Reliable EMQ Model with Price and Seasonal Time Dependent Demand

In this paper, an Economic Manufacturing Quantity (EMQ) is set up under the effect of reliability with demand based on the selling price and seasonal time. The profit of the concern is absolutely depending on the manufacturing of the number of products equalizing the seasonal demand created for the product in the particular time and on the other hand based on fixing the selling price matching with the requirements of the customers and the demand. Hence, the production process of time demanded products should be reliable for the same. Due to wear and tear, breakdown of the machine and etc.. as a result, the production system may be severely affected and changed to out-of-control state. The imperfect system may increase the production time and costs and also produces less quality items. At the additional fixed cost, the less quality items are reworked or restored. Therefore every production process should be perfect to meet the unexpected seasonal demand. The time based manufacturing process is the critical one to make the system perfect till the seasonal demand is fulfilled within short span of time. To reduce the increasing cost of production and to supply the products at the required quantity with perfect quality in the desirable time , we consider reliability as a decision variable along with the improvement of cost and the production cost as a function of reliability. The profit function is maximized in this model by applying Euler-Lagrange formula. The numerical example and graphical illustrations are given to point up the model.