An integrated inventory model with controllable lead time and distribution‐free demand

The impact of lead time reduction on an integrated periodic review inventory system comprising a single vendor and multiple buyers with a step crashing cost function and service‐level constraints is studied. The probability distribution of demand during the protection period for each buyer is unknown, but the mean and the variance are given. Each production lot of the vendor can be delivered in a number of shipments to all buyers. A minimax distribution‐free procedure with Lagrange multipliers is applied to determining the lead time, the common shipment cycle time, the target levels of replenishments and the number of shipments per production cycle so that the expected total system cost is minimized. Numerical experiments along with sensitivity analysis were performed to illustrate the effects of parameters on the decision and the total system cost. Copyright © 2009 John Wiley & Sons, Ltd.     

需求分布未知且提前期可控的联合库存决策

在提前期内需求为自由分布且提前期依赖于订购批量和生产率的条件下,建立了同时考虑供需双方成本的联合库存决策模型,运用最小最大准则分析了模型最优解的存在性,设计了高效的最优解搜索算法.通过数值算例说明算法的有效性,分析了获取需求分布信息的代价与收益;并与供需独立的决策模型比较,表明了联合库存决策可以显著地降低供应链成本.     

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.     

A single-vendor and multiple-buyers production–inventory policy for a deteriorating item

This study develops a single-vendor, multi-buyers production–inventory policy for a deteriorating item with a constant production and demand rate. A mathematical model incorporating the costs of both the vendor and the buyers is developed. It can be shown that the integrated policy results in an impressive cost reduction when it is compared with the independent decisions made by the vendor and the buyers.     

Optimizing delivery lead time/inventory placement in a two-stage production/distribution system

In this paper we study a system composed of a supplier and buyer(s). We assume that the buyer faces random demand with a known distribution function. The supplier faces a known production lead time. The main objective of this study is to determine the optimal delivery lead time and the resulting location of the system inventory. In a system with a single-supplier and a single-buyer it is shown that system inventory should not be split between a buyer and supplier. Based on system parameters of shortage and holding costs, production lead times, and standard deviations of demand distributions, conditions indicating when the supplier or buyer(s) should keep the system inventory are derived. The impact of changes to these parameters on the location of system inventory is examined. For the case with multiple buyers, it is found that the supplier holds inventory for the buyers with the smallest standard deviations, while the buyers with the largest standard deviations hold their own inventory.     

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.     

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.     

Supply chain coordination with controllable lead time and asymmetric information

This paper considers coordinated decisions in a decentralized supply chain consisting of a vendor and a buyer with controllable lead time. We analyze two supply chain inventory models. In the first model we assume the vendor has complete information about the buyer’s cost structure. By taking both the vendor and the buyer’s individual rationalities into consideration, a side payment coordination mechanism is designed to realize supply chain Pareto dominance. In the second model we consider a setting where the buyer possesses private cost information. We design the coordination mechanism by using principal-agent model to induce the buyer to report his true cost structure. The solution procedures are also developed to get the optimal solutions of these two models. The results of numerical examples show that shortening lead time to certain extent can reduce inventory cost and the coordination mechanisms designed for both symmetric and asymmetric information situations are effective.     

The scheduling of deliveries in a production-distribution system with multiple buyers

In a real production and distribution business environment with one supplier and multiple heterogeneous buyers, the differences in buyers’ ordering cycles have influence on production arrangements. Consequently, the average inventory level (AIL) at the supplier’s end is affected by both the production policy and the ordering policy, typically by the scheduling of deliveries. Consequently, the average inventory holding cost is most deeply affected. In this paper, it is proposed that the scheduling of deliveries be formulated as a decision problem to determine the time point at which deliveries are made to buyers in order to minimize the supplier’s average inventory. A formulation of the average inventory level (AIL) in a production cycle at the supplier’s end using a lot-for-lot policy is developed. Under the lot-for-lot policy, the scheduling of deliveries (SP) is formulated as a nonlinear programming model used to determine the first delivery point for each buyer with an objective to minimize the sum of the product of the individual demand quantity and the first delivery time for each buyer. Thus, the SP model determines not only the sequence of the first deliveries to individual buyers, but also the time when the deliveries are made. An iterative heuristic procedure (IHP) is developed to solve the SP model assuming a given sequence of buyers. Six sequence rules are considered and evaluated via simulation.     

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 production plans and shipment schedules in a supply-chain system with multiple suppliers and multiple buyers

This research addresses an optimal policy for production and procurement in a supply-chain system with multiple non-competing suppliers, a manufacturer and multiple non-identical buyers. The manufacturer procures raw materials from suppliers, converts them to finished products and ships the products to each buyer at a fixed-interval of time over a finite planning horizon. The demand of finished product is given by buyers and the shipment size to each buyer is fixed. The problem is to determine the production start time, the initial and ending inventory, the cycle beginning and ending time, the number of orders of raw materials in each cycle, and the number of cycles for a finite planning horizon so as to minimize the system cost. A surrogate network representation of the problem developed to obtain an efficient, optimal solution to determine the production cycle and cycle costs with predetermined shipment schedules in the planning horizon. This research prescribes optimal policies for a multi-stage production and procurements for all shipments scheduled over the planning horizon. Numerical examples are also provided to illustrate the system.     

