This document is proposing an inventory system that is two-echelon for a supply chain that is coordinated and non-coordinated with one retailer and manufacturer. The retailer experiences the demand that is dependent on quadratic price and assumed to be price driven. Profit is completely dependent on the effectiveness of supply chain. Profit is the difference between the gross revenue and the total cost, whereas total cost includes carrying cost, transportation cost along with the cost of annual ordering. For a coordinated and non-coordinated supply chain, a mathematical model is being introduced. The primary objective of the mathematical model is to show the effective ordering quantity of the retailer, effective lot size of the producer, and the optimal quantity of the transportation from manufacturer to the retailer. The impact of the model parameters on objective function and variables is demonstrated with the help of a sensitivity analysis.

Dega Nagaraju

Department of Manufacturing Engineering

School of Mechanical Engineering

Vellore Campus

Narayanan S

Kumar B.K

Fulltext

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

Procedia Engineering

In this paper, a two echelon inventory system with a single-warehouse and single-retailer is considered. Mathematical model is developed for the retailer, warehouse and for the entire chain by incorporating the ordering/setup costs, carrying costs and transportation costs. Replenishment quantity at the retailer and the number of shipments from the warehouse to the retailer are considered as the decision variables. The objective of the proposed work is to demonstrate the optimality of centralised inventory &amp; shipment decisions and total relevant costs at the respective entities and the chain. Numerical example is considered and the model is solved using the computer program written in MATLAB. From the research findings, it is concluded that the percentage variation in optimality of total transportation cost of the supply chain is in decreasing order with respect to the increased ordering cost of the retailer and set-up cost of the manufacturer. Finally, few managerial implications are derived based on the sensitivity analysis.

Materials Today: Proceedings

Coordinated Two-Echelon Inventory Model for Optimal Inventory and Shipment Decisions under Exponential Price Dependent Demand

In this paper, a three-level supply chain with a single-manufacturer supplying a single kind of product to a single-distributor and then to a single-retailer is considered. Mathematical model is developed for optimal net revenue of the coordinated three-level supply chain by incorporating ordering cost, carrying cost and transportation cost. In the proposed model, the demand at the retailer is assumed as a cubic function of unit selling price. The objective of this work is to demonstrate the optimality of decision variables, i.e., inventory decisions and shipment policies for the respective entities under cubic price dependent demand. Also, it is aimed at demonstrating the optimal net revenue of the individual entities as well as the entire chain. For the purpose of numerical illustration, a computer program is written in MATLAB and the model is solved to determine the optimal values of decision variables and objective function. Also, sensitivity analysis is carried out and few managerial implications are derived.

Integrated Three-Level Supply Chain Model for Optimality of Inventory and Shipment Decisions under Cubic Price Dependent Demand

Background/Objectives: The objective of the work carried out in this paper is to present the literature based on different Supply Chain (SC) coordination mechanisms. Also, it is intended to explore various coordination models proposed by various researchers from the literature. Methods/Statistical Analysis: The literature is reviewed by considering 142 articles published from 2000 to till date and classified as two-level models and three-level models. All these articles are further discussed based on few coordination mechanisms such as trade credit, quantity discounts, revenue sharing contract and information sharing. In addition, the literature is reviewed on Vendor Managed Inventory and price dependent demand variations and the coordination issues are discussed. Findings: From the findings of this research, it is observed that sufficient volume of papers reported the coordination mechanism in a two-level SC. The number of papers discussing three-level SC coordination is few in number. Especially, in the perspective of trade credit and quantity discount option, very few articles are reported discussing coordination in a three-level SC. Further, it is also found that most of the articles addressed the coordination mechanism incorporating ordering and carrying costs. Very few articles addressed the implications of transportation cost in SC coordination mechanism. Application/Improvement: From the outcomes of this work, it is observed that study of the effect of space cost and advertisement cost on SC performance is highly significant. The use of simulation is highly emphasized as the activities of SC are becoming highly dynamic and challenging with the ever growing global competition.

Indian Journal of Science and Technology

Supply Chain Coordination Models: A Literature Review

This paper describes about the optimal values of the variables decision and function of objective of the entire supply chain under credit period with price dependent demand. Methods/Statistical Analysis: Initially the problem is framed with the expressions of the overall variable cost of the retailer and manufacturer is developed separately. Later the problem can be organised with the expressions of the overall variable cost of the retailer and manufacturer is developed for the entire supply chain as a function of retailers ordering costs and manufacturer set up costs along with carrying costs, and transportation cost. Findings: Numerical example is illustrated along with computer programme is solved in MATLAB. The model is solved for optimal values of cycle time, inventory level, number of shipments and the total annual cost of the individual entities and the entire supply chain. Also, the sensitivity analysis is carried out. From the research findings, it is evident that with credit period interpretation, the total annual cost is decreased with increase in trade credit. Applications/Improvements: Based on the research findings, it is concluded that total annual relevant cost of the supply chain becomes less, if the manufacturer permits to delay the retailer payments in more number of days.

Optimality of Cycle Time and Inventory Decisions in a Two Echelon Inventory System with Price Dependent Demand under Credit Period

In this paper, a three echelon inventory system with a single manufacturer supplying a single kind of a product to a single distributor and then to a single retailer, is considered. Mathematical model is developed for annual total relevant costs of the coordinated and non-coordinated supply chain. The novel idea of the proposed model is that the demand is a function of retailer's unit selling price, which in turn is a function of retailer's replenishment quantity with dependence factor. The objective of the model is to demonstrate the optimality of inventory decisions, shipment frequencies and total relevant costs with respect to dependence factor. Numerical illustration is carried out to demonstrate the optimality of replenishment decisions. Finally, managerial insights are inferred in selecting the optimal replenishment quantity and shipment frequency that minimises the total relevant cost of the supply chain.

International Journal of Logistics Systems and Management

Centralised and decentralised three echelon inventory model for optimal inventory decisions under price dependent demand

In recent Indian economic scenario, consumer price index (CPI) at the retailer is escalated very high where-as wholesale price index (WPI) at the manufacturer reduced very low, especially in the case of essential commodities. Under these circumstances, illustrating the effect of reduced WPI and increased CPI on the gross profit of the supply chain as well as at individual echelons is worthwhile in taking inventory decisions. In this paper, a model for a two echelon supply chain under WPI and CPI with price dependent demand is developed to analyse the variation of optimal gross profit, cycle time, average inventory levels and total relevant costs of inventory of both the manufacturer and retailer, with and without coordination. Numerical results are presented to demonstrate the application of the model developed. Results show that gross profit of the retailer increases significantly where as that of manufacturer reduces with decrease in WPI and increase in CPI, while overall gross profit of the supply chain increases.

Journal	Data powered by TypesetProcedia Engineering
Publisher	Data powered by TypesetElsevier BV
ISSN	1877-7058
Open Access	Yes