Leader-follower Game in VMI System with Limited Production Capacity Considering Wholesale and Retail Prices

VMI (Vendor Managed Inventory) is a widely used cooperative inventory policy in supply chains in which each enterprise has its autonomy in pricing. This paper discusses a leader-follower Stackelberg game in a VMI supply chain where the manufacturer, as a leader, produces a single product with a limited production capacity and delivers it at a wholesale price to multiple different retailers, as the followers, who then sell the product in dispersed and independent markets at retail prices. An algorithm is then developed to determine the equilibrium of the Stackelberg game. Finally, a numerical study is conducted to understand the influence of the Stackelberg equilibrium and market related parameters on the profits of the manufacturer and its retailers. Through the numerical example, our research demonstrates that: (a) the market related parameters have significant influence on the manufacturer’ and its retailers’ profits; (b) a retailer’s profit may not be necessarily lowered when it is charged with a higher inventory cost by the manufacturer; (c) the equilibrium of the Stackelberg equilibrium benefits the manufacturer.Stackelberg Game;Supply Chain;Vendor Managed Inventory

Optimal production and delivery scheduling models for a supply chain system of deteriorating items

The market is varying from minute to minute nowadays. Increase cooperation and pursue the optimal interest of the integrated supply chain become a more effective way than act alone in the competition. In this research, an integrated inventory policy between singleproducer and multi-buyer is developed and two inventory models are built. The first model extends the research of Lin and Lin (2007) by changing the single-buyer system to the multibuyers one. Both backorder of buyers and deteriorating items of each party (producer’s level, buyers’ level, and during transport) are considered herein. The second model is based on the research of Woo et al.(2001) and Model 1 by takes raw material cost and remanufacturing proceeds into account additional. In both model, the producer and buyers collaboratively work at minimizing their total operation cost and the problems are solved under an assumption of equal replenishments and production cycles. The algorithms to find the optimal solutions are given, and numerical examples are presented. Sensitivity for systems parameters is also analyzed and all calculations are completed by software Matlab and Maple

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

Application of Optimization in Production, Logistics, Inventory, Supply Chain Management and Block Chain

The evolution of industrial development since the 18th century is now experiencing the fourth industrial revolution. The effect of the development has propagated into almost every sector of the industry. From inventory to the circular economy, the effectiveness of technology has been fruitful for industry. The recent trends in research, with new ideas and methodologies, are included in this book. Several new ideas and business strategies are developed in the area of the supply chain management, logistics, optimization, and forecasting for the improvement of the economy of the society and the environment. The proposed technologies and ideas are either novel or help modify several other new ideas. Different real life problems with different dimensions are discussed in the book so that readers may connect with the recent issues in society and industry. The collection of the articles provides a glimpse into the new research trends in technology, business, and the environment

Optimal common manufacturing cycle length for a multi-product inventory system with rework and an outside contractor

Facing global market’s rigid competition, today’s manufacturers need not only to satisfy the timely demands of multiproduct, but also to ensure quality of their goods. For the purpose of reducing fabrication cycle time so as to meet timely demands, outsourcing is always a helpful option in production planning. To address the aforementioned real issues, the present study derives the optimal common manufacturing cycle length for a multi-product inventory system, wherein a part of lot-size of each end product is supplied by an outside contractor, and in each cycle a rework process repairs random defects produced by the in-house process. The schedule of receipt time for outsourced items is practically assumed to be in the end of rework. A specific decision model is built to cautiously portray such a hybrid inventory problem. Through modeling, analysis, and derivation the expected annual system cost is obtained, and using optimization technique the optimal cycle length that minimizes system cost is gained. The proposed decision model not only can help find optimal solution to the problem, but also enables manufacturers to obtain diverse essential information, such as the critical outsourcing rate, individual manufacturing related cost for each end product, and influence or joint effects of variations in different system factor(s) on the problem. Without our in-depth exploration, the aforementioned information will still be unavailable to support managerial decision makings

