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.     

Coordinating order quantity decisions in the supply chain contract under random demand

In this paper, we are concerned with the coordinating quantity decision problem in a supply chain contract. The supply chain contract is composed of one manufacturer and one retailer to meet the random demand of a single product with a short lifecycle. Our analysis show that the retailer expects to obtain higher profit under proper ordering policies, which can also maximize the expected profit of the supply chain. The manufacturer may induce the retailer to order the coordinated quantity by adjusting the unit return price. As a result, the supply chain is expected to achieve the optimal expected profit.     

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.     

Mesoscopic supply chain simulation

This paper reviews and compares existing approaches for supply chain modeling and simulation and applies the mesoscopic modeling and simulation approach using the simulation software MesoSim, an own development. A simplified real-world supply chain example is modeled with discrete event, mesoscopic and system dynamics simulation. The objective of the study is to compare the process of model creation and its validity using each approach. The study examines advantages of the mesoscopic approach for the simulation. Major benefits of the mesoscopic approach are that modeling efforts are balanced with the necessary level of detail and facilitate quick and simple model creation and simulation.     

A multi-objective approach to supply chain visibility and risk

This paper investigates the twin effects of supply chain visibility (SCV) and supply chain risk (SCR) on supply chain performance. Operationally, SCV has been linked to the capability of sharing timely and accurate information on exogenous demand, quantity and location of inventory, transport related cost, and other logistics activities throughout an entire supply chain. Similarly, SCR can be viewed as the likelihood that an adverse event has occurred during a certain epoch within a supply chain and the associated consequences of that event which affects supply chain performance. Given the multi-faceted attributes of the decision making process which involves many stages, objectives, and stakeholders, it beckons research into this aspect of the supply chain to utilize a fuzzy multi-objective decision making approach to model SCV and SCR from an operational perspective. Hence, our model incorporates the objectives of SCV maximization, SCR minimization, and cost minimization under the constraints of budget, customer demand, production capacity, and supply availability. A numerical example is used to demonstrate the applicability of the model. Our results suggest that decision makers tend to mitigate SCR first then enhance SCV.     

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.     

On a multi-period supply chain system with supplementary order opportunity

This paper considers a supplementary supply–order system in a multi-period situation. In each period, the buyer first places an initial order based on the demand prediction; he has the opportunity to place a supplementary order with the supplier after the demand of that period is realized. The supplier maintains an inventory, and decides the quantity to be produced and the quantity to be provided for the supplementary order in each time period. We formulate the problem as a multi-period inventory game, and derive the optimal production and order policies for the supplier and buyer, respectively. The existence and uniqueness of Nash equilibrium is proved in the generalized multi-period setting, and the closed-form Nash equilibrium solution is obtained when the parameters are stationary. Numerical study is performed to reveal more managerial insights. We find that the supplementary supply–order mechanism, if designed properly, can effectively improve the multi-period supply chain performance.     

The value of early order commitment in a two-level supply chain

One approach to supply chain coordination is early order commitment, whereby a retailer commits to purchase a fixed-order quantity at a fixed delivery time before demand uncertainty is resolved. In this paper, we develop an analytical model to quantify the cost savings of an early order commitment in a two-level supply chain where demand is serially correlated. A decision rule is derived to determine whether early order commitment will benefit the supply chain, and accordingly to determine the optimal timing for early commitment. Our results indicate that the supply chain would experience greater savings from early order commitment when – (a) the inventory item receives less value-added activities at the retailer site; (b) the manufacturing lead time is short; (c) demand correlation over time is positive but weak; or (d) the delivery lead time is long (if a condition exists). We also propose a rebate scheme for the supply chain partners to share the gains of practicing early order commitment.     

Managing a dual-channel supply chain under price and delivery-time dependent stochastic demand

Several leading manufacturers recently combined the traditional retail channel with a direct online channel to reach a wider range of customers. We examine such a dual-channel supply chain under price and delivery-time dependent stochastic customer demand. We consider five decision variables, the price and order quantity for both the retail and the online channels and the delivery time for the online channel. Uncertainty frequently arises in both retail and online channels and so additional inventory management is required to control shortage or overstock and that has an effect on the optimal order quantity, price, and lead time. We developed mathematical models with the profit maximization motive. We analyze both centralized and decentralized systems for unknown distribution function of the random variables through a distribution-free approach and also for known distribution function. We examine the effect of delivery lead time and customers’ channel preference on the optimal operation. For supply chain coordination a hybrid all-unit quantity discount along a franchise fee contract is used. Moreover, we use the generalized asymmetric Nash bargaining for surplus profit distribution. A numerical example illustrates the findings of the model and the managerial insights are summarized for centralized, decentralized, and coordinated scenarios.     

