Aims:
This article analyzes an inventory system for deteriorating items. The demand is quadratic function of time and is dependent on time, price and advertisement. Shortages are allowed and partially backlogged.
Background:
Demand and pricing are the two most crucial factors in inventory policy for any business to be successful. In today’s era of competitive circumstances, any product is promoted through advertisement, which plays a vital role in changing the demand pattern among the community. The marketing and demonstration of an item by time-to-time with fashionable advertisements through well-known media such as TV, radio, newspaper, magazine, etc. However, this idea is not always true for some goods like wheat, vegetables, fruits, food grains, medicines and other perishable goods due to their deteriorating nature and this in turn decreases demand for such goods. Deterioration may define as decay, damage, spoilage, evaporation, obsolescence, pilferage. Hence, deterioration effect is a major part in inventory control theory. So in this article demand rate is considered to be a function of selling price, time and occurrence of advertisement instantaneously.
Objective:
A solution procedure is obtained to find optimal number of price changes and optimal selling price to maximize the total profit.
Method:
Classical Optimization.
Result:
From the sensitivity analysis table, it can be seen that the optimal profit is highly sensible to advertisement coefficient and purchase cost. With an increment in rate of deterioration, selling price decreases. Scale demand has reasonable effect on cycle time and selling price. When the value of increase, the cycle length and profit goes on decreasing. Growth in profit is observed if we increase parameter b, higher will be the profit. Price elasticity is sensible parameter with respect to selling price. If backlogging rate increases, the profit will decreases. The inventory parameters holding cost, back order cost and lost sale cost have marginal effect on total profit.
Conclusion:
In this article, an inventory model is proposed for deteriorating items with variable demand depends upon the advertisement, selling price of the item and time. Shortages are allowed and partially backlogged and backlogging rate depends on the waiting time for the next replenishment. From this article, we can conclude that the parameters are insensible with respect to optimal profit, cycle time and selling price and rest of the parameters have practical output on total profit.
