A production inventory model with fuzzy coefficients using parametric geometric programming approach
- PDF / 313,925 Bytes
- 7 Pages / 595.276 x 790.866 pts Page_size
- 30 Downloads / 203 Views
ORIGINAL ARTICLE
A production inventory model with fuzzy coefficients using parametric geometric programming approach G. S. Mahapatra • T. K. Mandal • G. P. Samanta
Received: 11 October 2010 / Accepted: 12 April 2011 / Published online: 6 May 2011 Springer-Verlag 2011
Abstract In general, cost constant parameters of inventory or production models are not rigid in real life rather these are imprecise in nature. In this paper we have presented imprecise cost constant parameters for an economic production quantity model. The unit production cost of this economic production quantity model is demand and reliability dependent. The imprecise parameters of the production model are considered as fuzzy in nature. The fuzzy model is solved by fuzzy parametric geometric programming technique. Finally, production model is numerically illustrated using fuzzy parametric geometric programming. Keywords Economic order quantity Production Inventory Fuzzy set Parametric geometric programming
1 Introduction In general the classical inventory problems are designed by considering that the demand rate and the unit price of item is constant and independent in nature [1–3]. Practically, unit price and demand rate of an item may be related to each other. When the demand of an item is high, an item is produced in large numbers and the fixed costs of production are spread over a large number of items. Hence the unit cost of the item decreases, i.e., the unit price of an item inversely relates to the demand of that item. So, demand G. S. Mahapatra (&) Department of Mathematics, Siliguri Institute of Technology, P.O.-Sukna, Siliguri 734009, West Bengal, India e-mail: [email protected] T. K. Mandal G. P. Samanta Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah 711103, West Bengal, India
rate of an item may be considered as a decision variable. Economic order quantity (EOQ) model with production process reliability consideration has been discussed by several researchers [4–13]. Geometric programming (GP) method [14] is an efficient method to solve a non-linear programming problem. It has certain advantages over the other optimization methods. The advantage of GP is that is usually much simpler to work with the dual than the primal. GP method is now widely used to solve the optimization problem in inventories. Ata et al. [15] and Chen [16] developed some inventory problems and solved by GP method. Worral and Hall [17] analyzed the inventory models with some constraints and solved by GP technique. Abou-el-ata and Kotb [18] and Hariri and Abou-el-ata [19] gave a new idea on GP to solve multi-item inventory problems. Jung and Klein [20] formulated the economic production quantity (EPQ) problem and solved using GP method. Jung and Klein [21] presented three total cost minimization EOQ based inventory problems are modeled and analyzed using GP techniques. Jung and Klein [22] establish and analyze three EOQ based inventory models under profit maximization via GP techniques. Liu [23] studies econo
Data Loading...
