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.     

Controlling the bullwhip effect in a supply chain system with constrained information flows

The bullwhip effect problem is one of the most important issues in supply chain management. Limited information sharing increases the difficulty of reducing the bullwhip effect and leads to inefficient supply chain management. The purpose of this paper is to explore new ways to reduce the bullwhip effect in supply chain systems that face uncertainties with respect to information sharing. We first present a supply chain state transition model, based on which we explore the endogenous mechanism of bullwhip effect, especially those related to impacts from limited information sharing. Then we propose a novel inventory control method and study the corresponding control optimization problem, with the aim of reducing inventory volatility in supply chains. Both quantitative analysis and simulation study are conducted. Simulation results show the effectiveness and flexibility of our proposed method in reducing bullwhip effect and in improving supply chain performance, even under conditions of limited information sharing.     

The bullwhip effect in supply chain networks

This paper analyzes the propagation and amplification of order fluctuations (i.e., the bullwhip effect) in supply chain networks operated with linear and time-invariant inventory management policies. The supply chain network is allowed to include multiple customers (e.g., markets), any network structure, with or without sharing information. The paper characterizes the stream of orders placed by any supplier for any stationary customer demand processes, and gives exact formulas for the variance of the orders placed and the amplification of order fluctuations. The paper also derives robust analytical conditions, based only on inventory management policies, to predict the presence of the bullwhip effect for any network structure, any inventory replenishment policies, and arbitrary customer demand processes. Numerical examples show that the analytical results accurately quantify the bullwhip effect; managerial insights are drawn from the analysis. The methodology presented in this paper generalizes those in previous studies for serial supply chains.     

The effect of information sharing on supply chain stability and the bullwhip effect

This paper analyzes the bullwhip effect in multi-stage supply chains operated with linear and time-invariant inventory management policies and shared supply chain information. Such information includes past order sequences and inventory records at all supplier stages. The paper characterizes the stream of orders placed at any stage of the chain when the customer demand process is known and ergodic, and gives an exact formula for the variance of the orders placed. The paper also derives robust analytical conditions, based only on inventory management policies, to predict the presence of the bullwhip effect and bound its magnitude. These results hold independently of the customer demand. The general framework proposed in this paper allows for any inventory replenishment policies, any ways of sharing and utilizing information, and any customer demand processes. It is also shown as a special case that sharing customer demand information across the chain significantly reduces, but does not completely eliminate, the bullwhip effect.     

Analyzing the effect of the inventory policy on order and inventory variability with linear control theory

In this paper we apply linear control theory to study the effect of various inventory policies on order and inventory variability, which are key drivers of supply chain performance. In particular, we study a two-echelon supply chain with a stationary demand pattern under the influence of three inventory policies: an inventory-on-hand policy that bases orders on the visible inventory at an installation, an installation-stock policy that bases orders on the inventory position (on-hand plus on-order inventory) at an installation, and an echelon-stock policy that bases orders on the inventory position at that installation and all downstream installations. We prove analytically that the inventory-on-hand policy is unstable in practical settings, confirming analytically what has been observed in experimental settings and in practice. We also prove that the installation-stock and echelon-stock policies are stable and analyze their effect on order and inventory fluctuation. Specifically, we show the general superiority of the echelon-stock in our setting and demonstrate analytically the effect of forecasting parameters on order and inventory fluctuations, confirming the results in other research.     

Coordination in a two-stage capacitated supply chain with multiple suppliers

The aim of this paper is to coordinate the inventory policies in a decentralized supply chain with stochastic demand by means of contracts. The system considered is a decentralized two-stage supply chain consisting of multiple independent suppliers and a manufacturer with limited production capacities. The suppliers operate on a make-to-stock basis and apply base stock policy to manage their inventories. On the other hand, the manufacturer employs a make-to-order strategy. Under the necessary assumptions, each supplier is modeled as an M/M/1 make-to-stock queue; and the manufacturer is modeled as a GI/M/1 queue after deriving an approximate distribution for the interarrival times of the manufacturer. Once the supply chain is modeled as a queuing system, centralized and decentralized models are developed. Comparison of the optimal solutions to these models reveals that the supply chain needs coordination. Three different transfer payment contracts are examined in this paper. These are the backorder and holding cost subsidy contracts, the transfer payment contract based on Pareto improvement, and the cost sharing contract. Each contract is evaluated according to its coordination ability and whether it is Pareto improving or not. The results indicate that all three contracts can coordinate the supply chain. However, when the Pareto improvement is taken into account, the cost sharing contract seems to be the one that will be preferred by all parties.     

