Single Supplier�CBuyer Integrated Inventory Model Under Multiple JIT Delivery and Stock-Dependent Demand

In this paper, an integrated inventory model for a supply chain comprising of single buyer and single supplier is studied when demand is stock-dependent and units in inventory deteriorate at a constant rate. The total cost of the integrated system consists of the transportation cost, inspection cost and the cost of less flexibility under the assumption of JIT deliveries. The total integrated cost of single-supplier and single-buyer is minimized with respect to number of inspections and deliveries, the cycle time of deliveries and the delivery size for the replenishment time. A numerical example is given to validate the model. The sensitivity analysis carried out suggests that the unit inspection cost, deterioration rate of units in inventory and stock-dependent parameter are the critical factors.     

基于系统动力学的供应链库存策略仿真研究

针对一个动态、多级的供应链库存系统,应用系统动力学的方法,建立了供应链(s,S)库存策略下的物流成本模型,并通过动态仿真,分析了库存策略的变动对于供应链库存系统各级成员间库存供需的动态行为,提出了(s,S)策略下的供应链库存系统的有效管理方法.     

需求率基于库存的变质物品的两货栈模型

针对需求受库存水平影响的变质品的两货栈系统,本文首先考虑了允许缺货但缺货要补情形下,分别给出了L₁系统(库存系统只用自己的货栈存放物品)和L₂系统(库存系统使用自己货栈和租用货栈存放物品)时,销售商的库存和运输策略模型。其次给出了允许缺货但缺货不补L₁系统和L₂系统时,销售商的库存和运输策略,并对模型最优解作了相关分析,最后给出算例,给销售商实际的库存管理提供了理论依据。     

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.     

A comprehensive extension of optimal ordering policy for stock-dependent demand under progressive payment scheme

In a recent paper, Soni and Shah (2008) presented an inventory model with a stock-dependent demand under progressive payment scheme, assuming zero ending-inventory and adopting a cost-minimization objective. However, with a stock-dependent demand a non-zero ending stock may increase profits resulting from the increased demand. This work is motivated by Soni and Shah’s (2008) paper extending their model to allow for: (1) a non-zero ending-inventory, (2) a profit-maximization objective, (3) a limited inventory capacity and (4) deteriorating items with a constant deterioration rate. For the resulted model sufficient conditions for the existence and uniqueness of the optimal solution are provided. Finally, several economic interpretations of the theoretical results are also given.     

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.     

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.     

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.     

Finite time control of a class of nonlinear switched systems in spite of unknown parameters and input saturation

This article is devoted to the problem of robust stabilization of uncertain nonlinear switched systems with canonical structure. It is assumed that the constant parameters of the subsystems are unknown and cannot be adopted in the controller design. In addition, the dynamics of the subsystems are perturbed via modeling errors and external disturbances. The effects of unknown actuator saturation are compensated via proper adaptive control signals. The derived controller is based on the terminal sliding mode theory and does not need any prior knowledge about the bounds of the lumped uncertain terms. It is proved that once the system states reach the prescribed sliding manifold in a finite time interval, the whole system becomes insensitive to both the lumped uncertainties and the switching dynamics of the system. The common assumption of having known quadratic Lyapunov functions for the subsystems is relaxed and the derived adaptive approach does not force any limitation on the switching signal of the system. Subsequently, non-conservative conditions are provided to guarantee the global finite time bounded stability of the equilibrium state for the overall uncertain nonlinear switched system under arbitrary switching signals. A numerical computer simulation demonstrates the robust performance of the proposed controller.     

