Unwanted fluctuations and instability in operations can significantly increase the operational costs of closed-loop supply chains (CLSCs). Given the coexistence of variance amplifications of order, on-hand inventory, and work-in-process inventory in CLSCs, measuring the overall system variance amplification to support coordinated production and inventory decisions can support performance improvement. However, existing research has largely focused on variance amplification in order and on-hand inventory volumes, ignoring work-in-process variance which can also have significant economic implications. Also, most relevant studies examined the behaviour of each variance separately or adopted a weighted average of inventory and order variances with fixed, predetermined weights. Motivated by these gaps, we propose a novel System Dynamics Stochastic rank Index (SDSI) approach to analyse the total variance amplification of CLSCs. The results showed that different inventory control strategies should be implemented based on different weights among variance amplifications. However, the values of manufacturing lead times, remanufacturing lead times, and return rate that minimise the total variance amplification remain similar under different relative weights. Furthermore, the lead time and yield paradox phenomena were observed under the SDSI framework, suggesting relevant trade-offs between economic and sustainable operations in CLSCs.

Closed-loop supply chains (CLSCs) are becoming increasingly important for sustainable operations, but their dynamic behaviour remains underexplored when new and remanufactured products are not perfect substitutes. Furthermore, existing CLSCs dynamics studies rarely examine how market-level customer preference for remanufactured products and stochastic price dynamics jointly affect the bullwhip effect (BE) and net stock amplification (NSAmp). To address this gap, this study develops a two-echelon CLSC system dynamics model including an independent manufacturer and remanufacturer under the order-up-to policy. The demand model incorporates customer preference for remanufactured products and exogenous prices for new and remanufactured products, whose price dynamics follow first-order autoregressive processes. Exact closed-form expressions of the BE and NSAmp for both product types are derived based on variance analysis. Also, system dynamics simulation is conducted to examine the effects of customer preference, price dynamics, lead times, and return rate on the BE and NSAmp. The results show when the autoregressive parameter of the new-product price exceeds that of the remanufactured-product price, stronger customer preference for remanufactured products reduces BE for both products and lowers NSAmp for new products, but increases it for remanufactured products; the opposite holds when the remanufactured-product price is more autoregressive. Both price autoregressive parameters exhibit inverse U-shaped relationships with the BE and NSAmp. In addition, lead times and return rate significantly affect the BE and NSAmp, leading to dynamic instability. This study extends CLSCs dynamics research by relaxing the perfect-substitution assumption and providing analytical and managerial insights concerning pricing, remanufacturing promotion, and return management.

This study explores the bullwhip behaviour of a hybrid manufacturing-remanufacturing system, replenished by the order-up-to policy, under auto-correlated autoregressive and integrated moving average (ARIMA) demand and corrected returns. The phenomena of demand auto-correlation are common in various industries such as automobile, beverage, and fruit and vegetables industries. However, only first-order vector autoregressive (VAR(1)) and independent and identically distributed (i.i.d.) process have been studied in the context of closed loop supply chains (CLSCs) system dynamics. Therefore, by using z-transform and discrete-time simulation, we explore bullwhip and inventory variance under i.i.d, AR (1), first-order moving average (MA(1)) and first-order autoregressive and moving average (ARMA(1,1)) demand processes. It is found that, for products that have autoregressive demand characteristics, bullwhip decreases with the autoregressive demand parameter, while autoregressive return parameter has a U-shaped impact on the bullwhip. For those with moving average demand patterns, bullwhip increases with the moving average demand parameter and decreases with the moving average return parameter. Also, system parameters including return rate, inventory proportional controller and forecasting smoothing not only directly impact on bullwhip and inventory variance, but also act as the moderator in influencing the relationship between demand processes and bullwhip/inventory variance. These findings imply important managerial implication to control the bullwhip costs associated with products characterised by both autoregressive and moving average demand processes.