A measure of bullwhip effect in supply chains with a mixed autoregressive-moving average demand process

In this paper, we quantify the impact of the bullwhip effect – the phenomenon in which information on demand is distorted as moving up a supply chain – for a simple two-stage supply chain with one supplier and one retailer. Assuming that the retailer employs a base stock inventory policy, and that the demand forecast is performed via a mixed autoregressive-moving average model, ARMA(1, 1), we investigate the effects of the autoregressive coefficient, the moving average parameter, and the lead time on the bullwhip effect.     

Measure of bullwhip effect in supply chains with autoregressive demand process

In supply chain management, one of the most critical problems which require a lot of effort to deal with is how to quantify and alleviate the impact of bullwhip effect – the phenomenon in which information on demand is distorted while moving upstream. Although it is well established that demand forecast, lead time, order batching, shortage gaming and price fluctuation are the main sources that lead to the bullwhip effect, the problem of quantifying bullwhip effect still remain unsolved in many situations due to the complex nature of the problem. In this research, a measure of bullwhip effect will be developed for a simple two-stage supply chain that includes only one retailer and one supplier in the environment where the retailer employs base stock policy for their inventory and demand forecast is performed through the first-order autoregressive model, AR(1). The effect of autoregressive coefficient and lead time on this measure will then be investigated.     

Robust tests for the bullwhip effect in supply chains with stochastic dynamics

This paper analyzes the bullwhip effect in single-echelon supply chains driven by arbitrary customer demands and operated nondeterministically. The supply chain, with stochastic system parameters, is modeled as a Markovian jump linear system. The paper presents robust analytical conditions to diagnose the bullwhip effect and bound its magnitude. The tests are independent of the customer demand. Examples are given. Ordering policies that pass these tests, and thus avoid the bullwhip effect in random environments for arbitrary customer demands, are shown to exist. The paper also presents possible extensions to multi-echelon chains.     

Inventory control of supply chains: Mitigating the bullwhip effect by centralized and decentralized Internal Model Control approaches

In this paper, a two-degrees-of-freedom Internal Model Control structure is incorporated in production inventory control for a supply chain system. This scheme presents an intuitive and simple parametrization of controllers, where inventory target tracking and disturbance (demand) rejection in the inventory level problems are treated separately. Moreover, considering that the lead times are known, this scheme presents a perfect compensation of the delay making the stabilization problem easier to handle. This control structure is formulated for a serial supply chain in two ways (by using a centralized and a decentralized control approach). The behavior of these inventory control strategies is analyzed in the entire supply chain. Analytical tuning rules for bullwhip effect avoidance are developed for both strategies. The results of controller evaluations demonstrate that centralized control approach enhances the behavior with respect to the inventory target tracking, demand rejection and bullwhip effect in the supply chain systems.     

Bullwhip effect in a supply chain model with multiple delivery delays

We develop a model of differential equations for a supply chain with delivery time delays between every adjacent firms. Based on the supply chain model, we provide a new perspective of the bullwhip effect and show that the bullwhip effect is intrinsic in supply chains in the sense that the equilibrium state of each firm in the supply chain is a cumulative forward product of the ratios of order fulfillment and placement between adjacent firms toward the end customer demand. We also show that it is the multiple time delays instead of the constant end consumer demand that determine the stability of the equilibrium states. However, the consumer demand has impacts on the stability of the equilibrium states of the supply chain when the end retailer’s inventory decisions are linearly related to the end consumer demand.     