Profitability ratio maximization in an inventory model with stock-dependent demand rate and non-linear holding cost

This paper studies a deterministic inventory model with a stock-dependent demand pattern where the cumulative holding cost is a non-linear function of both time and stock level. When the monetary resources are limited and the inventory manager can invest his/her money in buying different products, it seems reasonable to select the ones that provide a higher profitability. Thus, a new approach with the aim of maximizing the profitability ratio (defined as the profit/cost quotient) is considered in this paper. We prove that the profitability ratio maximization is equivalent to minimizing the inventory cost per unit of an item. The optimal policy is obtained in a closed form, whose general expression is a generalization of the classical EOQ formula for inventory models with a stock-dependent demand rate and a non-linear holding cost. This optimal solution is different from the other policies proposed for the problems of minimum cost or maximum profit per unit time. A complete sensitivity analysis of the optimal solution with respect to all the parameters of the model is developed. Finally, numerical examples are solved to illustrate the theoretical results and the solution methodology.     

考虑疫情风险与双重时效性的生鲜品供应中断库存控制策略研究

为解决重大疫情引发的供应中断导致生鲜品库存水平振荡,在市场需求随机变化的情形下,建立一个由供应商、配送中心和零售商组成的三级生鲜供应链库存系统,考虑由疫情引起的三种风险情景,引入系统动力学模型对零售商动态库存系统运营进行仿真分析。研究发现：受疫情风险传导系数和变质率两个序参量影响,供应链库存呈现振荡趋势;通过确定不同供应中断时长下的疫情风险情景提出优化保鲜投入策略、安全库存策略、以及共享库存联合提前转运策略有效降低零售端库存水平振荡并使其呈现渐稳趋势,实现产品在交付过程中的双重时效性,达到供需匹配,缓解疫情风险带来的影响,为相关零售企业提供决策支持。     

Ergodic chaos in inventory oscillations: An example

This study reveals the dynamic structure of a nonlinear Metzlerian inventory cycle model that can generate complex dynamics. As a first step, it focuses on how the rational behavior of the supply side is responsible for the emergence of complex inventory fluctuations. To this end, the supply side is constructed on the basis of intertemporal optimization representing the short-run profit maximizing behavior of a firm. On the other hand, the demand side is constructed to be as simple as possible (i.e. the linear expenditure function). The firm is assumed to have a piecewisely flexible inventory-expected sales ratio. The resultant inventory adjustment system becomes piecewise-linear. This study demonstrates that the inventory accumulation may follow a wide range of complex dynamics including stable cycles, window phenomenon and ergodic chaos. It also shows that various types of dynamic behavior depend on the relationship between the marginal propensity to consume and marginal propensity to invest. Thus it can be concluded that the source of such a wide spectrum of complex inventory dynamics is an interaction between demand and supply.     

Uniform stability of switched nonlinear systems

In this paper, we investigate the stability properties of a general class of nonautonomous switched nonlinear systems. Sufficient conditions for uniform stability, uniform asymptotic stability and uniform exponential stability are derived via multiple Lyapunov functions. Our results provide stability criteria for switched systems with both stable and unstable subsystems. Particularly, our results include some existing results as special cases or improve those in the literature. Several numerical examples are worked out to illustrate our results.     

The simplified solution procedure for deteriorating items under stock-dependent demand and two-level trade credit in the supply chain management

Min et al. [1] (J. Min, Y.W. Zhou, J. Zhao, An inventory model for deteriorating items under stock-dependent demand and two-level trade credit, Appl. Math. Model. 34 (2010) 3273–3285.) develop an inventory model for deteriorating items under stock-dependent demand and two-level trade credit. They provide the necessary and sufficient conditions of the existence and uniqueness of the optimal solutions that could maximize the retailer’s average profit per unit time. Basically, their paper is correct and interesting. Recently, several researchers have been showing a huge interest in developing simple and easy to implement solution procedures in management science. Therefore this paper indicates that Min et al.’s solution procedure can be further improved and simplified. So, the main purpose of this paper is to present simple and easy to understand solution procedures to locate the optimal solutions of an inventory model that considers deteriorating items under stock-dependent demand and two-level trade credit.     

