Application of Generalized Hukuhara derivative approach in an economic production quantity model with partial trade credit policy under fuzzy environment

Abstract

In this present study, a production inventory model with partial trade credit is formulated and solved in fuzzy environment via Generalized Hukuhara derivative approach. To capture the market, a supplier offers a trade credit period to its retailers. Due to this facility, retailer also offers a partial trade credit period to his/her customer to boost the demand of the item. In practical life situation, demands are generally dependent upon time. Constant demand of an item varies time to time. In this vague situation, demands are taken as time dependent, where its constant part is taken as Left Right - type fuzzy number. In this paper, Generalized Hukuhara derivative approach is used to solve the fuzzy inventory model. Four different cases are considered by using Generalized Hukuhara-(i) differentiability and Generalized Hukuhara-(ii) differentiability. The objective of this paper is to find out the optimal time so as the total inventory cost is minimum. Finally the model is solved by generalized reduced gradient method. The proposed model and technique are illustrated by numerical examples. Some sensitivity analyses both in tabular and graphical forms are presented and the effects of minimum cost with respect to various inventory parameters are discussed.

Keywords

• Left-Right fuzzy number
• Generalized Hukuhara derivative approach
• Partial trade credit policy
• Deterioration
• α-cut
• Economic production quantity