In anticipation of price hikes and shortages caused by supplier disruptions and manufacturer production stops, customers might stockpile extra products. In the case of a supplier disruption, a manufacturer may decide to continue producing using a contingent source. Capturing the price dynamics in four disruption-related periods (i.e., responding, rising, recovering, and recovered), we derive optimal hoarding policies for customers. The results indicate that customer hoarding decisions fall into multiple patterns depending on the interactions between disruption events, market responses (quick and slow), and market recovery (instant, quick, slow, and never). We next present contingent sourcing tactics for manufacturers to mitigate disruptions with and without customer hoarding. We find that future price increases could induce contingent sourcing even if it is unprofitable to resume production during the price-responding phase. Our results offer recommendations regarding when and how to use hoarding and contingent sourcing accounting for uncertain disruption duration and asymmetric information along with disruption- and recovery-driven price dynamics. These recommendations can be of particular value for supply chain decision-making at times of growing inflation. We also demonstrate the impacts of customer hoarding and disruption information on the value of contingent sourcing.

Purpose This paper aims to explore blockchain integration strategies within a three-level livestock meat supply chain in which consumers have a preference for quality trust in livestock meat products. The paper investigates three questions: First, how does consumers’ preference for quality trust affect blockchain integration and transaction decisions among supply chain participants? Second, under what circumstances will retailers choose to participate in the blockchain? Finally, how can other factors such as blockchain costs and supplier–retailer partnership value affect integration decisions? Design/methodology/approach This paper formulates a supply chain network equilibrium model and employs the logarithmic-quadratic proximal prediction-correction method to obtain equilibrium decisions. Extensive numerical studies are conducted using a pork supply chain network to analyze the implications of blockchain integration for different supply chain participants. Findings The results reveal several key insights: First, suppliers’ increased blockchain integration, driven by higher quality trust preference, can negatively affect their profits, particularly, with excessive trust preferences and high blockchain costs. Second, an increase in consumers’ preference for quality trust expands the range of unit operating costs for retailers engaging in blockchain. Finally, the supplier–retailer partnership drives retailer blockchain participation, facilitating enhanced information sharing to benefit the entire supply chain. Originality/value This study provides original insights into blockchain integration strategies in an agricultural supply chain through the application of the supply chain network equilibrium model. The investigation of several key factors on equilibrium decisions provides important managerial implications for different supply chain participants to address consumers’ preference for quality trust and enhance overall supply chain performance.

With the significant growth of the e-commerce business, the retail industry is experiencing rapid developments, leading to the explosion of the number of stock-keeping units (SKUs). Therefore, it calls for forecasting algorithms to forecast a large number of product-level demands over a short forecasting horizon. We developed a novel machine learning algorithm-the spatial-temporal gradient boosting tree (ST-GBT)-for demand forecasting for the retail industry. By incorporating the cross-section and time-series information in the existing gradient-boosting decision tree algorithm, our new algorithm can accurately forecast tremendous SKUs in one process. Furthermore, we show potential factors related to the retail industry, while new factors, such as higher-order statistics and risk-free interest, are also proposed for demand forecasting tasks. The numerical experiment results based on a large e-commerce company's historical transaction records support the comparative merits of the new algorithm with superior accuracy and automation ability.

The effective operations of closed-loop supply chains (CLSCs) can help companies achieve sustainability goals and boost economic performance. In practice, CLSCs must collect used products, a complex process that is often constrained by collection station capacity. However, how collection station capacity influences the bullwhip effect and the dynamic performance of CLSCs remains unclear. Here, we develop a system dynamics model for CLSCs that integrates traditional manufacturing with remanufacturing and explore the effects of the stochastic capacity constraint of the collection station on the bullwhip effect of CLSCs. We find that, generally speaking, a collection station with looser or more stable capacity constraints tends to reduce bullwhip of CLSCs. However, pertinent interactions emerge between the relevant parameters; in some situations, reducing the capacity level of a collection station may be reasonable and beneficial when the stochastic capacity constraint is very stable, or when customer demand is highly variable. We also consider the partial backlog in return collection, a phenomenon associated with the stochastic capacity constraint of a collection station, and identify a new trade-off between CLSC sustainability and economic performance. Ultimately, our findings provide evidence that will guide managers' plans for the capacity management of return collection in CLSCs.