Integration of production, maintenance and quality : Modelling and solution approaches

Dans cette thèse, nous analysons le problème de l'intégration de la planification de production et de la maintenance préventive, ainsi que l'élaboration du système de contrôle de la qualité. Premièrement, on considère un système de production composé d'une machine et de plusieurs produits dans un contexte incertain, dont les prix et le coût changent d'une période à l'autre. La machine se détériore avec le temps et sa probabilité de défaillance, ainsi que le risque de passage à un état hors contrôle augmentent. Le taux de défaillance dans un état dégradé est plus élevé et donc, des coûts liés à la qualité s’imposent. Lorsque la machine tombe en panne, une maintenance corrective ou une réparation minimale seront initiées pour la remettre en marche sans influer ses conditions ou le processus de détérioration. L'augmentation du nombre de défaillances de la machine se traduit par un temps d'arrêt supérieur et un taux de disponibilité inférieur. D'autre part, la réalisation des plans de production est fortement influencée par la disponibilité et la fiabilité de la machine. Les interactions entre la planification de la maintenance et celle de la production sont incorporées dans notre modèle mathématique. Dans la première étape, l'effet de maintenance sur la qualité est pris en compte. La maintenance préventive est considérée comme imparfaite. La condition de la machine est définie par l’âge actuel, et la machine dispose de plusieurs niveaux de maintenance avec des caractéristiques différentes (coûts, délais d'exécution et impacts sur les conditions du système). La détermination des niveaux de maintenance préventive optimaux conduit à un problème d’optimisation difficile. Un modèle de maximisation du profit est développé, dans lequel la vente des produits conformes et non conformes, les coûts de la production, les stocks tenus, la rupture de stock, la configuration de la machine, la maintenance préventive et corrective, le remplacement de la machine et le coût de la qualité sont considérés dans la fonction de l’objectif. De plus, un système composé de plusieurs machines est étudié. Dans cette extension, les nombres optimaux d’inspections est également considéré. La fonction de l’objectif consiste à minimiser le coût total qui est la somme des coûts liés à la maintenance, la production et la qualité. Ensuite, en tenant compte de la complexité des modèles préposés, nous développons des méthodes de résolution efficaces qui sont fondées sur la combinaison d'algorithmes génétiques avec des méthodes de recherches locales. On présente un algorithme mimétique qui emploi l’algorithme Nelder-Mead, avec un logiciel d'optimisation pour déterminer les valeurs exactes de plusieurs variables de décisions à chaque évaluation. La méthode de résolution proposée est comparée, en termes de temps d’exécution et de qualités des solutions, avec plusieurs méthodes Métaheuristiques. Mots-clés : Planification de la production, Maintenance préventive imparfaite, Inspection, Qualité, Modèles intégrés, MétaheuristiquesIn this thesis, we study the integrated planning of production, maintenance, and quality in multi-product, multi-period imperfect systems. First, we consider a production system composed of one machine and several products in a time-varying context. The machine deteriorates with time and so, the probability of machine failure, or the risk of a shift to an out-of-control state, increases. The defective rate in the shifted state is higher and so, quality related costs will be imposed. When the machine fails, a corrective maintenance or a minimal repair will be initiated to bring the machine in operation without influencing on its conditions or on the deterioration process. Increasing the expected number of machine failures results in a higher downtime and a lower availability rate. On the other hand, realization of the production plans is significantly influenced by the machine availability and reliability. The interactions between maintenance scheduling and production planning are incorporated in the mathematical model. In the first step, the impact of maintenance on the expected quality level is addressed. The maintenance is also imperfect and the machine conditions after maintenance can be anywhere between as-good-as-new and as-bad-as-old situations. Machine conditions are stated by its effective age, and the machine has several maintenance levels with different costs, execution times, and impacts on the system conditions. High level maintenances on the one hand have greater influences on the improvement of the system state and on the other hand, they occupy more the available production time. The optimal determination of such preventive maintenance levels to be performed at each maintenance intrusion is a challenging problem. A profit maximization model is developed, where the sale of conforming and non-conforming products, costs of production, inventory holding, backorder, setup, preventive and corrective maintenance, machine replacement, and the quality cost are addressed in the objective function. Then, a system with multiple machines is taken into account. In this extension, the number of quality inspections is involved in the joint model. The objective function minimizes the total cost which is the sum of maintenance, production and quality costs. In order to reduce the gap between the theory and the application of joint models, and taking into account the complexity of the integrated problems, we have developed an efficient solution method that is based on the combination of genetic algorithms with local search and problem specific methods. The proposed memetic algorithm employs Nelder-Mead algorithm along with an optimization package for exact determination of the values of several decision variables in each chromosome evolution. The method extracts not only the positive knowledge in good solutions, but also the negative knowledge in poor individuals to determine the algorithm transitions. The method is compared in terms of the solution time and quality to several heuristic methods. Keywords : Multi-period production planning, Imperfect preventive maintenance, Inspection, Quality, Integrated model, Metaheuristic

