriorating item having two separate warehouses, own (OW) and rented (RW), with time dependent demand (which is increasing at decreasing rate) and interval valued lead-time over finite time horizon. Inflation rate and time value of money are taken into account. Deterioration rate depends on the warehouse. Shortages are partially blocked. The replenishment cycle lengths are of equal length and in each cycle the stocks of RW are transported to OW in a continuous release pattern. Using the interval arithmetic, the objective function for profit is changed to the corresponding multi-objective functions. These functions are maximized and solved by the multi-objective genetic algorithm developed for this purpose. The results are illustrated numerically.