Stackcelberg Game Inventory Model With Progressive Permissible Delay of Payment Scheme

Supplier has many schemes to motivate retailer to buy more and of them one is a progressive permissible delay of payment. Instead of analyst from the retailer side alone, in this chapter, we develop the inventory model of supplier and retailer. In reality, some suppliers and retailers cannot have collaboration and they try to optimize their own decision so we develop a Stackelberg Game model. Two models are developed wherein the first model supplier acts as the leader and in the second model, the retailer acts a leader. Since the models are complex, a hybrid Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) is developed to solve the model. A numerical analysis and sensitivity analysis are conducted to get management insights of the model. The results show that a Stackelberg Game model for progressive permissible delay of payment is sensitive in varies values of the first and second delay interest rate if supplier acts as a leader. The retailer gets less inventory cost when he acts as a leader compared to when vendor acts a leader at high interest rate of the first and second delay period

An integrated pricing and deteriorating model and a hybrid algorithm for a VMI (vendor-managed-inventory) supply chain

This paper studies a vendor-managed-inventory (VMI) supply chain where a manufacturer, as a vendor, procures a type of nondeteriorating raw material to produce a deteriorating product, and distribute it to multiple retailers. The price of the product offered by one retailer is also influenced by the prices offered by other retailers because consumers can choose the product from any of the retailers. This paper is one of the first papers that propose an integrated model to study the influence of pricing and deterioration on the profit of such a VMI system. A hybrid approach combining genetic algorithms and an analytical method is developed for efficiently determining the optimal price of the product of each retailer, the inventory policies of the product and the raw material. Our results of a detailed numerical study show that parameters related to the market and deterioration have significant influences on the profit of the VMI system. However, different from common intuition, we find that an increase in the substitution elasticity of the product among different retailers can bring an increase in the retail prices of the product, while the increase of the market scale can reduce the retail prices. © 2011 IEEE.published_or_final_versio

A Bi-objective Optimization for Vendor Managed Inventory Model

Vendor managed inventory is a continuous replenishment program that is designed to provide major cost saving benefits for both vendors and retailers. Previous research on this area mainly included single objective optimization models where the objective is to minimize the total supply chain costs or to maximize the total supply chain benefits. This paper presents a bi-objective mathematical model for single-manufacture multi-retailer with multi-product in order to maximize their benefits. It is assumed that demand is a decreasing and convex function of the retail price. In this paper, common replenishment cycle is considered for the manufacturer and its retailers. Then, the proposed model converts to the single-objective optimization problem using a weighted sum method. A genetic algorithm (GA) is applied to solve it and response surface methodology is employed to tune the GA parameters. Finally, several numerical examples are investigated to demonstrate the applicability of the proposed model and solution approach

Inventory methods in order to minimize raw materials at the inventory level in the supply chain

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Examining price and service competition among retailers in a supply chain under potential demand disruption

© 2017 Elsevier Ltd Supply chain disruptions management has attracted significant attention among researchers and practitioners. The paper aims to examine the effect of potential market demand disruptions on price and service level for competing retailers. To investigate the effect of potential demand disruptions, we consider both a centralized and a decentralized supply chain structure. To analyze the decentralized supply chain, the Manufacturing Stackelberg (MS) game theoretical approach was undertaken. The analytical results were tested using several numerical analyses. It was shown that price and service level investment decisions are significantly influenced by demand disruptions to retail markets. For example, decentralized decision makers tend to lower wholesale and retail prices under potential demand disruptions, whereas a proactive retailer needs to increase service level with an increased level of possible disruptions. This research may aid managers to analyze disruptions prone market and to make appropriate decision for price and service level. The manufacturer or the retailers will also be able to better determine when to close a market based on the proposed analysis by considering anticipated disruptions. The benefits and usefulness of the proposed approach are explained through a real-life case adopted from a toy supply chain in Bangladesh

Nash Game Model for Optimizing Market Strategies, Configuration of Platform Products in a Vendor Managed Inventory (VMI) Supply Chain for a Product Family

This paper discusses how a manufacturer and its retailers interact with each other to optimize their product marketing strategies, platform product configuration and inventory policies in a VMI (Vendor Managed Inventory) supply chain. The manufacturer procures raw materials from multiple suppliers to produce a family of products sold to multiple retailers. Multiple types of products are substitutable each other to end customers. The manufacturer makes its decision on raw materials’ procurement, platform product configuration, product replenishment policies to retailers with VMI, price discount rate, and advertising investment to maximize its profit. Retailers in turn consider the optimal local advertising and retail price to maximize their profits. This problem is modeled as a dual simultaneous non-cooperative game (as a Nash game) model with two sub-games. One is between the retailers serving in competing retail markets and the other is between the manufacturer and the retailers. This paper combines analytical, iterative and GA (genetic algorithm) methods to develop a game solution algorithm to find the Nash equilibrium. A numerical example is conducted to test the proposed model and algorithm, and gain managerial implications.supply chain management;nash game model;vendor managed inventory