We consider a component manufacturing and remanufacturing system where, due to the end-of-life warranty, new and after-sales demand must be satisfied. Two kinds of demand exhibit different lifecycle patterns with different scales and a time lag, while a third correlated component return lifecycle with again a different lag and scale, driven by adoption of remanufacturing, is also presented. To achieve supply and demand balance during demand lifecycles, companies need a strategic decision on their remanufacturing: remanufacturing outsourcing strategy (ROS) or remanufacturing in-house strategy (RIS), yet inadequately studied from system dynamics perspective. We developed base-stock system dynamics models and analytically explored the dynamic implications of RIS and ROS remanufacturing strategies under correlated lifecycle demand and returns. Applying z-transform and discrete time simulation, we found that RIS outperforms ROS system including less peak capacity cost, less inventory holding cost and less backlog cost. Also, the bullwhip of the RIS is always less than the ROS system. However, the adoption of the RIS may result longer-lasting manufacturing production and thus lead to a higher cost: an important cost needs to be strategically considered. Thereby, from system dynamics perspective, the component manufacturer needs carefully consider trade-offs between production and inventory costs, as well as their demand lifecycle characteristics to choose the right remanufacturing strategy.

Consumers' demand for fresh agricultural products (FAPs) and their quality requirements are increasing in the current agricultural-product consumption market. FAPs' unique perishability and short shelf-life features mean a high level of delivery efficiency is required to ensure their freshness and quality. However, consumers' demand for FAPs is contingent and geographically dispersed. Therefore, the conflicting relationship between the costs associated with the logistics distribution and the level of delivery quality is important to consider. In this paper, the authors consider a fresh agricultural-product distribution path planning problem with time windows (FAPDPPPTW). To address the FAPDPPPTW under demand uncertainty, a mixed-integer linear programming model based on robust optimization is proposed. Moreover, a particle swarm optimization algorithm combined with a variable neighborhood search is designed to solve the proposed mathematical model. The numerical experiment results show the robustness and fast convergence of the algorithm.

The hybrid closed-loop supply chain (CLSC) system, commonly observed in the consumer electronics and automotive industries, may include one or more product recovery options, such as product repair and core remanufacturing. From system dynamics perspective, one important strategic decision is how many recovery options (and in which locations) should be invested to minimise poor dynamic behaivor such as bullwhip effect. This motivates us to investigate the impact of the number and locations of recovery options on the dynamic behaviour. We adopt step and sinusoidal functions as customer demand, representing a sudden sustained shift in demand and seasonally unadjusted demand, respectively. We also consider different return rates for each echelon of the CLSC. Our simulation results indicate that the bullwhip effect and inventory variance can be significantly reduced in all CLSC scenarios in comparison to a traditional open loop supply chain. However, a increased number of product recovery options does not improve the dynamic performance of the CLSC. Moreover, the bullwhip effect and inventory variance may be reduced if product recovery options are located at downstream echelons that are closer to end customers (e.g. retailers) and have high return rates. Further, return rates play a key role in mitigating the bullwhip effect, consistent with the prior literature. Our findings provide strategic insights for managers seeking to improve their CLSCs performance from system dynamics perspective.

Managing order pipeline inventory is important for controlling unwanted system dynamics, especially the bullwhip effect. We analytically explore the impact of desired target order pipeline inventory, advocated as a key decision in managing pipeline inventory, on system dynamics performance. Using control theory and system dynamics simulation, we evaluate two control mechanisms, termed as Reactive Pipeline Control (RPC) and Proactive Pipeline Control (PPC) approaches, in a nonlinear forbidden returns supply chain. We derive the analytical expressions of bullwhip under shock and seasonal demands and propose bullwhip avoidance strategies. The results indicate that an RPC based system always shows slower inventory convergence speed than that in the PPC based system, although the system with PPC policy may produce more unwanted oscillatory behaviour. Also, PPC always generates more bullwhip than that in an RPC-controlled system regardless of physical delays and system control parameters e.g. forecasting and inventory adjustment. Furthermore, compared with the linear system, the nonlinear forbidden returns system always generates less bullwhip and less oscillation at the expense of slow inventory recovery speed regardless of order pipeline control policies. Managers may consider different order pipeline control policies by jointly assessing their inherent system structure, control policies and customer demand characteristics, such as frequency and variance.