The effect of replenishment policies on the bullwhip effect: A transfer function approach

An important phenomenon in supply chain management, known as the bullwhip effect, suggests that demand variability increases as one moves up a supply chain. This paper examines the influence of different replenishment policies on the occurrence of the bullwhip effect. The paper demonstrates that certain replenishment policies can in themselves be inducers of the bullwhip effect, while others inherently lower demand variability. The main causes of increase in variability are projections of future demand expectations, which result in over-exaggerated responses to changes in demand. We suggest that through appropriate selection and use of certain replenishment rules, the bullwhip effect can be avoided, subsequently allowing supply chain management costs to be lowered.     

Understanding supply chain dynamics: A chaos perspective

Variability in orders or inventories in supply chain systems is generally thought to be caused by exogenous random factors such as uncertainties in customer demand or lead time. Studies have shown, however, that orders or inventories may exhibit significant variability even if customer demand and lead time are deterministic. In this paper, we investigate how this class of variability, chaos, may occur in a multi-level supply chain and offer insights into how to manage relevant supply chain factors to eliminate or reduce system chaos. The supply chain is characterized by the classical beer distribution model with some modifications. We observe the supply chain dynamics under the influence of various factors: demand pattern, ordering policy, demand-information sharing, and lead time. Through proper decision-region formation, the effect of various factors on system chaos is investigated using a factorial design. The degree of system chaos is quantified using the Lyapunov exponent across all levels of the supply chain. This study shows that, to reduce the degree of chaos in the supply chain system, the adjustment parameters for both inventory and supply line discrepancies should be more comparable in magnitude. Counter-intuitively, in certain decision regions, sharing demand information can do more harm than good. Similar to the bullwhip effect observed previously in demand, we discover the phenomenon of “chaos-amplification” in inventory across supply chain levels.     

Artificial intelligence-based inventory management: a Monte Carlo tree search approach

The coordination of order policies constitutes a great challenge in supply chain inventory management as various stochastic factors increase its complexity. Therefore, analytical approaches to determine a policy that minimises overall inventory costs are only suitable to a limited extent. In contrast, we adopt a heuristic approach, from the domain of artificial intelligence (AI), namely, Monte Carlo tree search (MCTS). To the best of our knowledge, MCTS has neither been applied to supply chain inventory management before nor is it yet widely disseminated in other branches of operations research. We develop an offline model as well as an online model which bases decisions on real-time data. For demonstration purposes, we consider a supply chain structure similar to the classical beer game with four actors and both stochastic demand and lead times. We demonstrate that both the offline and the online MCTS models perform better than other previously adopted AI-based approaches. Furthermore, we provide evidence that a dynamic order policy determined by MCTS eliminates the bullwhip effect.

     

Central versus local multiple stage inventory planning: An analysis of solutions

Supply chain management refers to the integration of all activities associated with moving goods from raw material stages through to end users. Yet this system-wide vision of inventory planning often requires the coordination of several commercially independent entities, such as suppliers, manufacturers and distributors. This study explores the issue of friction between replenishment policies, defined as the disparity between centrally and locally planned solutions to 98,820 deterministic, multiple stage inventory planning problems modeling systems of varying levels of complexity. Friction is found to be strongly related to certain cost factors, suggesting that certain supply chains could be more vulnerable to tension and inefficiencies when replenishment policies are derived without cooperation between commercially independent yet logistically interdependent stages. These results can also be applied to identify relationships between the findings of otherwise seemingly disparate previous studies of coordination schemes for supply chain partners.     

