In this paper, an attempt is made to develop two inventory models for deteriorating items with variable demand dependent on the selling price and frequency of advertisement of items. In the first model, shortages are not allowed whereas in the second, these are allowed and partially backlogged with a variable rate dependent on the duration of waiting time up to the arrival of next lot. In both models, the deterioration rate follows three-parameter Weibull distribution and the transportation cost is considered explicitly for replenishing the order quantity. This cost is dependent on the lot-size as well as the distance from the source to the destination. The corresponding models have been formulated and solved. Two numerical examples have been considered to illustrate the results and the significant features of the results are discussed. Finally, based on these examples, the effects of different parameters on the initial stock level, shortage level (in case of second model only), cycle length along with the optimal profit have been studied by sensitivity analyses taking one parameter at a time keeping the other parameters as same.

In this paper, a single item deterministic inventory model with two separate warehouses called
owned warehouse/show-room (OW) and rented warehouse (RW) is developed. The proposed
model of this paper also considers a realistic assumption regarding the storage capacity of the
rented warehouse. Demand is a function of selling price, advertisement of an item and
displayed inventory level in OW. The stocks of RW are shipped to OW under bulk release
pattern where shortages are not allowed. We discuss different scenarios of the proposed model
to address relative size of stock dependency parameters and the capacity of owned warehouse.
For each scenario, the corresponding problem is formulated as a constrained mixed integer
nonlinear programming problem with three integer and two non-integer variables and a real
coded genetic algorithm (RCGA) is developed to solve the resulted problem. The proposed
model of the paper is also examined using some numerical examples and sensitivity analysis is
performed.