Multi-Objective Two Echelon Supply Chain Inventory Model with Lot Size and Customer Demand Dependent Purchase Cost and Production Rate Dependent Production Cost

Abstract

This paper develops an integrated production inventory model for a two echelon supply chain consisting of one manufacturer and one retailer. Purchase cost for the manufacturer is dependent on inventory lot size, production cost of the manufacturer is dependent on production rate. Purchase cost of the retailer is dependent on demand rate of the customer. Idle time cost has been considered. Multi-item has been considered in this supply chain inventory model. Average cost in integrated inventory model has been calculated per unit time. The formulated problem has been solved by various techniques like as Fuzzy programming technique with hyperbolic membership functions (FPTHMF), Fuzzy non-linear programming technique (FNLP) and Fuzzy additive goal programming technique (FAGP),  weighted Fuzzy non-linear programming technique (WFNLP) and weighted Fuzzy additive goal programming technique (WFAGP). A numerical example is provided to justify the proposed model. Finally graphical illustrations are considered and its sensitivity analysis is provided to test feasibility of the model.