We study the dynamic behaviour of a hybrid system where manufacturing and remanufacturing operations occur simultaneously to produce the same serviceable inventory for order fulfilment. Such a hybrid system, commonly found in the photocopier and personal computer industries, has received considerable attention in the literature. However, its dynamic performance and resulting bullwhip effect, under push and pull remanufacturing policies, remain unexplored. Relevant analysis would allow considering the adoption of appropriate control strategies, as some of the governing rules in a push-based environment may break down in pull-driven systems, and vice versa. Using nonlinear control theory and discrete-time simulation, we develop and linearise a nonlinear stylised model, and analytically assess bullwhip performance of push-and pull-controlled hybrid systems. We find the product return rate to be the key influencing factor of the order variance performance of pull-controlled hybrid systems, and thus, to play an important role towards push or pull policy selection. Product demand frequency is another important factor, since order variance has a U-shaped relation to it. Moreover, the product return delay shows a supplementary impact on the system's dynamics. In particular, the traditional push-controlled hybrid system may be significantly influenced by this factor if the return rate is high. The results highlight the importance of jointly considering ordering structure and product demand characteristics for bullwhip avoidance.(c) 2021 The Author(s). Published by Elsevier B.V.This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

The bullwhip effect, also known as demand information amplification, is one of the principal obstacles in supply chains. In recent decades, extensive studies have explored its operational causes and have proposed corresponding solutions in the context of production inventory and supply chain systems. However, the underlying assumption of these studies is that human decision-making is always rational. Yet, this is not always the case, and an increasing number of recent studies have argued that behavioural and psychological factors play a key role in generating the bullwhip effect in real-world supply chains. Given the prevalence of such research, the main objective of this study is to provide a systematic literature review on the bullwhip effect from the behavioural operations perspective. Using databases, including Scopus, Wiley Online Library, Google Scholar and Science Direct, we selected, summarised and analysed 53 academic studies. We find that most studies build their models and simulations based on the 'beer distribution game' and analyse the results at the individual level. We also demonstrate the importance of studying human factors in the bullwhip effect through adapting Sterman's double-loop learning model. Based on this model, we categorise and analyse the behavioural factors that have been studied and identify the explored behavioural factors for future research. Based on our findings, we suggest that future studies could consider social and cultural influences on decision-making in studying the bullwhip effect. In addition, further aspects of human mental models that cause this effect can be explored.

System dynamics play a critical role in influencing supply chain performance. However, the dynamic property of the assemble-to-order (ATO) system remain unexplored. Based on control theory, the inventory and order based production control system (IOBPCS) family, can be utilized as a base framework for assessing system dynamics. However, the underlying assumption in traditional IOBPCS-based analytical studies is that the system is linear and the delivery time to end customers is negligible or backlog is used as a surrogate indicator. Our aim is to incorporate customer delivery lead-time variance as the third assessment measure alongside capacity availability and inventory variance as part of the so-called ‘performance triangle’– capacity at the supplier, the customer order decoupling point (CODP) inventory and the delivery lead-time. Using the ‘performance triangle’ and adopting non-linear control engineering techniques, we assess the dynamic behaviour of an ATO system in the electronics sector. We benchmark the ATO system dynamics model against the IOBPCS family. We exploit frequency response analysis to ensure a robust system design by considering three measures of the ‘performance triangle’. The findings suggest delivery LT variance can be minimised by maintaining the ATO system as a true Push-Pull hybrid state with sufficient CODP stock, although increased operational cost driven by bullwhip and CODP variance need to be considered. However, if the hybrid ATO system 'switches' to the pure Push state, the mean and variance of delivery LT can be significantly increased.

