International Journal of Research and Scientific Innovation (IJRSI) | Volume III, Issue VII, July 2016 | ISSN 2321–2705 www.rsisinternational.org Page 43 Reliable EMQ Model with Price and Seasonal Time Dependent Demand W. Ritha 1 , S. Sutha 2 1 Holy Cross College( Autonomous ) ,Tiruchirapalli – 620 002. 2 Government Arts College, Trichirapalli – 620 022. Abstract: 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. Key words: Inventory – Product Reliability – EMQ – Profit Maximization - Price and Seasonal Time Dependent Demand . I. INTRODUCTION he numerous research efforts during the past several decades have been undertaken to develop the basic economic manufacturing quantity(EMQ) by integrating various assumptions such that the model more suitable to the real production process in all the situations. Especially, the demand of the seasonal products is vary with time and price. The production before the season to meet the unexpected demand may cause to spoilage as it cannot be stored till the particular time arises or it cannot be perfectly estimated the demand. As a result, firm faces the problem of determining the model for the production of seasonal items, estimating the reliability of the factors of production to undertake the orders from the customers, budgeting the costs to be incurred to set up the EMQ model, analyzing the profits during the particular season and fluctuation of variables relating to the production and supply the items. Hence the manufacturer establishes suitable production process. Markov Process were presented by Rishel and Olsder and Suri, Porteus analysed the imperfect production process relating to quality and the lot size and evaluated an optimal investment in the process of quality improvement and the set up cost reduction.. Gronevelt discussed an inventory model with an optimal production lot size and a safety stock level. They considered a probalistic distributed repair time and an exponentially distributed failure time. Sarkar et al. discussed on inventory model for the variable reliability. They used Kuhn-tucker method to find the optimal solution for the reliability, the production lot size. The inventory models concentrating on seasonal products can be classified into three main types of models according to their demand characteristic; stock-dependent demand, time-dependent demand and price-dependent demand. In this paper, the last two demand patterns, we refer the readers to Urban for a review of inventory models with stock-dependant demand. In the classical EOQ model, demand is assumed to be constant. However, in reality, demand for a product may vary with the time and price. Since Silver and Meal proposed a heuristic solution to determine lot size quantities for the general case of a time-dependent demand, numerous inventory control papers have investigated the time- dependent demand pattern. In this direction, an inventory model with planned shortages and price-dependent demand was discussed by Burwell et at. An optimal and heuristic replenishment model for deteriorating item with an exponentially time-varying demand was derived by Hariga and Bankherour. Datta and Pal discussed an inventory model with both price and stock dependent demand under a finite time horizon. Papchristos and Skouri developed an inventory model for deteriorating items with some quantity discounts, pricing and time-dependent partial backlogging. You developed some different types of inventory policies with price and time dependent demand. An economic production quantity model for deteriorating items with price and stock-dependent demand T