Inventory replenishment and delivery planning in a two-level supply chain with compound Poisson demands

This paper presents a model for integrating inventory replenishment and delivery planning in a two-level supply chain consisting of a supplier and a retailer. The supplier is authorized to manage the inventory level of the retailer by using the information on demands from final customers and the inventory level of the retailer. The problem considered here is to determine order-up-to levels of the supplier and the retailer simultaneously for the objective of minimizing the expected long-run average cost, which is composed of replenishment cost at the supplier, delivery cost to the retailer, and inventory holding costs at both members. We develop a renewal theoretic optimization model for a case of compound Poisson demands with distribution-free order quantities and present an approximation method for obtaining a solution of the problem. In addition, a closed-form solution is derived for the problem with a special case of compound Poisson demands, in which demand quantities follow an exponential distribution. A series of simulation tests show that the solutions obtained from the approximated cost functions are reasonably good.     

基于确定需求的作业层库存路径问题研究

研究了传统零售商管理库存模式下,基于确定需求的由一个供应商多个零售商组成的两级配送系统中作业层库存路径问题.首先采用传统C-W节约算法,讨论了供应商和零售商独立决策时的订货与配送策略.然后基于时间距离的思想,在滚动周期策略的框架下,设计了两级系统的联合配送策略.最后,用具体算例比较了独立决策和联合决策下的系统年度费用,验证了联合配送策略的有效性,并给出了相应的作业层日常运营补货时间和车辆路径.     

Synchronization in multi-echelon supply chain applying timing discount

Due to the increasing emphasis on the effective management of the supply chain, synchronization and cooperation issues between suppliers and retailers in decentralized multi-echelon inventory/distribution systems have gained much attention in the recent years. In this paper, we consider coordination issues of a distribution system composed of a manufacturer, a supplier (distributor), and several retailers. The supplier outsourcing a third party offers a timing discount to multiple retailers in order to synchronize the timing of their orders with the order cycle. It is also assumed that retailers are allowed to face stock outs. In this paper, a mathematical model is developed to analyze the problem. Results show that while synchronizing the supplier and the outsourcer enhances the supply chain efficiency, offering any type of timing discount by the supplier decreases the supply chain efficiency. It is also noted that having coordination between the manufacturer and the supplier has no impact on the supplier’s profit but may decrease the retailer’s costs. It is believed that our findings provide potential and significant managerial implications in the area of supply chain coordination when these systems are decentralized.     

A two-level distribution inventory system with stochastic lead time at the lower echelon

We consider a two-level distribution inventory system with a number of identical retailers at the lower echelon and a single supplier at the upper echelon. The replenishment policy is continuous review policy (R, Q) at all installations. We assume independent Poisson demands with stochastic lead time for the retailers and a constant transportation time for replenishing supplier orders from an external warehouse. Unsatisfied demands are assumed to be lost in the retailers and unsatisfied retailer orders are backordered in the supplier. We develop an approximate cost function to find optimal reorder points for given batch sizes in all installations, and the related accuracy is assessed through simulation. We present numerical examples for the gamma distributed lead time for the retailers orders at the supplier.     

Simultaneous coordination of capacity building and price decisions in a decentralized supply chain

In this paper, we investigate the simultaneous coordination of price and capacity building decisions in a dyadic supply chain. This problem is a combination of capacity reservation problem and pricing problem. While the coordination of supply chain with stochastic demand and fixed prices has received much attention in the literature, price-dependent and stochastic demand has been less considered. We study the latter case where a price-setting retailer faces a linear decreasing demand with respect to price. To capture the uncertainty of the demand, we add a stochastic variable to the demand function. In addition, we incorporate production rate and inventory cost on the supplier side. We propose Revenue Sharing Reservation Contract with Penalty (RSRP) as a coordination mechanism to align the price and capacity decisions. We then extend the model to include multiple retailers which are geographically dispersed. We next conduct a comprehensive numerical example with an extensive sensitivity analysis to understand the behavior and robustness of the supply chain under a RSRP, and finally, we draw some managerial implications.     