季节性供应链零售商补货策略研究——基于牛鞭效应视角

通过建立含有季节性自回归移动平均需求过程的供应链,零售商采用最小均方差预测技术预测提前期需求,分析(R,D)、(R,S)、(R,βS)、(R,γO)和(R,γO,βS)五种补货策略下的牛鞭效应.研究结果表明:(R,γO)补货策略是弱化牛鞭效应的最优补货策略,然而(R,γO)补货策略时出现了反牛鞭效应,无法保证供应链的安全供给.实践中当库存量调节系数和订货量调节系数较大时,(R,βS)补货策略能有效弱化牛鞭效应,当库存量调节系数和订货量调节系数较小时,(R,γO,βS)补货策略能有效弱化牛鞭效应;对于(R,βS)和(R,γO,βS)补货策略,牛鞭效应随着库存平滑系数的增大而增大;对于(R,γO)和(R,γO,βS)补货策略,牛鞭效应随着订货平滑系数的增大而增大;对于(R,S)、(R,βS)和(R,γO,βS)补货策略,牛鞭效应随着订货提前期的增大而增大;对于(R,γO)和(R,γO,βS)补货策略,牛鞭效应随着时刻t的增大而增大,但时刻t增大到一定程度时,牛鞭效应值基本不变.     

Measuring endogenous supply chain volatility: Beyond the bullwhip effect

Most recent research on supply chain volatility has focused on one particular dimension of that volatility, namely the amplification of upstream order variability. While not ignoring this aspect of supply chain volatility, we focus on a different but equally critical aspect of volatility: the cyclical oscillation of on-hand and on-order inventories about their target values. We prove that such cyclicality does not require oscillatory or random retailer demand as a prerequisite; the resulting volatility is therefore endogenous rather than simply an amplification of exogenous demand inputs. We also measure the amount of amplification resulting from a step increase in demand. The order amplification is the product of two factors, each of which is clearly linked to either on-hand or on-order inventory. Our results attest that supply chain volatility can arise in the absence of exogenous oscillatory or random demand and suggest strategies for avoiding or minimizing such volatility.     

Analysis of supply chains with quantity based fixed incentives

This paper examines the use of quantity based fixed incentives to coordinate inventory decisions in a decentralized supply chain. We consider a two stage supply chain of autonomous supplier and distributor and prove that the optimal ordering policy for the newsvendor distributor under fixed incentives is an (s,S)$(s\text{,}S)$ type policy. We further show that external and internal quantity based incentives can restore channel coordination in single period and channel members can benefit through arbitrary splitting of the resulting additional chain profit. The single period results are extended to multiple periods and the impact of fixed incentives on the distributor’s optimal stocking policy and channel efficiency are examined under three different multi-period supplier strategies. Numerical examples are used to compare the multi-period strategies and to provide additional managerial insights. The results show that contrary to common belief, incentive plans developed and maintained based only on current inventory data perform poorly in long term and that such incentive plans must be periodically updated to enhance their efficiency. Furthermore, we show that high level of incentives designed to push too much inventory downstream of the supply chain can actually reduce the chain’s efficiency.     

Order-Up-To policies in Information Exchange supply chains

Collaboration in Supply Chains (SC) is concerned with the alignment of the decision making process amongst SC partners. This is crucial in the planning and inventory management area where this alignment is enabled by the exchange of information. Several benefits deriving from such effective collaboration exist, such as: excess inventory elimination, lead times reduction, improved customer service, efficient product development, etc. Operations Management literature proclaims the virtues of collaboration and information sharing but academicians and practitioners have recently identified various gaps that still need further work. More specifically it has been shown that several deleterious phenomena as the bullwhip effect; inventory instability and intermittent orders are not completely eliminated in Information Exchange supply chains. The reason is mainly because companies adopt order policies that are prone to create instability along the SC. In this paper we show how the performance of an Information Exchange SC can be improved by shifting from a myopic periodic review Order-Up-To policy to a periodic review Order-Up-To with feedback gain. To do so, we model the SC structure through difference equations and study the system response in term of internal process efficiency and customer service level.     

Internal supply chain coordination in the electric utility industry

Electric utilities have a well-established vertical internal and external supply chain. Theoretically, information sharing, involving production, inventory, and other policy variables, between chain entities can improve supply chain performance. Such sharing relies on a systematic determination of the optimal policy variables for the chain. This paper presents an analysis of the electric utility’s decision problem based on an optimal control model in a competitive market environment. Optimal production and inventory policies are developed for a centralized supply chain under full information sharing. The model and policies are tested with electric utility industry data, and performance implications are discussed for electric utility managers and public regulators.