Learning-by-doing may not be enough to sustain competitiveness in a market

The economic order quantity model and its variants are the oldest reported scientific inventory models in the literature. They are mathematically simple to use and understand. This characteristic contributed to their popularity. However, they have limitations that restrict their application in practice. Researchers have extended those models by relaxing some of their restrictive assumptions. One of the main limitations of the EOQ model is the estimation of its cost parameters, such as setup and holding costs, which include some hidden (or difficult to estimate) components. Emerging research proposes using the second law of thermodynamics when to measure the hidden (entropy) costs of inventory systems. Another research stream focuses on learning-by-doing, which reduces the unit cost of a product, thus reducing its price and enhancing a firm's competitiveness. This paper assumes that a buyer receives a shipment from its vendor following the EOQ model. The buyer invests in the vendor's process to accelerate learning (mainly workers training, among other things). The buyer's unit purchase cost reduces because of learning at the vendor's side. The buyer's competitors also learn, increasing competitiveness. For this purpose, we develop an EOQ model where price-dependent demand is analogous to a heat transfer equation, which is used to determine the entropy cost. It accounts for improvement by learning as a result of the buyer's investment to compete in a market. The implementation and management of improvement programs are not usually smooth, resulting in disorder quantified by an entropy cost function. The developed EOQ model is investigated with and without entropy costs. Numerical results representing different scenarios are provided to illustrate the behavior of the models and identify the factors affecting the decision variables and, subsequently, the buyer's profitability. The results showed that in a competitive market, the buyer has to maintain a learning rate faster than those of its competitors to ensure a prolonged, but indefinite, profitability. The results also showed that investment in learning is meaningful when the competition is fierce.     

Supply chain model for a deteriorating product with time-varying demand and production rate

The paper develops a two-echelon supply chain model with a single-buyer and a single-vendor. The buyer sells a seasonal product over a short selling period and its inventory is subject to deterioration at a constant rate over time. The vendor's production rate is dependent on the buyer's demand rate, which is a linear function of time. Also, the vendor's production process is not perfectly reliable; it may shift from an in-control state to an out-of-control state at any time during a production run and produce some defective (non-conforming) items. Assuming that the vendor follows a lot-for-lot policy for replenishment made to the buyer, the average total cost of the supply chain is derived and an algorithm for finding the optimal solution is developed. The numerical study shows that the supply chain coordination policy is more beneficial than those policies obtained separately from the buyer's and the vendor's perspectives.     

Optimal Risk-Sharing When Risk Preferences are Uncertain

In many cases, a firm or agency needs a product that only one vendor can supply and for which the final cost is uncertain. An optimal risk-sharing arrangement is sought when the buyer and contractor agree on the probability distribution of cost but the buyer is uncertain of the contractor's risk-preferences. We find that when the buyer and contractor have exponential utilities, the optimal profit arrangement for the higher risk-averse contractor is no longer linear but concave in the costs. The degree of concavity is affected by the probabilistic beliefs on the contractor's risk-preferences. As the more risk-averse contractor becomes more likely, her chosen profit arrangement becomes less concave approaching the ideal, linear arrangement. The less risk-averse contractor is provided a profit arrangement with a certainty equivalent above her reservation price. This is the price the buyer must pay in order to entice a less risk-averse contractor into agreeing to accept a more risky profit arrangement.Another formulation is considered that assumes the buyer and contractor maximize approximations to their certainty equivalents in order to provide a more practical and possibly viable approach to sole-source contracting.     

Particle swarm optimization for bi-level pricing problems in supply chains

With rapid technological innovation and strong competition in hi-tech industries such as computer and communication organizations, the upstream component price and the downstream product cost usually decline significantly with time. As a result, an effective pricing supply chain model is very important. This paper first establishes two bi-level pricing models for pricing problems with the buyer and the vendor in a supply chain designated as the leader and the follower, respectively. A particle swarm optimization (PSO) based algorithm is developed to solve problems defined by these bi-level pricing models. Experiments illustrate that this PSO based algorithm can achieve a profit increase for buyers or vendors if they are treated as the leaders under some situations, compared with the existing methods.     

Integrated inventory models considering the two-level trade credit policy and a price-negotiation scheme

This paper develops the integrated inventory models with permissible delay in payment, in which customers’ demand is sensitive to the buyer’s price. The models consider the two-level trade credit policy in the vendor–buyer and buyer–customer relationships in supply chain management. A simple recursive solution procedure is proposed for the integrated models to determine the buyer’s optimal pricing and production/order strategy. Although the total profit from the buyer and vendor increases together, the buyer’s share lessens. To compensate the buyer’s loss due to the cooperative relationship, a negotiation system is presented in order to allocate the profit increase to the vendor and buyer to determine the pricing and production/order strategy. A numerical example and sensitivity analysis are provided to illustrate the proposed model. The results indicate that the total profit from the buyer and vendor together can increase, although a price discount is given to the buyer in the proposed models.     