一对多供应链在传统、信息共享和供应商管理库存模式下的绩效比较

比较分析了一对多两阶段供应链在传统、信息共享和供应商管理库存三种供应链管理模式下的供应链绩效,其中绩效指标选取为平均成本.针对三种模式分别构建了供应商、零售商以及供应链整体的运作模型,给出了其成本的解析表达式,最后通过数值实验的方法,比较了三种模式下的供应链绩效.结果表明,对于零售商和整个供应链而言,信息共享模式优于传统模式,并且供应商管理库存模式优于信息共享模式;而对于供应商而言,信息共享和供应商管理库存模式均优于传统模式,但供应商管理库存模式与信息共享模式相比,在一定条件下,有可能带来供应商成本的增加.     

General bounds for the optimal value of retailers’ reorder point in a two-level inventory control system with and without information sharing

In this study, an inventory system consisting of a single product, one supplier, and multiple identical retailers is considered. Each retailer replenishes inventory from the supplier according to the well known (R,Q) policy. Transit times are constant and retailers face independent Poisson demand. The supplier utilizing the retailers' information in decision making for replenishment policy with a given order size starts with m initial batches (of size Q) and places an order in a batch of size Q to an outside source when a new order is placed. In this inventory system, excess demand is backordered, delayed orders are satisfied on a first-come first-serve basis, and no partial shipment is allowed. By partitioning the cost function of this system, general upper and lower bounds for the optimal value of R are determined. Based on several numerical examples, it is shown that these bounds (especially the lower bound) allow the optimal reorder point to be found more effectively with a shorter solving time.     

Optimal production policy for a manufacturing system with volume flexibility in a supply chain under lumpy demand

A batch production system with volume flexibility in a supply chain where a manufacturer procures raw materials and/or component parts from multiple suppliers in a lot and processes them into a single product, is considered in this research. First of all, a decision-making model is developed for an optimal production rate selection in the volume-flexibility production system, where a single type of finished products is delivered periodically in fixed quantities within a fixed interval of time. In this model, the production rate is perceived as a decision variable and unit production cost becomes a function of production rate. This model takes into account not only inventory costs of raw materials and finished goods, but production costs as well. Then, a pragmatic computation approach is presented to solve the proposed model for special unit-production-cost functions. It is used to determine an optimal production rate, and thus to decide an optimal ordering policy for procurement of raw materials from suppliers and an optimal manufacturing batch size. Some observations are made for optimal production rate analysis. Finally, a numerical study is conducted to illustrate the solution and a set of data with ten problems is tested and compared.     

Minimizing transportation cost of a joint inventory location model using modified adaptive differential evolution algorithm

Transportation is a key issue in supply chain management and is a major concern for a company. This paper considers a joint-location inventory problem involving a set of suppliers producing different products and a set of retailers where some retailers are treated as distribution centers (DCs). The problem is to determine which retailers to be assigned as DCs, which retailers to receive direct shipments, how much of the retailer’s demand to allocate to the DCs, and how much of the DC’s demand is to be met by different suppliers. The problem is formulated as a mixed integer model and it has been solved through an adaptive differential evolution algorithm known as modified J. Adaptive Differential Evolution. The solutions obtained are compared with that of simple genetic algorithm. This paper also shows that the proposed model is robust in nature and offers near-optimal results for different distributions. The sum of the cost of establishing some retailers as DCs and the total transportation cost incurred in shipping products from the suppliers to the retailers via DCs(for some retailers) or directly (for the other retailers) is also compared with the total transportation cost incurred when all the products are shipped directly from the suppliers to the retailers.     

