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.     

Interpreting supply chain dynamics: A quasi-chaos perspective

Chaotic phenomena, chaos amplification and other interesting nonlinear behaviors have been observed in supply chain systems. Chaos can be defined theoretically if the dynamics under study are produced only by deterministic factors. However, deterministic settings rarely present themselves in reality. In fact, real data are typically unknown. How can the chaos theory and its related methodology be applied in the real world? When the demand is stochastic, the interpretation and distribution of the Lyapunov exponents derived from the effective inventory at different supply chain levels are not similar to those under deterministic demand settings. Are the observed dynamics of the effective inventory random, chaotic, or simply quasi-chaos? In this study, we investigate a situation whereby the chaos analysis is applied to a time series as if its underlying structure, deterministic or stochastic, is unknown. The result shows clear distinction in chaos characterization between the two categories of demand process, deterministic vs. stochastic. It also highlights the complexity of the interplay between stochastic demand processes and nonlinear dynamics. Therefore, caution should be exercised in interpreting system dynamics when applying chaos analysis to a system of unknown underlying structure. By understanding this delicate interplay, decision makers have the better chance to tackle the problem correctly or more effectively at the demand end or the supply end.     

Managing the order pipeline to reduce supply chain volatility

The bullwhip effect in particular, and supply chain volatility in general, has been the subject of much analytical and empirical investigation by researchers. One goal of this work has been to determine supply chain designs and policies that minimize volatility. Using a system dynamics approach, we use three distinct supply chain volatility metrics to compare the ability of two alternative pipeline inventory management policies to respond to a demand shock. The results indicate that no one policy dominates on all three metrics of supply chain volatility. A simplistic static pipeline policy minimizes the bullwhip effect and lessens the likelihood of on-hand inventory oscillations, while a more sophisticated dynamic pipeline policy may converge more rapidly to the new equilibrium. In addition, simulation results suggest that the dynamic policy provides better customer service through fewer stockouts and backorders.     

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.     

A stochastic and asymmetric-information framework for a dominant-manufacturer supply chain

Consider a dominant manufacturer wholesaling a product to a retailer, who in turn retails it to the consumers at $p/unit. The retail-market demand volume varies with p according to a given demand curve. This basic system is commonly modeled as a manufacturer-Stackelberg ([mS]) game under a “deterministic and symmetric-information” (“det-sym-i”) framework. We first explain the logical flaws of this framework, which are (i) the dominant manufacturer-leader will have a lower profit than the retailer under an iso-elastic demand curve; (ii) in some situations the system’s “correct solution” can be hyper-sensitive to minute changes in the demand curve; (iii) applying volume discounting while keeping the original [mS] profit-maximizing objective leads to an implausible degenerate solution in which the manufacturer has dictatorial power over the channel. We then present an extension of the “stochastic and asymmetric-information” (“sto-asy-i”) framework proposed in Lau and Lau [Lau, A., Lau, H.-S., 2005. Some two-echelon supply-chain games: Improving from deterministic–symmetric-information to stochastic-asymmetric-information models. European Journal of Operational Research 161 (1), 203–223], coupled with the notion that a profit-maximizing dominant manufacturer may implement not only [mS] but also “[pm]”—i.e., using a manufacturer-imposed maximum retail price. We show that this new framework resolves all the logical flaws stated above. Along the way, we also present a procedure for the dominant manufacturer to design a profit-maximizing volume-discount scheme using stochastic and asymmetric demand information.     

A multi-structural framework for adaptive supply chain planning and operations control with structure dynamics considerations

A trend in up-to-date developments in supply chain management (SCM) is to make supply chains more agile, flexible, and responsive. In supply chains, different structures (functional, organizational, informational, financial, etc.) are (re)formed. These structures interrelate with each other and change in dynamics. The paper introduces a new conceptual framework for multi-structural planning and operations of adaptive supply chains with structure dynamics considerations. We elaborate a vision of adaptive supply chain management (A-SCM), a new dynamic model and tools for the planning and control of adaptive supply chains. SCM is addressed from perspectives of execution dynamics under uncertainty. Supply chains are modelled in terms of dynamic multi-structural macro-states, based on simultaneous consideration of the management as a function of both states and structures. The research approach is theoretically based on the combined application of control theory, operations research, and agent-based modelling. The findings suggest constructive ways to implement multi-structural supply chain management and to transit from a “one-way” partial optimization to the feedback-based, closed-loop adaptive supply chain optimization and execution management for value chain adaptability, stability and crisis-resistance. The proposed methodology enhances managerial insight into advanced supply chain management.     