Stability of switched systems with time delay

In this paper, we study the qualitative properties of linear and nonlinear delay switched systems which have stable and unstable subsystems. First, we prove some inequalities which lead to the switching laws that guarantee: (a) the global exponential stability to linear switched delay systems with stable and unstable subsystems; (b) the local exponential stability of nonlinear switched delay systems with stable and unstable subsystems. In addition, these switching laws indicate that if the total activation time ratio among the stable subsystems, unstable subsystems and time delay is larger than a certain number, the switched systems are exponentially stable for any switching signals under these laws. Some examples are given to illustrate the main results.     

考虑需求依赖库存及分摊运费的供应链协调

针对单个销售商和单个生产商组成的两层供应链,假定需求依赖于当前库存水平,考虑运输费用与订货量相关,研究了采用分摊运费策略的供应链协调问题.首先在分散式系统下,建立了供需双方的Stackelberg博弈模型;然后设计了分担运输费用的协调策略,建立了供需双方的利润模型.研究结果表明该协调策略不仅能提高供需双方的利润,而且使得供应链达到了完美协调.     

A two-echelon inventory model for a deteriorating item with stock-dependent demand,partial backlogging and capacity constraints

This study investigates a two-echelon supply chain model for deteriorating inventory in which the retailer’s warehouse has a limited capacity. The system includes one wholesaler and one retailer and aims to minimise the total cost. The demand rate in retailer is stock-dependent and in case of any shortages, the demand is partially backlogged. The warehouse capacity in the retailer (OW) is limited; therefore the retailer can rent a warehouse (RW) if needed with a higher cost compared to OW. The optimisation is done from both the wholesaler’s and retailer’s perspectives simultaneously. In order to solve the problem a genetic algorithm is devised. After developing a heuristic a numerical example together with sensitivity analysis are presented. Finally, some recommendations for future research are presented.     

Robust controlling of chaotic behavior in supply chain networks

The supply chain network is a complex nonlinear system that may have a chaotic behavior. This network involves multiple entities that cooperate to meet customers demand and control network inventory. Although there is a large body of research on measurement of chaos in the supply chain, no proper method has been proposed to control its chaotic behavior. Moreover, the dynamic equations used in the supply chain ignore many factors that affect this chaotic behavior. This paper offers a more comprehensive modeling, analysis, and control of chaotic behavior in the supply chain. A supply chain network with a centralized decision-making structure is modeled. This model has a control center that determines the order of entities and controls their inventories based on customer demand. There is a time-varying delay in the supply chain network, which is equal to the maximum delay between entities. Robust control method with linear matrix inequality technique is used to control the chaotic behavior. Using this technique, decision parameters are determined in such a way as to stabilize network behavior.     

区块链技术影响下的供应链系统动态响应性研究

为解决供应链系统中信息时滞和不对称问题,加快推动区块链技术在供应链管理中的创新发展,本文运用控制理论构建由分销商和零售商组成的二级供应链系统控制模型,引入区块链技术影响下的信息校正因子,推导系统的传递函数,通过MATLAB仿真不同需求信号下的订单可变性和库存波动。仿真结果表明:(1)区块链技术的应用提高了库存系统的精准性和稳定性;(2)高库存可变性伴随着高订单可变性;(3)指数平滑系数和区块链技术影响下的信息校正因子有效抑制供应链中的牛鞭效应;(4)信息延迟时间越长,区块链技术影响下的信息校正因子对控制系统的抑制作用越显著。本研究量化了区块链技术对供应链中牛鞭效应的影响,提高了供应链系统的精准性和稳定性,丰富了区块链技术在供应链管理中的应用,为企业管理者提供新的研究思路。     

Analysis and design of switched normal systems

In this paper, we study the stability property for a class of switched linear systems whose subsystems are normal. The subsystems can be continuous-time or discrete-time ones. We show that when all the continuous-time subsystems are Hurwitz stable and all the discrete-time subsystems are Schur stable, a common quadratic Lyapunov function exists for the subsystems and thus the switched system is exponentially stable under arbitrary switching. We show that when unstable subsystems are involved, for a desired decay rate of the system, if the activation time ratio between stable subsystems and unstable ones is less than a certain value (calculated using the decay rate), then the switched system is exponentially stable with the desired decay rate.