| Article ID: | iaor201525885 |
| Volume: | 22 |
| Issue: | 3 |
| Start Page Number: | 342 |
| End Page Number: | 365 |
| Publication Date: | Mar 2015 |
| Journal: | International Journal of Operational Research |
| Authors: | Dey Jayanta Kumar, Kar Samarjit, Maity K, Hazari Samar |
| Keywords: | management, advertising, fuzzy sets, production, inventory, control, supply & supply chains, combinatorial optimization, quality & reliability |
In this study, a problem for advertising policy and an imperfect production for single item are formulated with reliability parameter over a finite time horizon. The advertisement and production rates are function of time which are taken as control variables. In a competitive market on long run business, the demand face the depreciation of sale which is at a constant rate and decrease the demand rate but the advertisement policy has the positive effect to the demand rate. The reliability of the production process is an important factor to improve the quality of product and decrease the defective rate. So the quality of the product and advertisement policy play an important role to capture the customers in a competitive market. The selling price, holding cost and advertisement cost are bi‐fuzzy in nature and using bi‐fuzzy technique, the problem is converted into equivalent crisp problem and solved using Pontryaginn's maximum principle and generalised reduced gradient (GRG) method. Finally, numerical experiment and graphical representation are provided to illustrate the model.