Coordination of cooperative cost-reduction efforts in a supply chain partnership

We study cooperative cost reduction in a decentralized supply chain with a single manufacturer and multiple suppliers. The manufacturer assembles components that are procured from the suppliers to produce a final product. Both the manufacturer and the suppliers invest in reducing the unit production costs of the components. We see that neither of the two well-known conventional contracts, the wholesale price contract and the cost-plus pricing contract, generally coordinates the supply chain, i.e., under both of these types of contract, the individual optimal cost-reduction efforts of players deviate from the centralized system-optimal solution. However, this result is not surprising because these contracts encourage either only the manufacturer or only the suppliers alone to invest in cost reduction.     

Coordinating the supply chain in the agricultural seed industry

This paper examines contract practices between suppliers and retailers in the agricultural seed industry. We construct and analyze single-retailer models of various contract types actually used in the industry, which include, for example, certain “bonus” and “penalty” features. With no assumption on the demand distribution, we establish sufficient conditions for contract parameters to guarantee supply chain coordination. Under the assumption of uniform demand, we fully characterize all coordinating contracts. In addition, we compare the models studied herein with other models in the literature and demonstrate that current behavior in the agricultural seed industry is substantively different than that captured by other models. Conversely, we argue why other existing models are not reasonable to implement in the agricultural seed industry.     

Adaptive fuzzy vendor managed inventory control for mitigating the Bullwhip effect in supply chains

This paper proposes an adaptive fuzzy control application to support a vendor managed inventory (VMI). The methodology applies fuzzy control to generate an adaptive smoothing constant in the forecast method, production and delivery plan to eliminate, for example, the rationing and gaming or the Houlihan effect and the order batching effect or the Burbidge effects and finally the Bullwhip effect. The results show that the adaptive fuzzy VMI control surpasses fuzzy VMI control and traditional VMI in terms of mitigating the Bullwhip effect and lower delivery overshoots and backorders. This paper also guides management in allocating inventory by coordinating suppliers and buyers to ensure minimum inventory levels across a supply chain. Adaptive fuzzy VMI control is the main contribution of this paper.     

A fuzzy newsvendor approach to supply chain coordination

In the absence of a clear command and control structure, a key challenge in supply chain management is the coordination and alignment of supply chain members who pursue divergent and often conflicting goals. The newsvendor model is typically used as a framework to quantify the cost of misalignment and to assess the impact of various coordination initiatives. The application of the newsvendor framework, however, requires the specification of some probability distribution for the sources of uncertainty, and in particular, for the market demand. The specification of an adequate demand distribution becomes difficult in the absence of statistical data. We therefore consider a fuzzy approach to the newsvendor problem. We use several fuzzy parameters in the model for the demand, the wholesale price, and the market sales price. We solve the fuzzy newsvendor problem to study three coordination policies: quantity discounts, profit sharing, and buyback. For each coordination policy, the optimal order quantity of the retailer is computed. The possible profits of the members in the supply chain are calculated with minimum sharing of private information. We further extend the fuzzy newsvendor model to a setting with a single manufacturer and multiple retailers under the assumption of ample capacity for the manufacturer. Detailed numerical examples are also provided.     

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.     

Coordination mechanisms of supply chain systems

Supply chain management (SCM) has become an important management paradigm. As supply chain members are often separate and independent economic entities, a key issue in SCM is to develop mechanisms that can align their objectives and coordinate their activities so as to optimize system performance. In this paper, we provide a review of coordination mechanisms of supply chain systems in a framework that is based on supply chain decision structure and nature of demand. This framework highlights the behavioral aspects and information need in the coordination of a supply chain. The identification of these issues points out several directions of future research in this area.     

Endogenous information acquisition in supply chain management

In this paper, we analyze an endogenous determination of efforts put into information acquisition and its impact on supply chain management. More specifically, we consider a supplier who sells a product to a buyer during a single selling season. Prior to placing an order with the supplier, the buyer has an option to acquire additional information about the demand by hiring experts (who are capable of providing forecasts). Because a commission fee must be paid to each hired expert, there exists a tradeoff between the cost and the value of the information, and the buyer needs to determine how much information to acquire. We derive the optimal information-acquisition level in an integrated setting and compare it with that determined in a decentralized setting. We also analyze several types of supply contracts to examine if they can coordinate the supply chain and allow an arbitrary division of system profit between the supplier and the buyer.     

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.     

Possibilistic linear-programming approach for supply chain networking decisions

Supply chain networking decisions are very important for the medium- and long-term planning success of manufacturing companies. The inputs to supply chain planning models are subject to environmental and system uncertainties. In this paper, a fuzzy set theory-based model is proposed to deal with those uncertainties. For this purpose, a possibilistic linear programming (PLP) model is used to make strategic resource-planning decisions using fuzzy demand forecasts and fuzzy yield rates as well as other inputs such as costs and capacities. The objective of the proposed PLP is to maximize the total profit of the enterprise. The model is applied to Mercedes–Benz Türk, one of the largest bus-manufacturing companies in the world, and conclusions and suggestions for further research are provided.