Quality improvement and setup reduction in the joint economic lot size model

The co-maker concept has become accepted practice in many successful global business organizations. This fact has resulted in a class of inventory models known as joint economic lot size (JELS) models. Heretofore such models assumed perfect quality production on the part of the vendor. This paper relaxes this assumption and proposes a quality-adjusted JELS model. In addition, classical optimization methods are used to derive models for the cases of setup cost reduction, quality improvement, and simultaneous setup cost reduction and quality improvement for the quality-adjusted JELS. Numerical results are presented for each of these models. Comparisons are made to the basic quality-adjusted model. Results indicate that all three policies exhibit significantly reduced total cost. However, the simultaneous model results in the lowest cost overall and the smallest lot size. This suggests a synergistic impact of continuous improvement programs that focus on both setup and quality improvement of the vendor's production process. Sensitivity analysis indicates that the simultaneous model is robust and representative of practice.     

Solving the vendor–buyer integrated inventory system with arithmetic–geometric inequality

In the past, economic order quantity (EOQ) and economic production quantity (EPQ) were treated independently from the viewpoints of the buyer or the vendor. In most cases, the optimal solution for one player was non-optimal to the other player. In today’s competitive markets, close cooperation between the vendor and the buyer is necessary to reduce the joint inventory cost and the response time of the vendor–buyer system. The successful experiences of National Semiconductor, Wal-Mart, and Procter and Gamble have demonstrated that integrating the supply chain has significantly influenced the company’s performance and market share (Simchi-Levi et al. (2000) [1]). Recently, Yang et al. (2007) [2] presented an inventory model to determine the economic lot size for both the vendor and buyer, and the number of deliveries in an integrated two stage supply chain. In this paper, we present an alternative approach to determine the global optimal inventory policy for the vendor–buyer integrated system using arithmetic–geometric inequality.     

A fuzzy mathematical model for the joint economic lot size problem with multiple price breaks

This paper applies fuzzy mathematical programming to solve the joint economic lot size problem with multiple price breaks. In order to entice the buyer to increase the order quantity, it is a common practice for the seller to offer quantity discounts to the buyer. From the system viewpoint, the joint cost for the seller and buyer can be minimized only when the buyer increases his economic order quantity. The problem is how to determine the number of price breaks, as well as the quantity discount and order quantity at each price break, to achieve the optimal joint cost. Fuzzy mathematical programming provides a very efficient algorithm to solve the above problem simultaneously from the perspectives of the seller and the buyer. Another common problem in joint economic lot size model is how to split the system profit between the seller and the buyer. Whereas the traditional approach to this problem is to divide the profit based on a certain ratio determined by the bargaining power of both parties, fuzzy mathematical programming can achieve the same satisfaction level to both parties based on their respective cost functions.     

Joint Vendor-buyer Policy in JIT Manufacturing

In this study, we show that a co-operative batching policy, based on cost information exchange between the vendor and the buyer, can reduce total cost significantly in the just-in-time (JIT) environment. We examine the impact of such co-operation on total costs, including ordering, set-up, transportation and inventory holding costs for a long-term supply relationship. The study shows that joint optimization of both the vendor and the buyer's operations does not necessarily result in a common lot size. We further examine the sensitivity of the resulting cost savings due to the exchange of cost information to changes in the relevant operating parameters.     

A comprehensive extension of an integrated inventory model with ordering cost reduction and permissible delay in payments

Huang (2010) [1] proposed an integrated inventory model with trade credit financing in which the vendor decides its production lot size while the buyer determines its expenditure to minimize the annual integrated total cost for both the vendor and the buyer. In this paper, we extend his integrated supply chain model to reflect the following four facts: (1) generated sales revenue is deposited in an interest-bearing account for the buyer, (2) the buyer’s interest earned is not always less than or equal to its interest charged, (3) the total number of shipments in one lot size is the vendor’s decision variable to minimize the cost, and (4) it is vital to have a discrimination term which can determine whether the buyer’s replenishment cycle time is less than the permissible delay period or not. We then derive the necessary and sufficient conditions to obtain the optimal solution, and establish some theoretical results to characterize the optimal solution. Finally, numerical examples are presented to illustrate the proposed model and its optimal solution.     

