Fuzzy knowledge-based token-ordering policies for bullwhip effect management in supply chains

The “Bullwhip Effect” is a well-known example of supply chain inefficiencies and refers to demand amplification as moving up toward upstream echelons in a supply chain. This paper concentrates on representing a robust token-based ordering policy to facilitate information sharing in supply chains in order to manage the bullwhip effect. Takagi–Sugeno–Kang and hybrid multiple-input single-output fuzzy models are proposed to model the mechanism of token ordering in the token-based ordering policy. The main advantage of proposed fuzzy models is that they eliminate the exogenous and constant variables from the procedure of obtaining the optimal amount of tokens which should be ordered in every period. These fuzzy approaches model the mentioned mechanism through a push–pull policy. A four-echelon SC with fuzzy lead time and unlimited production capacity and inventory is considered to survey the outcomes. Numerical experiments confirm the effectiveness of proposed policies in alleviating BWE, inventory costs and variations.     

A study on inventory replenishment policies in a two-echelon supply chain system

Inventory control plays an important role in supply chain management. Properly controlled inventory can satisfy customers’ demands, smooth the production plans, and reduce the operation costs; yet failing to budget the inventory expenses may lead to serious consequences. The bullwhip effect, observed in many supply chain management cases, causes excessive inventory due to information distortion, i.e. the order amount is exaggerated while a minor demand variation occurs, and the information amplified dramatically as the supply chain moves to the upstream. In this paper, one of the main causes of bullwhip effect, order batching, is considered. A simplified two-echelon supply chain system, with one supplier and one retailer that can choose different replenishment policies, is used as a demonstration. Two types of inventory replenishment methods are considered: the traditional methods (the event-triggered and the time-triggered ordering policies), and the statistical process control (SPC) based replenishment method. The results show that the latter outperforms the traditional method in the categories of inventory variation, and in the number of backlog when the fill-rate of the prior model is set to be 99%. This research provides a different approach to inventory cost-down other than the common methods like: information sharing, order batch cutting, and lead time reduction. By choosing a suitable replenishment policy, the number of backorder and the cost of inventory can be reduced.     

The impact of information sharing and inventory control coordination on supply chain performances

The lack of coordination in supply chains can cause various inefficiencies like bullwhip effect and inventory instability. Extensive researches quantified the value of sharing and forecasting of customer demand, considering that all the supply chain partners can have access to the same information. However, only few studies devoted to identify the value of limited collaboration or information visibility, considering their impact on the overall supply chain performances for local and global service level. This paper attempts to fill this gap by investigating the interaction of collaboration and coordination in a four-echelon supply chain under different scenarios of information sharing level. The results of the simulation study show to what extent the bullwhip effect and the inventory variance increase and amplify when a periodic review order-up-to level policy applies, noting that more benefits generate when coordination starts at downstream echelons. A factorial design confirmed the importance of information sharing and quantified its interactions with inventory control parameters, proving that a poor forecasting and definition of safety stock levels have a significant contribution to the instability across the chain. These results provide useful implications for supply chain managers on how to control and drive supply chain performances.     

Quantifying and mitigating the bullwhip effect in a benchmark supply chain system by an extended prediction self-adaptive control ordering policy

An undesired observation known as the bullwhip effect in supply chain management leads to excessive oscillations of the inventory and order levels. This paper presents how to quantify and mitigate the bullwhip effect by introducing model predictive control (MPC) strategy into the ordering policy for a benchmark supply chain system. Instead of quantifying the bullwhip effect with commonly used statistical measure, we derive equivalently the expression of bullwhip metric via control-theoretic approach by applying discrete Fourier transform and (inverse) z-transform when the demand signal is stationary stochastic. A four-echelon supply chain is formulated and its dynamical features are analyzed to give the discrete model. An extended prediction self-adaptive control (EPSAC) approach to the multi-step predictor is implemented in the development of MPC formulation. The closed-form solution to MPC problem is derived by minimizing a specified objective function. The transfer function for MPC ordering policy is then obtained graphically from an equivalent representation of this closed-form solution. A numerical simulation shows that MPC ordering policy outperforms the traditional ordering policies on reducing bullwhip effect.     