An Integrated Lot-size Model of Deteriorating Item for one Vendor and Multiple Retailers Considering Market Pricing Using Genetic Algorithm

In this paper, we propose a model to study influence of pricing and deteriorating rate on the supply chain level net profit and total inventory where genetic algorithm is used for determine the optimal solution. A one-vendor and multi-retailer supply chain for a single deteriorating finished product and raw materials is analyzed. Under the proposed strategy, the vendor buys a non-deteriorating materials to vendor a deteriorating finished product, delivers the finished product to all retailers by common replenishment periods based on VMI (vendor managed inventory) being implemented. All retailers who buy the finished product sell the finished product on their markets. In all of these markets, the finished product in different markets has substitution each other since consumers may have opportunity to buy the finished product from different retailer and Cobb-Douglas demand function is introduced to describe this market attribute. After developing an integrated product-inventory-marketing model for deteriorating product, genetic algorithm is conducted to calculate the optimal pricing and inventory policies. Finally we present the results of a detailed numerical study that analyses the market and deteriorating rate related parameters influence on the supply chain level net profit and inventory level

Efficient inventory control for imperfect quality items

In this paper, we present a general EOQ model for items that are subject to inspection for imperfect quality. Each lot that is delivered to the sorting facility undertakes a 100 per cent screening and the percentage of defective items per lot reduces according to a learning curve. The generality of the model is viewed as important both from an academic and practitioner perspective. The mathematical formulation considers arbitrary functions of time that allow the decision maker to assess the consequences of a diverse range of strategies by employing a single inventory model. A rigorous methodology is utilised to show that the solution is a unique and global optimal and a general step-by-step solution procedure is presented for continuous intra-cycle periodic review applications. The value of the temperature history and flow time through the supply chain is also used to determine an efficient policy. Furthermore, coordination mechanisms that may affect the supplier and the retailer are explored to improve inventory control at both echelons. The paper provides illustrative examples that demonstrate the application of the theoretical model in different settings and lead to the generation of interesting managerial insights

The lot sizing problem: A tertiary study

This paper provides a survey of literature reviews in the area of lot sizing. Its intention is to show which streams of research emerged from Harris' seminal lot size model, and which major achievements have been accomplished in the respective areas. We first develop the methodology of this review and then descriptively analyze the sample. Subsequently, a content-related classification scheme for lot sizing models is developed, and the reviews contained in our sample are discussed in light of this classification scheme. Our analysis shows that various extensions of Harris' lot size model were developed over the years, such as lot sizing models that include multi-stage inventory systems, incentives, or productivity issues. The aims of our tertiary study are the following: firstly, it helps primary researchers to position their own work in the literature, to reproduce the development of different types of lot sizing problems, and to find starting points if they intend to work in a new research direction. Secondly, the study identifies several topics that offer opportunities for future secondary research