Capacity allocation,ordering, and pricing decisions in a supply chain with demand and supply uncertainties

This paper studies coordinated decisions in a decentralized supply chain that consists of one Original Equipment Manufacturer (OEM), one manufacturer, and one distributor, and possesses uncertainties at both demand and supply sides. These uncertainties emerge, respectively, from random demand the distributor faces and randomness of capacity with which the OEM processes the manufacturer’s outsourced quantity. Sharing supply and demand uncertainty information along the supply chain enables us to develop three models with different coordination efforts—the OEM and manufacturer coordination, the manufacturer and distributor coordination, and the OEM, manufacturer, and distributor coordination—and quantify the coordinated decisions in these three models. Our analysis of these coordination models suggests that coordinating with the OEM improves the manufacturer’s probability of meeting downstream demand and his expected profit, yet coordinating with the manufacturer is not necessarily beneficial to the OEM when downstream coordination is lacking.     

The use of a premium-payment scheme in a supply chain involving capacity acquisition

We study a practice whereby a downstream firm makes to his supplier a premium-payment for a certain quantity of products. We show that the adoption of this practice can induce the supplier to build bigger capacity. The higher capacity level enables the supplier to satisfy a larger portion of demands from the downstream firm, and this leads to higher payoffs for both parties in the supply chain. With the assistance of an under-capacity penalty imposed on the supplier, this premium-payment scheme can help lure the parties into taking the channel-optimal actions. Our numerical examples help reveal various features of the scheme.     

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.     

Control and system-theoretic identification of the supply chain dynamics domain for planning,analysis and adaptation of performance under uncertainty

The analysis of how to achieve planned economic performance in a real-time, uncertain and perturbed execution environment is a vital and up-to-date issue in many supply chains. Although it is intuitive that uncertainty is likely to have impacts on performance, the research on systematic terminology and quantitative analysis in this domain is rather limited as compared with the well-established domain of supply chain optimal planning. This study is among the first to address the operative perspective of the supply chain dynamics domain. The methodology of this conceptual paper is based on the business and technical literature analysis and fundamentals of control and systems theory. In contributing to the existing studies in this domain, the paper proposes a possible systemization and classification of related terminology from different theoretical perspectives, and important practical problems. For the supply chain dynamics domain, the paper identifies and groups possible problem classes of research, corresponding quantitative methods, and describes the general mathematical formulations. The results of this study may be of interest to both academics and practitioners.     

Flexible long-term capacity planning in closed-loop supply chains with remanufacturing

We deal with long-term demand-driven capacity planning policies in the reverse channel of closed-loop supply chains (CLSCs) with remanufacturing, under high capacity acquisition cost coupled with uncertainty in actual demand, sales patterns, quality and timing of end-of-use product returns. The objective is to facilitate the decision-making when the management faces the dilemma of implementing either a strategy of early large-scale investments to benefit from economies of scale and capacity readiness, or a flexible strategy of low volume but more frequent capacity expansions. We consider a CLSC with two sequential product-types. We study the system’s response in terms of transient flows, actual/desired capacity level, capacity expansions/contractions and total supply chain profit, employing a simulation-based system dynamics optimization approach. Extensive numerical investigation covers a broad range of real-world remanufacturable products under alternative scenarios in relation to the market preference over product-types. The key findings propose flexible policies as improved alternatives to large-scale capacity expansions/contractions in terms of adaptability to the actual pattern of end-of-use product returns and involved risk in the investments’ turnover. Flexible policies are also proposed as practices to avoid overcapacity phenomena in collection and remanufacturing capacity and as robust policies to product demand. Their implementation is revealed to be even more important for the case of remanufacturing, when a high capacity acquisition unit-cost ratio (remanufacturing/collection) is coupled with strong economies of scale. Finally, results under different information sharing structures show changes in remanufacturing policies, thus justifying the importance of coordination between the decision-maker and the distributor.     

Make-or-buy service capacity decision in a supply chain providing after-sales service

We consider a supply chain comprising a manufacturer and a retailer. The manufacturer supplies a product to the retailer, while the retailer sells the product bundled with after-sales service to consumers in a fully competitive market. The sales volume is affected by the retailer’s service-level commitment. The retailer can build service capacity in-house at a deterministic price before service demand is realized, or buy the service from an outsourcing market at an uncertain price after service demand realization. We find that the outsourcing market encourages the retailer to make a higher level of service commitment, while prompting the manufacturer to reduce the wholesale price, resulting in more demand realization. We analyze how the expected cost of the service in the outsourcing market and the retailer’s risk attitude affect the decisions of both parties. We derive the conditions under which the retailer is willing to build service capacity in-house and under which it will buy the service from the outsourcing market. Moreover, we find that the manufacturer’s sharing with the retailer the cost to build service capacity improves the profits of both parties.     