Determination of the economical policy of a three-echelon inventory system with (R, Q) ordering policy and information sharing

In this work, we consider a three-echelon serial inventory system with two warehouses (suppliers) and one retailer with information exchange. The retailer applies continuous review (R, Q) policy. The warehouses have online information on the inventory position and demand activities of the retailer. We present a new ordering policy to share information among inventory echelons. The warehouse I and II start with m ₁ and m ₂ initial batches of the same order size of the retailer, respectively. The warehouse I places an order to an outside source immediately after the retailer’s inventory position reaches an amount equal to the retailer’s order point plus a fixed value s ₁, and the warehouse II places an order to the warehouse I immediately after the retailer’s inventory position reaches an amount equal to the retailer’s order point plus a fixed value s ₂. Transportation times are constant and the retailer faces independent Poisson demand. The lead times of the retailer and the warehouse II are determined not only by the constant transportation time but also by the random delay incurred due to the availability of stock at the warehouses. In this paper using the idea of the one-for-one policy, we implicitly incorporate the distribution function of the random delay to obtain the exact value of the expected inventory system cost. Resorting some numerical examples in three different scenarios, we show how information sharing reduces the inventory costs.     

折价促销所致提前购买行为对供应链收益影响的研究

供应链中批发商为了加快库存周转,获得更多收益,往往会通过折价促销促使零售商大批量订购,但所导致的零售商的提前购买行为不一定能保证双方均受益。从促销前后成本变化角度建立数学模型,得出了关于批发商起订量和零售商合理采购区间的结论,并建议批发商应主动合作,向零售商让利,方可保证供应链收益最大化。     

基于熵的直运型供应链库存协调研究

为解决不对称信息下直运型供应链库存协调问题,提出了一种基于信息熵的库存协调方法。首先,研究了由一个供应商和一个分销商组成的直运型供应链系统,给出了库存保管成本信息不对称下的库存协调补偿机制,并从供应商角度提出了优化模型。模型中含有一个与供应商所掌握信息量相关的参数。为选择恰当的模型参数,提出了运用极大熵准则,确定库存保管成本分布概率的基本方法。最后,给出了一个应用示例。计算结果表明,协调后供应商和分销商的利润都有一定程度的增加。     

Developing a two-echelon mathematical model for a vendor-managed inventory (VMI) system

Vendor-managed inventory (VMI) system is a mechanism where the supplier creates the purchase orders based on the demand information exchanged by the retailer/customer. In this paper, the performance of the traditional and VMI system is compared. Mathematical modeling is applied and total inventory cost in the supply chain is used as the performance measure. The supply chain is considered in two levels, i.e., buyer and supplier, with the assumption that the supplier faces only one buyer as the contract party. Since none of the previous works quantitatively directed the practitioners to select the traditional or VMI system, the extent point is introduced in which the difference in total cost of both systems is minimal. It is applied to investigate how increasing or reducing the related parameters changes total cost of two systems with respect to each other. A numerical example and sensitivity analysis are provided to illustrate the theory and derive the extent points and percentage of difference in total cost of the traditional and VMI system. The results show that VMI works better and delivers lower cost in all conditions including back order, and as one goes farther from the extent point, the application of VMI is more justified.     

基于共同补给期的直运型供应链库存协调模型及仿真

研究了二级直运供应链通过共同补给期协调库存的策略问题。在该供应链中,单一的供应商向面临随机需求的多个零售商提供单一产品。在提出的库存协调策略下,当零售商接受供应商提供的共同补给期时,供应商则提供给零售商一定的价格折扣。最后,通过数值仿真分析,验证了该策略可以降低供应商的成本,而零售商成本的增加则可以通过价格折扣来补偿,从而显著地降低了供应链的总成本。     

Deriving the cost function for a class of three-echelon inventory system with N-retailers and one-for-one ordering policy

A three-echelon inventory system with two warehouses and N-retailers is considered in this paper. Transportation times are constant and retailers face independent Poisson demand. Replenishments are one-for-one. The lead time of a retailer is determined not only by the constant transportation time but also by the random delay incurred due to the availability of stock at the warehouses. Axsäter [2] evaluated the value of the expected two-echelon inventory system cost with the same assumptions, but in this paper, we add a warehouse as third echelon and therefore this may lead to having one more delay in shipment which was incurred in the new warehouse. We obtained the cost function for the inventory system and tested it by several examples.     