The governing dynamics of supply chains: The impact of altruistic behaviour

This paper analyses an infinite horizon two-echelon supply chain inventory problem and shows that a sequence of the optimum ordering policies does not yield globally optimal solutions for the overall supply chain. First-order autoregressive demand pattern is assumed and each participant adopts the order-up-to (OUT) policy with a minimum mean square error forecasting scheme to generate replenishment orders. To control the dynamics of the supply chain, a proportional controller is incorporated into the OUT policy, which we call a generalised OUT policy. A two-echelon supply chain with this generalised OUT policy achieves over 10% inventory related cost reduction. To enjoy this cost saving, the attitude of first echelon player to cost increases is an essential factor. This attitude also reduces the bullwhip effect. An important insight revealed herein is that a significant amount of benefit comes from the player doing what is the best for the overall supply chain, rather than what is the best for local cost minimisation.     

Decentralized and centralized model predictive control to reduce the bullwhip effect in supply chain management

Mitigating the bullwhip effect is one of crucial problems in supply chain management. In this research, centralized and decentralized model predictive control strategies are applied to control inventory positions and to reduce the bullwhip effect in a benchmark four-echelon supply chain. The supply chain under consideration is described by discrete dynamic models characterized by balance equations on product and information flows with an ordering policy serving as the control schemes. In the decentralized control strategy, a MPC-EPSAC (Extended Prediction Self-Adaptive Control) approach is used to predict the changes in the inventory position levels. A closed-form solution of an optimal ordering decision for each echelon is obtained by locally minimizing a cost function, which consists of the errors between predicted inventory position levels and their setpoints, and a weighting function that penalizes orders. The single model predictive controller used in centralized control strategy optimizes globally and finds an optimal ordering policy for each echelon. The controller relies on a linear discrete-time state-space model to predict system outputs. But the predictions are approached by either of two multi-step predictors depending on whether the states of the controller model are directly observed or not. The objective function takes a quadratic form and thus the resulting optimization problem can be solved via standard quadratic programming method. The comparisons on performances of the two MPC strategies are illustrated with a numerical example.     

Agent-based web service for the design of a dynamic coordination mechanism in supply networks

The theory of network coordination presents an effective approach to improve the business processes within supply networks. The automation of the negotiation process among buyers and suppliers has become an important policy in the transactional networks. This leads to assessing the roles of both quantifiable and non-quantifiable parameters in coordination mechanisms with the aim of achieving higher performance. Here, we develop an e-based supply chain multi-agent model for the design of mass-customized on-line services. The model addresses the bullwhip effect in multi-stage supply chain and also clarifies the evaluation of inventory policies in various supply and demand uncertainties. To illustrate the feasibility of the approach, we implement a prototype system and evaluate its performance by simulation using Colored Petri Nets (CPNs). The validation results reveal the model efficiency in providing a more realistic optimization process that takes the dynamic information flow in uncertainty environments into consideration.     

Smoothing inventory decision rules in seasonal supply chains

A major cause of supply chain deficiencies is the bullwhip effect, which implies that demand variability amplifies as one moves upstream in supply chains. Smoothing inventory decision rules have been recognized as the most powerful approach to counteract the bullwhip effect. Although several studies have evaluated these smoothing rules with respect to several demand processes, focusing mainly on the smoothing order-up-to (OUT) replenishment rule, less attention has been devoted to investigate their effectiveness in seasonal supply chains. This research addresses this gap by investigating the impact of the smoothing OUT on the seasonal supply chain performances. A simulation study has been conducted to evaluate and compare the smoothing OUT with the traditional OUT (no smoothing), both integrated with the Holt-Winters (HW) forecasting method, in a four-echelon supply chain experiences seasonal demand modified by random variation. The results show that the smoothing OUT replenishment rule is superior to the traditional OUT, in terms of the bullwhip effect, inventory variance ratio and average fill rate, especially when the seasonal cycle is small. In addition, the sensitivity analysis reveals that employing the smoothing replenishment rules reduces the impact of the demand parameters and the poor selection of the forecasting parameters on the ordering and inventory stability. Therefore, seasonal supply chain managers are strongly recommended to adopt the smoothing replenishment rules. Further managerial implications have been derived from the results.     

The value of information sharing in a supply chain with a seasonal demand process

This paper considers a two echelon seasonal supply chain model that consists of one supplier and one retailer, with the assumption that external demand from the customer follows a seasonal autoregressive moving average (SARMA) process, including marketing actions that cannot be deduced from the other parameters of the demand process. In our model, the supplier and the retailer employ order-up-to policy to replenish their inventory. In order to evaluate the value of information sharing in a two echelon seasonal supply chain, three levels of information sharing proposed by Yu, Yan, and Cheng (2002) are used. The results for optimal inventory policies under these three levels of information sharing are derived. We show that the seasonal effect has an important impact on optimal inventory policies of the supplier under the three levels of information sharing. Our findings also demonstrate that the replenishment of lead time must be less than the seasonal period in order to benefit from information sharing. Thus, this result provides managers with managerial insights to improve supply chain performance through information sharing integration partnerships.     

