Optimal lot size model for deteriorating items with demand rate dependent on displayed stock level (DSL) and partial backordering

In this paper, we consider the problem of determining the lot size of a single deteriorating item with the demand rate dependent on displayed stock level, selling price of an item and frequency of advertisement in the popular electronic and print media, also through the sales representatives. Shortages, if any, are allowed and partially backlogged with a variable rate which depends on the duration of waiting time up to the arrival of next lot. Here, the transportation cost for replenishing the goods is considered explicitly and the storage capacity of the showroom/shop is assumed to be limited (finite). According to the relative size of the stock level dependency demand parameters and the storage capacity of the showroom/shop, different scenarios with sub scenarios have been mentioned and solved with the help of GRG (generalised reduced gradient) method and the computational procedure. The convexity analysis is done by showing the average profit function in each case as pseudo concave. To illustrate the results and their significant features, a numerical example is given. Finally, to study the effect of changes of demand parameters, deterioration, backlogging parameters and mark-up rate on the maximum initial stock level, shortage level, frequency of advertisement per cycle along with the maximum average profit are presented numerically.