Large scale stochastic inventory routing problems with split delivery and service level constraints

A stochastic inventory routing problem (SIRP) is typically the combination of stochastic inventory control problems and NP-hard vehicle routing problems, which determines delivery volumes to the customers that the depot serves in each period, and vehicle routes to deliver the volumes. This paper aims to solve a large scale multi-period SIRP with split delivery (SIRPSD) where a customer’s delivery in each period can be split and satisfied by multiple vehicle routes if necessary. This paper considers SIRPSD under the multi-criteria of the total inventory and transportation costs, and the service levels of customers. The total inventory and transportation cost is considered as the objective of the problem to minimize, while the service levels of the warehouses and the customers are satisfied by some imposed constraints and can be adjusted according to practical requests. In order to tackle the SIRPSD with notorious computational complexity, we first propose an approximate model, which significantly reduces the number of decision variables compared to its corresponding exact model. We then develop a hybrid approach that combines the linearization of nonlinear constraints, the decomposition of the model into sub-models with Lagrangian relaxation, and a partial linearization approach for a sub model. A near optimal solution of the model found by the approach is used to construct a near optimal solution of the SIRPSD. Randomly generated instances of the problem with up to 200 customers and 5 periods and about 400 thousands decision variables where half of them are integer are examined by numerical experiments. Our approach can obtain high quality near optimal solutions within a reasonable amount of computation time on an ordinary PC

Linearization and Decomposition Methods for Large Scale Stochastic Inventory Routing Problem with Service Level Constraints

A stochastic inventory routing problem (SIRP) is typically the combination of stochastic inventory control problems and NP-hard vehicle routing problems, for a depot to determine delivery volumes to its customers in each period, and vehicle routes to distribute the delivery volumes. This paper aims to solve a large scale multi-period SIRP with split delivery (SIRPSD) where a customer’s delivery in each period can be split and satisfied by multiple vehicles if necessary. The objective of the problem is to minimize the total inventory and transportation cost while some constraints are given to satisfy other criteria, such as the service level to limit the stockout probability at each customer and the service level to limit the overfilling probability of the warehouse of each customer. In order to tackle the SIRPSD with notorious computational complexity, we propose for it an approximate model, which significantly reduces the number of decision variables compared to its corresponding exact model. We develop a hybrid approach that combines the linearization of nonlinear constraints, the decomposition of the model into sub-models with Lagrangian relaxation, and a partial linearization approach for a sub model. A near optimal solution of the model can be found by the approach, and then be used to construct a near optimal solution of the SIRPSD. Numerical examples show that, for an instance of the problem with 200 customers and 5 periods that contains about 400 thousands decision variables where half of them are integer, our approach can obtain high quality near optimal solutions with a reasonable computational time on an ordinary PC

Nash Game Model for Optimizing Market Strategies, Configuration of Platform Products in a Vendor Managed Inventory (VMI) Supply Chain for a Product Family

This paper discusses how a manufacturer and its retailers interact with each other to optimize their product marketing strategies, platform product configuration and inventory policies in a VMI (Vendor Managed Inventory) supply chain. The manufacturer procures raw materials from multiple suppliers to produce a family of products sold to multiple retailers. Multiple types of products are substitutable each other to end customers. The manufacturer makes its decision on raw materials’ procurement, platform product configuration, product replenishment policies to retailers with VMI, price discount rate, and advertising investment to maximize its profit. Retailers in turn consider the optimal local advertising and retail price to maximize their profits. This problem is modeled as a dual simultaneous non-cooperative game (as a Nash game) model with two sub-games. One is between the retailers serving in competing retail markets and the other is between the manufacturer and the retailers. This paper combines analytical, iterative and GA (genetic algorithm) methods to develop a game solution algorithm to find the Nash equilibrium. A numerical example is conducted to test the proposed model and algorithm, and gain managerial implications

Nash game model for optimizing market strategies, configuration of platform products in a Vendor Managed Inventory (VMI) supply chain for a product family

This paper discusses how a manufacturer and its retailers interact with each other to optimize their product marketing strategies, platform product configuration and inventory policies in a VMI (Vendor Managed Inventory) supply chain. The manufacturer procures raw materials from multiple suppliers to produce a family of products sold to multiple retailers. Multiple types of products are substitutable each other to end customers. The manufacturer makes its decision on raw materials' procurement, platform product configuration, product replenishment policies to retailers with VMI, price discount rate, and advertising investment to maximize its profit. Retailers in turn consider the optimal local advertising investments and retail prices to maximize their profits. This problem is modeled as a dual simultaneous non-cooperative game (as a dual Nash game) model with two sub-games. One is between the retailers serving in competing retail markets and the other is between the manufacturer and the retailers. This paper combines analytical, iterative and GA (genetic algorithm) methods to develop a game solution algorithm to find the Nash equilibrium. A numerical example is conducted to test the proposed model and algorithm, and gain managerial implications. © 2010 Elsevier B.V. All rights reserved.postprin