Measure of bullwhip effect in supply chains with first-order bivariate vector autoregression time-series demand model

With supply chains becoming increasingly global, the issue of bullwhip effect, a phenomenon attributable to demand fluctuation in the upstream section of the supply chains, has received greater attention from many researchers. However, most existing research studies on quantifying the bullwhip effect were conducted under the first-order autoregressive [AR(1)] incoming demand process or its variants as the fundamental demand process, thereby failing to account for the retailer demand dependency. This research work thus examined the bullwhip effect for the first-order bivariate vector autoregression [VAR(1)] demand process in a two-stage supply chain consisting of one supplier and two retailers. The impacts of the correlation parameters of the demand process, the correlation coefficient between the two error terms, and the variances of the error terms on the bullwhip effect were investigated. As such, the measure of the bullwhip effect was established using an analytical approach in which the minimum mean square error (MMSE) forecasting method and the base stock policy were applied to all members of the supply chain. Numerical experiments were then conducted to illustrate the behavior of the bullwhip effect with respect to various parameters of the demand processes to see in which situations the bullwhip effect would be absent. In addition, an evaluation of the inventory variance ratio was analyzed.     

Assessing effect of global inventory planning with enterprise-wide information for a large manufacturer

This paper studies how a global manufacturer with many subsidiaries can achieve enhanced business value for the organization by sharing information within its supply chain network. Specifically, the uncertainties in the demands from the downstream distribution center affect the inventory levels at the upstream distribution center under different inventory policies, considering the uncertain lead times and the given order fill rates. With a generic simulation model and real data, we evaluate the magnitude of savings in inventory under the new inventory policy where information can be shared among subsidiaries, compared to the status quo where subsidiaries run independently with no information sharing. The results show that average inventory level at the upstream DC under the new policy would be reduced by approximately 3%. Considering the given manufacturer's global supply chain distribution network holds about $4 billion in average inventory, the 3% improvement is a very significant savings.     

A supply chain contract with flexibility as a risk-sharing mechanism for demand forecasting

Demand forecasting is one of the main causes of the bullwhip effect in a supply chain. As a countermeasure for demand uncertainty as well as a risk-sharing mechanism for demand forecasting in a supply chain, this article studies a bilateral contract with order quantity flexibility. Under the contract, the buyer places orders in advance for the predetermined horizons and makes minimum purchase commitments. The supplier, in return, provides the buyer with the flexibility to adjust the order quantities later, according to the most updated demand information. To conduct comparative simulations, four-echelon supply chain models, that employ the contracts and different forecasting techniques under dynamic market demands, are developed. The simulation outcomes show that demand fluctuation can be effectively absorbed by the contract scheme, which enables better inventory management and customer service. Furthermore, it has been verified that the contract scheme under study plays a role as an effective coordination mechanism in a decentralised supply chain.     

信息共享受限条件下的供应链网络系统牛鞭效应控制策略

研究在信息共享受限条件下供应链网络库存系统的牛鞭效应控制问题,建立了包括市场需求、信息可获得性、信息及时性等不确定性因素的库存网络系统状态转移模型,从系统内部动力学机制的角度分析了牛鞭效应的成因,提出了动态库存控制策略,并给出了策略参数设计的线性矩阵不等式组算法.运用系统稳定性理论,深入分析了信息共享对牛鞭效应的影响,并通过仿真结果验证了库存控制策略的有效性和实用性.     

基于物联网技术的供应链信息共享

文章先介绍供应链中存在的牛鞭效应现象,提出供应链结构、时间延迟、需求预测等六个对牛鞭效应的成因。然后结合新型物联网技术,对信息共享进行了分析讨论。最后得出实施信息共享可以有效减弱牛鞭效应的结论。     

The impact of replenishment parameters and information sharing on the bullwhip effect: A computational study

Demand variability amplification across the supply chain, known as the bullwhip effect, results in serious inefficiencies across the chain. Managers are expected to minimize this phenomenon in their chain in order to reduce costs and increase customer satisfaction by making critical decisions on replenishment policy. We study how specific replenishment parameters affect order variability amplification, product fill rates and inventory levels across the chain. Furthermore, we study how demand information sharing can help towards reducing order oscillations and inventory levels in upper nodes of a supply chain. A two-stage supply chain consisting of a warehouse and stores that face customer demand is modeled. Real demand data are used as the underlying customer demand during the experiments.     