Non-linearities can lead to unexpected dynamic behaviours in supply chain systems that could then either trigger disruptions or make the response and recovery process more difficult. In this chapter, we take a control-theoretic perspective to discuss the impact of non-linearities on the ripple effect. This chapter is particularly relevant for researchers wanting to learn more about the different types of non-linearities that can be found in supply chain systems, the existing analytical methods to deal with each type of non-linearity and future scope for research based on the current knowledge in this field.

The hybrid assembly-to-order (ATO) supply chain, combining make-to-stock and make-to-order (MTS-MTO) production, separated by a customer order decoupling point (CODP), is well recognised in many sectors. Based on the well-established Inventory and Order Based Production Control Systems (the IOBPCS family), we develop a hybrid ATO system dynamics model and analytically study the impact of nonlinearities on its dynamic performance. Nonlinearities play an important, sometimes even a dominant, role in influencing the dynamic performance of supply chain systems. However, most IOBPCS based analytical studies assume supply chain systems are completely linear and thereby greatly limit the applicability of published results, making it difficult to fully explain and describe oscillations caused by internal factors. We address this gap by analytically exploring the non-negative order and capacity constraint nonlinearities present in an ATO system. By adopting nonlinear control engineering and simulation approaches, we reveal that, depending on the mean and amplitude of the demand, the non-negative order and capacity constraints in the ATO system may occur and their significant impact on system dynamics performance should be carefully considered. Failing to monitor non-negative order constraints may underestimate the mean level of inventory and overestimate the inventory recovery speed. Sub-assemblers may suffer increased inventory cost (i.e. the consequence of varying inventory levels and recovery speed) if capacity and non-negative order constraints are not considered at their production site. Future research should consider the optimal trade-off design between CODP inventory and capacity and the exploration of delivery lead-time dynamics.

In 1994, through classic control theory, John, Naim and Towill developed the ‘Automatic Pipeline, Inventory and Order-based Production Control System’ (APIOBPCS) which extended the original IOBPCS archetype developed by Towill in 1982 ─ well-recognised as a base framework for a production planning and control system. Due to the prevalence of the two original models in the last three decades in the academic and industrial communities, this paper aims to systematically review how the IOBPCS archetypes have been adopted, exploited and adapted to study the dynamics of individual production planning and control systems and whole supply chains. Using various databases such as Scopus, Web of Science, Google Scholar (113 papers), we found that the IOBPCS archetypes have been studied regarding the a) modification of four inherent policies related to forecasting, inventory, lead-time and pipeline to create a ‘family’ of models, b) adoption of the IOBPCS ‘family’ to reduce supply chain dynamics, and in particular bullwhip, c) extension of the IOBPCS family to represent different supply chain scenarios such as order-book based production control and closed-loop processes. Simulation is the most popular method adopted by researchers and the number of works based on discrete time based methods is greater than those utilising continuous time approaches. Most studies are conceptual with limited practical applications described. Future research needs to focus on cost, flexibility and sustainability in the context of supply chain dynamics and, although there are a few existing studies, more analytical approaches are required to gain robust insights into the influence of nonlinear elements on supply chain behaviour. Also, empirical exploitation of the existing models is recommended.

The inventory and order based production control system (IOBPCS) is mainly a model of a forecast driven production system where the production decision is based on the forecast in combination with the deviation between target inventory and actual inventory. The model has been extended in various directions by including e.g. WIP feedback but also by interpreting the inventory as an order book and hence representing a customer order driven system. In practice a system usually consists of one forecast driven subsystem in tandem with a customer order driven subsystem and the interface between the two subsystems is represented by information flows and a stock point associated with the customer order decoupling point (CODP). The CODP may be positioned late in the flow, as in make to stock systems, or early, as in make to order systems, but in any case the model should be able to capture the properties of both subsystems in combination. A challenge in separating forecast driven from customer order driven is that neither the inventory nor the order book should be allowed to take on negative values, and hence non-linearities are introduced making the model more difficult to solve analytically unless the model is first linearized. In summary the model presented here is based on two derivatives of IOBPCS that are in tandem, and interfaces between them related to where the demand information flow is decoupled and the position of the CODP.