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.     

An optimal batch size for integrated production–inventory policy in a supply chain

This study presents a new integrated production–inventory policy under a finite planning horizon and a linear trend in demand. We assume that the vendor makes a single product and supplies it to a buyer with a non-periodic and just-in-time (JIT) replenishment policy in a supply chain environment. The objective is to minimize the joint total costs incurred by the vendor and the buyer. In this study, first, we develop a mathematical model and prove that it has the optimal solution. Then, we describe an explicit solution procedure for obtaining the optimal solution. Finally, we provide two numerical examples to illustrate both increasing and decreasing demands in our proposed model, and we show that the performance of the integrated consideration is better than the performance of any independent decision from either the buyer or the vendor.     

Two substitutable perishable product disaster inventory systems

A disaster inventory system is considered in which two substitutable items are stored for disaster management. In the event of disaster management, a particular product may become stock-out and the situation warrants that a demand for the particular product during its stock-out period may be substituted with another available similar product in the inventory. From the utility point of view, continuous review inventory models are quite appropriate in disaster inventory management. In this paper, a continuous review two substitutable perishable product disaster inventory model is proposed and analyzed. Since the inventory is maintained for disaster management, an adjustable joint reordering policy for replenishment is adopted. There is no lead time and the replenishment is instantaneous. For this model, some measures of system performance are obtained. The stationary behavior of the model is also considered. Numerical examples are also provided to illustrate the results obtained.     

A robust optimization approach to reduce the bullwhip effect of supply chains with vendor order placement lead time delays in an uncertain environment

Supply chain management is important for companies and organizations to improve their business and enhance competitiveness in the global marketplace. The bullwhip effect problem of supply chain systems with vendor order placement lead time delays in an uncertain environment is addressed in this paper. Among the numerous causes of bullwhip effect, we focus on uncertainties with respect to demand, production process, supply chain structure, inventory policy implementation and especially vendor order placement lead time delays. Minimizing the negative effect of these uncertainties in inducing bullwhip effect creates a need for developing dynamical inventory policy that increases responsiveness to demand and decreases volatility in inventory replenishment. First, a dynamic model of supply chain with above uncertainties is developed. Then, a novel uncertainty-dependent robust inventory control method using inventory position information is proposed. Additionally, the maximum allowable vendor order placement lead time delay that ensures the stability of supply chains and the suppression of bullwhip effect under the proposed inventory control policy is explored and measured. We find that vendor order placement lead time delays do play important role in supply chain dynamics and contribute to its turbulence and volatility. The effectiveness and flexibility of proposed method is verified through simulation study.     

Global optimal policy for vendor–buyer integrated inventory system within just in time environment

Traditionally, inventory problems for the vendor and the buyer are treated separately. In modern enterprises, however, the integration of vendor–buyer inventory system is an important issue. This co-operative approach to inventory management contributes to the success of supply chain management by minimizing the joint inventory cost. The joint inventory cost and the response time can further be reduced when the buyer orders and the vendor replenishes the required items just in time (JIT) for their consumption. The inclusion of the JIT concept in this model contributes significantly to a joint inventory cost reduction. A numerical example and sensitivity analysis are carried out. The derived results show an impressive cost reduction when compared with Goyal’s model.     

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。     

具有定价和开机成本的生产-库存系统的最优(s,d,S)策略

考虑一个具有有限容量和开机成本的连续盘点生产-库存系统, 其控制策略为(s,d,S)策略. 未被满足的需求都会丢失. 当机器处于关闭状态时,库存产品可以两个不同的价格进行销售. 当机器处于开机状态时,库存只能以较高的价格进行销售. 研究了如何发现该系统下的最优(s,d,S)策略,并开发了用于计算最优控制参数的有效算法.     

Temporary price increase during replenishment lead time

Pricing and inventory management make up together revenue management, which is a significant effort to boost revenues out of available resources. Firms use various forms of dynamic pricing, including personalized pricing, markdowns, promotions, coupons, discounts, and clearance sales, to respond to market fluctuations and demand uncertainty. In this paper, we study a temporary price increase policy, a form of dynamic pricing, for a non-perishable product, a practice used by several giant retailers such as Amazon, Walmart, and Apple. We develop a continuous review inventory model that allows for joint replenishment and pricing decisions, where the lead time is not zero. A replenishment decision controls supply, while a pricing decision controls demand. A manager exercises a temporary price increase to slow demand and avoid a stock-out situation while waiting for a shipment, which may not necessarily increase revenues, but decrease stock-out costs. The problem is to solve for the optimal replenishment and the pricing policy parameters that maximize the long-run expected profit. That is, when and how much to order and when to raise the price. In this paper, the inventory level and time trigger a price increase. We solve many numerical examples and perform extensive sensitivity analyses. Our results show that compared to a model that focuses on fixed pricing, our model brings an additional increase in profit of about 13%.     

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.