Optimal Pricing and Ordering Policy for Two Echelon Varying Production Inventory System

The paper proposes a two-stage supply chain model for price sensitive demand in imperfect production system while manufacturer and supplier are the members of the chain. The supplier screens the raw materials first and supplies good materials to the manufacturer at a constant rate. The production rate varies randomly within a finite interval. The inventory cycle of the manufacturer starts with shortages and production and it finishes with shortages again, in which shortages are partially backlogged. We consider a mixture of LIFO (last in, first out) and FIFO (first in, first out) dispatching policies to fill the backlogged demand. Thus, the objective of the proposed paper is to determine the optimal ordering lot-size and selling price of the manufacturer such that the per unit average integrated expected profit of the supply chain model is maximized. A numerical example is provided to analyze and illustrate the behavior and application of the model. Finally, sensitivity analysis of the key parameters are presented to test feasibility of the model. 1. Introduction Nowadays, the production inventory management has absorbed a lot of interest, among the researchers as well as practitioners, because production process is one of the most important parts to the companies for their business strategy. In reality, manufacturing companies have been facing big challenges to adjust and control the proper production rate, considering the limitations of labor, machines, power, technology, raw materials, environment, and so forth. Careful production planning is necessary to enrich any businesses, otherwise companies may face overages or shortages of the products. In the increased globalization and competitive marketing system, it is main concern for the industries to find out marketing strategies in production process. Now, our aim is to study a supply chain model consisting of supplier and manufacturer incorporating the important factors: production, pricing, partial backlogging, dispatching policy, defective items, and so forth. Joint pricing and replenishment policy for deteriorating inventory, where demand decreases linearly with time and cost of items, was developed by Wee [1]. Abad [2] studied an optimal pricing and lot-sizing model under conditions of perishability and partial backordering. Salameh and Jaber [3] introduced a modified inventory model for imperfect quality items when using the EPQ/EOQ formulae. Hayek and Salameh [4] addressed a production inventory model where the production system was not perfect. They studied the effect of imperfect quality