Equilibrium analysis of supply chain structures under power imbalance

This paper investigates the implications of channel power on supply chain stability in a setting where multiple suppliers sell substitutable products through a common retailer. Such supply chains have been traditionally analyzed as one- or two-stage Stackelberg non-cooperative games with all suppliers sharing balanced (equal) decision-making power. In this paper, we relax this assumption and formulate game-theoretic models to examine scenarios where one supplier can act as the Stackelberg leader. Consequently, we analyze new supply chain structures and introduce the notion of structure dominance, a novel approach to analyze the performance of supply chains that has practical implications. Thus, a decision maker can employ the concepts of structure dominance to determine whether there exist supply chain scenarios that are more stable than others, i.e., less prone to power reconfigurations, at both agent and group level. We find that power imbalance causes significant declines in supply chain profits, and the more balanced the agents are the higher their profits when demand is linear, regardless of product competition. It develops that neither the Manufacturer Stackelberg nor the Retailer Stackelberg supply chains are stable structures in our generalized setting, but that structures where power is equally split between agents provide for best stability and performance.     

A two-echelon supply chain of a returnable product with fuzzy demand

This study investigates the effects of the manufacturer’s refund on retailer’s unsold products for the two-echelon decentralized and centralized supply chains of a short life and returnable product with trapezoidal fuzzy demand, in which retailer returns the unsold and the customer’s unsatisfactory products to the manufacturer. For each returnable chain, we obtain the closed-form solution of order quantity to maximize the total expected profit of the supply chain, and confirm that demand fuzziness does indeed affect the order quantity and the members’ expected profits. We provide a number of managerial insights by comparing both chains and show that each chain is more advantageous to the members depending on certain condition. Our models are appropriate for a supply chain with a returnable product that lacks information about the demand.     

A possibilistic decision model for new product supply chain design

This paper models supply chain (SC) uncertainties by fuzzy sets and develops a possibilistic SC configuration model for new products with unreliable or unavailable SC statistical data. The supply chain is modeled as a network of stages. Each stage may have one or more options characterized by the cost and lead-time required to fulfill required functions and may hold safety stock to prevent an inventory shortage. The objective is to determine the option and inventory policy for each stage to minimize the total SC cost and maximize the possibility of fulfilling the target service level. A fuzzy SC model is developed to evaluate the performance of the entire SC and a genetic algorithm approach is applied to determine near-optimal solutions. The results obtained show that the proposed approach allows decision makers to perform trade-off analysis among customer service levels, product cost, and inventory investment depending on their risk attitude. It also provides an alternative tool to evaluate and improve SC configuration decisions in an uncertain SC environment.     

Pricing and horizontal information sharing in a supply chain with capacity constraint

This paper aims to explore manufacturers horizontal information sharing strategy under competition. The model framework is based on a two-echelon supply chain composed of one upstream supplier and two downstream manufacturers with asymmetric capacity constraint. Analysis of the model establishes manufacturers’ information sharing strategies under different conditions and shows how supplier’s pricing decision can shape manufacturers’ information sharing incentives.     

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.     

Existence of equilibria in a decentralized two-level supply chain

In this paper, we analyze equilibria in competitive environments under constraints across players’ strategies. This means that the action taken by one player limits the possible choices of the other players. In this context, the usual approach to show existence of equilibrium, Kakutani’s fixed point theorem, cannot be applied directly. In particular, best replies against a given strategy profile may not be feasible. We devise a new fixed point correspondence to deal with the feasibility issue.     

Wholesale price rebate vs. capacity expansion: The optimal strategy for seasonal products in a supply chain

We consider a supply chain in which one manufacturer sells a seasonal product to the end market through a retailer. Faced with uncertain market demand and limited capacity, the manufacturer can maximize its profits by adopting one of two strategies, namely, wholesale price rebate or capacity expansion. In the former, the manufacturer provides the retailer with a discount for accepting early delivery in an earlier period. In the latter, the production capacity of the manufacturer in the second period can be raised so that production is delayed until in the period close to the selling season to avoid holding costs. Our research shows that the best strategy for the manufacturer is determined by three driving forces: the unit cost of holding inventory for the manufacturer, the unit cost of holding inventory for the retailer, and the unit cost of capacity expansion. When the single period capacity is low, adopting the capacity expansion strategy dominates as both parties can improve their profits compared to the wholesale price rebate strategy. When the single period capacity is high, on the other hand, the equilibrium outcome is the wholesale price rebate strategy.