Integrated inventory model with quantity discount and price-sensitive demand

Quantity discount has been a subject of study for a long time; however, little is known about its effect on integrated inventory models when price-sensitive demand is placed. The objective of this study is to find the optimal pricing and ordering strategies for an integrated inventory system when a quantity discount policy is applied. The pricing strategy discussed here is one in which the vendor offers a quantity discount to the buyer. Then, the buyer will adjust his retail price based on the purchasing cost, which will influence the customer demand as a result. Consequently, an integrated inventory model is established to find the optimal solutions for order quantity, retail price, and the number of shipments from vendor to buyer in one production run, so that the joint total profit incurred has the maximum value. Also, numerical examples and a sensitivity analysis are given to illustrate the results of the model.     

An integrated vendor–buyer inventory model with order-processing cost reduction and permissible delay in payments

Trade credit plays an important role in financing for many businesses and industries. For the buyers, purchased inventory can be considered to be financed in whole or in part with permissible delay in payments during the purchasing process. On the other hand, both the vendor and buyer take part in order-processing cost reduction by applying information technologies, such as EDI (electronic data interchange). The order-processing cost can also be reduced by adding certain capital investments, and this will affect the lot size decisions. This article develops an integrated inventory model to determine the optimal inventory policy under conditions of order-processing cost reduction and permissible delay in payments, and shows that the total annual variable cost function possesses some kinds of convexities. A solution procedure is provided to determine the optimal order policy. Finally, a numerical example is presented to illustrate the solution procedure.     

Single-manufacturer,multi-retailer consignment policy for retailers’ generalized demand distributions

Consignment policy (CP) is a novel approach to the inventory management in supply chains. It is based on strong interaction and reliable collaboration between vendor(s) and buyer(s), which is acquiring growing importance in today's industrial reality. Unlike most literature focusing on single-vendor single-buyer models and deterministic customer demand, a single-manufacturer (vendor) multi-retailer (buyer) generic model is developed under stochastic customer demand in this study. In order to understand the potential benefits of CP, it is compared with a traditional policy (TP) model developed in the similar approach. The models are tested with two scenarios of uniform and exponential demand distributions of the retailers. The results show how CP works better than the traditional uncoordinated optimization. It not only helps the manufacturer to generate higher profit, but also coordinates retailers to achieve a higher supply chain profit. At the same time, each retailer earns at least as much as they do in TP. Further price discount sensitivity analysis demonstrates the efficiency of CP when facing price-demand fluctuation.     

The optimal pricing and ordering policy for an integrated inventory model when trade credit linked to order quantity

In traditional inventory models, it is implicitly assumed that the buyer must pay for the purchased items as soon as they have been received. However, in many practical situations, the vendor is willing to provide the buyer with a permissible delay period when the buyer’s order quantity exceeds a given threshold. Therefore, to incorporate the concept of vendor–buyer integration and order-size-dependent trade credit, we present a stylized model to determine the optimal strategy for an integrated vendor–buyer inventory system under the condition of trade credit linked to the order quantity, where the demand rate is considered to be a decreasing function of the retail price. By analyzing the total channel profit function, we developed some useful results to characterize the optimal solution and provide an iterative algorithm to find the retail price, buyer’s order quantity, and the numbers of shipment per production run from the vendor to the buyer. Numerical examples and sensitivity analysis are given to illustrate the theoretical results, and some managerial insights are also obtained.     

Estimating the market shares of stores based on the shopper's search and purchase behavior

Suppose that a consumer has decided to shop around several retail stores in an attempt to find a desired product or service. From his or her past shopping experience, the shopper may know: (1) the assortment size of each store, (2) the search cost per visit, and (3) the price variation among the stores. For such a situation, we first consider the optimal sequence of stores and the optimal search strategy from the shopper's search-theoretic point of view. Based on the assumption that shoppers follow the optimal sequencing and search strategy that maximizes his or her expected net gain, we then estimate the market share of each store in the market area. With a numerical example, we finally analyze the effects of the assortment size, the search cost, and the price variation on the market shares of existing retail stores. Based on the shopper's search and purchase model, we attempt to explain: (1) why shoppers visit bigger stores first, (2) why they visit fewer stores if the search cost is relatively higher than the product price, and (3) why they shop around more stores if the price variation among the stores is large.     