含时滞的不确定性供应链网络系统牛鞭效应控制策略及其经济性能分析

考虑需求、生产能力、供应链结构等内外不确定性因素和供应链系统运作延迟,构建了不确定环境下含时滞的供应链库存网络系统状态转移模型.针对牛鞭效应问题,提出了基于库存水平波动状态的控制策略和相应的经济性能指标;借助线性矩阵不等式方法,深入分析库存策略的参数优化设计对牛鞭效应以及经济性能的影响.仿真结果表明,在经济性能约束下,该库存策略具有较强的牛鞭效应遏制能力,从而表明了策略的有效性和实用性.     

The benefit of VMI strategies in a stochastic multi-product serial two echelon system

We consider a multi-product serial two echelon inventory system with stochastic demand. Inventories at the downstream location are replenished periodically using an automatic ordering system. Under vendor managed inventory strategies the upstream stage is allowed to adapt these orders in order to benefit from economies of scale. We propose three different VMI strategies, aiming to reduce the order picking cost at the upstream location and the transportation costs resulting in reduced total supply chain costs. In a detailed numerical study the VMI strategies are compared with a retailer managed inventory strategy for two different demand models suitable for slow moving products. It is shown that if inventory holding costs are low, compared to handling and transportation costs, efficiencies at the warehouse are improved and total supply chain costs are reduced.     

Bullwhip effect measure in a seasonal supply chain

In this study, the bullwhip effect in a seasonal supply chain was quantified by considering a two echelon supply chain which consists of one supplier and one retailer. The external demand occurring at the customer was assumed to follow a SARMA (1, 0) X (0, 1) _s scheme, a seasonal autoregressive-moving average process, while the retailer employed an base-stock policy to replenish their inventory. The demand forecast was performed with a SARMA (1, 0) X (0, 1) _s using the minimum mean-square error forecasting technique. In order to develop the bullwhip effect measure in a seasonal supply chain, the lead time demand forecast, forecast error, and the optimal inventory policy at the retailer were derived in sequence. The variance of order quantity based on these results was obtained. Then, various properties were derived by analyzing the bullwhip effect measure. Specifically, it was determined that the seasonal cycle plays an important role in bullwhip effect under a seasonal supply chain. The findings also point out that the replenishment lead time must be less than the seasonal cycle in order to reduce the bullwhip effect. Therefore, the lead time needs to be reduced through collaboration between the retailer and supplier.     

A decision rule for coordination of inventory and transportation in a two-stage supply chain with alternative supply sources

This paper deals with a two-stage supply chain that consists of two distribution centers and two retailers. Each member of the supply chain uses a (Q,R) inventory policy, and incurs standard inventory holding and backlog costs, as well as ordering and transportation costs. The distribution centers replenish their inventory from an outside supplier, and the retailers replenish inventory from one of the two distribution centers. When a retailer is ready to replenish its inventory that retailer must decide whether it should replenish from the first or second distribution center. We develop a decision rule that minimizes the total expected cost associated with all outstanding orders at the time of order placement; the retailers then repeatedly use this decision rule as a heuristic. A simulation study which compares the proposed policy to three traditional ordering policies illustrates how the proposed policy performs under different conditions. The numerical analysis shows that, over a large set of scenarios, the proposed policy outperforms the other three policies on average.     

基于混合需求的供应链多级库存协同订货模型

针对供应链多级库存系统存在混合需求的情况,建立了基于混合需求的多级库存协同订货模型。该模型假设在供应链中只有最下游节点面临的需求是独立需求,而其他上游节点面临的需求都是与之相关的相关需求。由于相关需求是一种块状需求,其库存成本构成与独立需求明显不同。因此,通过对多级库存系统的库存成本构成进行重新分析,分别给出了需求确定时不允许缺货和允许缺货的协同订货模型。另外,还通过对安全库存的分析给出了需求不确定时的协同订货模型。最后,给出了模型求解的遗传算法,并进行了实例仿真分析,展示了这种协同订货模型在混合需求的供应链中的实用性。