双渠道多期供应链网络均衡模型研究

为适应信息化和高度动态化的发展,研究了在实体和网上两种交易渠道下,由制造市场、零售市场和需求市场组成的三层动态供应链网络的均衡问题,在静态供应链网络均衡模型的基础上,考虑了库存和网上交易对供应链网络的影响.分别对制造市场、零售市场和需求市场的决策者的独立决策行为及其相互作用进行了分析,构建了各层市场的有限维变分不等式,并将变分不等式问题转化为等价的互补问题的形式,给出了经济解释,得到了最终的双渠道多期供应链网络均衡模型,并给出了箅例分析.求解得到的均衡产量、交易量、库存量和均衡价格对供应链上企业的经营具有指导意义.     

A fuzzy reinforcement learning algorithm for inventory control in supply chains

In the real world, applications with very large state and action spaces and unknown state transition probability, classical reinforcement learning algorithms usually show poor performance. One way to address the performance problem is to approximate the policy or value function. Fuzzy rule-based systems are amongst the well-known function approximators. This paper presents a Flexible Fuzzy Reinforcement Learning algorithm, in which value function is approximated by a fuzzy rule-based system. The proposed algorithm has a separate module for tuning the structure of fuzzy rules. Moreover, the parameters of the system are tuned during the learning phase. Next, the proposed algorithm is applied to the problem of inventory control in supply chains. In this problem, a fuzzy agent (supplier) should determine the amount of orders for each retailer based on their utility for supplier, by considering its limited supply capacity. Finally, a simulation is performed to show the capability of the proposed algorithm.     

Determining the optimum production quantity in three-echelon production system with stochastic demand

This paper considers a three-echelon integrated production inventory model consisting of a central warehouse and a manufacturer including two independent departments as processing and assembly stages. To assemble the finished product, materials are carried to the assembly stage through two different flow channels. One group requires preprocessing in the processing stage, and the other one directly arrives from an outside supplier. Storing inventories either in a warehouse (as finished products) or in the stages (as work-in-process) and shipping them between the stages incur inventory costs that must be balanced to achieve minimum joint total cost. The central warehouse faces stochastic demand, which is assumed to be a generally distributed demand. It is controlled by continuous review (R,Q) policy. Additionally, warehouse ordering cost can be reduced through further investment. To analyze, we formulate a nonlinear cost function to aggregate all the costs. After, a simulated annealing algorithm has been suggested to solve the problem. Numerical experiments are presented to evaluate the performance and effectiveness of the proposed algorithm. Also, we use the branch and bound technique and a nonlinear optimization technique—generalized reduced gradient—for solving this problem. The experimental results show a fine performance of the proposed algorithm in comparison with two other methods.     

不完美生产品质的模糊经济生产批量模型

针对实际生产过程中出现不良品进行返修的情况,提出两种不良品可修复的模糊经济生产库存模型:一种是具有模糊成本和明确的生产数量,另一种是具有模糊成本和模糊生产数量。使用功能原则和梯级平均综合表示法来求解最优模糊经济生产批量,并将模糊产品存货总成本函数修正为循环周期内的库存总成本函数,最后采用数值算例来检验模型的有效性。     

供应链协同契约研究

为了使供应链达到协同,提出了利润共享与买回契约组合而成的新型混合契约,并用该契约对单供应商一单零售商,以及单供应商一多零售商组成的两级供应链模型进行了协同分析,整个分析过程采用了Stackel-berg博弈理论,其中供应商作为领导者,零售商作为跟随者.分析结果和数值实例说明,混合契约可以使供应商与零售商协同,并使供应链渠道总利润最大化.