Analyzing online B2B exchange markets: Asymmetric cost and incomplete information

This research applies the discriminating auction to analyze the online B2B exchange market in which a single buyer requests multiple items and several suppliers having equal capacity and asymmetric cost submit bids to compete for buyer demand. In the present model, we examine the impact of asymmetric cost and incomplete information on the participants in the market. Given the complete cost information, each supplier randomizes its price and the lower bound of the price range is determined by the highest marginal cost. In addition, the supplier with a lower marginal cost has a larger considered pricing space but ultimately has a smaller equilibrium one than others with higher marginal costs. When each supplier’s marginal cost is private information, the lowest possible price is determined by the number of suppliers and the buyer’s reservation price. Comparing these two market settings, we find whether IT is beneficial to buyers or suppliers depends on the scale of the bid process and the highest marginal cost. When the number of suppliers and the difference between the highest marginal cost and the buyer’s reservation price are sufficiently large, each supplier can gain a higher profit if the marginal costs are private information. On the contrary, when the highest marginal cost approaches the buyer’s reservation price, complete cost information benefits the suppliers.     

Economic selection of process mean for single-vendor single-buyer supply chain

Process mean selection for a container-filling process is an important decision in a single-vendor single-buyer supply chain. Since the process mean determines the vendor’s conforming and yield rates, it influences the vendor–buyer decisions regarding the production lot size and number of shipments delivered from the vendor to buyer. It follows, therefore, that these decisions should be determined simultaneously in order to control the supply chain total cost. In this paper, we develop a model that integrates the single-vendor single-buyer problem with the process mean selection problem. This integrated model allows the vendor to deliver the produced lot to buyer in number of unequal-sized shipments. Moreover, every outgoing item is inspected, and each item failing to meet a lower specification limit is reprocessed. Further, in order to study the benefits of using this integrated model, two baseline cases are developed. The first of which considers a hierarchical model where the vendor determines the process mean and schedules of production and shipment separately. This hierarchical model is used to show the impact of integrating the process mean selection with production/inventory decisions. The other baseline case is studied in the sensitivity analysis where the optimal solution for a given process is compared to the optimal solution when the variation in the process output is negligible. The integrated model is expected to lead to reduction in reprocessing cost, minimal loss to customer due to the deviation from the optimum target value, and consequently, providing better products at reduced cost for customers. Also, a solution procedure is devised to find the optimal solution for the proposed model and sensitivity analysis is conducted to investigate the effect of the model key parameters on the optimal solution.     

Mathematical modelling for determining economic batch size and optimal number of deliveries for EPQ model with quality assurance

The classic economic production quantity (EPQ) model assumes a continuous inventory-issuing policy for satisfying product demand and a perfect production for all items produced. However, in a real-life vendor–buyer integrated system, a multi-delivery policy is often used in lieu of continuous issuing policy and it is inevitable to generate defective items during a production run. This study addresses these issues by incorporating multiple deliveries of the finished batch, customer's inventory-holding cost and manufacturer's quality assurance cost into an EPQ model with the imperfect reworking of random defective items. Mathematical modelling and analyses are employed. Convexity of the long-run expected cost function is proved by the use of Hessian matrix equations, and the closed-form solutions in terms of the optimal lot size and optimal number of deliveries are obtained. The research results are demonstrated with a numerical example with a discussion on its practical usage.     

The impact of consumer returns policies on consignment contracts with inventory control

We consider a consignment contract with consumer non-defective returns behavior. In our model, an upstream vendor contracts with a downstream retailer. The vendor decides his consignment price charged to the retailer for each unit sold and his refund price for each returned item, and then the retailer sets her retail price for selling the product. The vendor gets paid based on net sold units and salvages unsold units as well as returned items in a secondary market. Under the framework, we study and compare two different consignment arrangements: the retailer/vendor manages consignment inventory (RMCI/VMCI) programs. To study the impact of return policy, we discuss a consignment contract without return policy as a benchmark. We show that whether or not the vendor offers a return policy, it is always beneficial for the channel to delegate the inventory decision to the vendor. We find that the vendor’s return policy depends crucially on the salvage value of returns. If the product has no salvage value, the vendor’s optimal decision is not to offer a return policy; otherwise, the vendor can gain more profit by offering a return policy when the salvage value turns out to be positive.     

基于两层供应链的VMI系统可行性分析研究

一般来说，供应商管理用户库存（VMI）能够给购买方带来更高的利润，而对供货方的影响却是不确定的。而现实中很多VMI策略都是由购买方主导的，购买方一般不愿和供货方分享收益，因此供货方必须自己判断是否接受VMI策略。本文在基于对安徽奇瑞汽车集团的零部件库存进行的调查的基础上，对VMI系统可行性分析的研究分两步进行：（1）假设供货方已经接受了购买方主导的VMI策略，它如何制定自己的最优送货策略；（2）通过比较供货方分别在RMI和VMI下的最小成本，供货方决定是否接受购买方主导的VMI策略。