A hybrid inventory management system responding to regular demand and surge demand

This paper proposes a hybrid policy for a stochastic inventory system facing regular demand and surge demand. The combination of two different demand patterns can be observed in many areas, such as healthcare inventory and humanitarian supply chain management. The surge demand has a lower arrival rate but higher demand volume per arrival. The solution approach proposed in this paper incorporates the level crossing method and mixed integer programming technique to optimize the hybrid inventory policy with both regular orders and emergency orders. The level crossing method is applied to obtain the equilibrium distributions of inventory levels under a given policy. The model is further transformed into a mixed integer program to identify an optimal hybrid policy. A sensitivity analysis is conducted to investigate the impact of parameters on the optimal inventory policy and minimum cost. Numerical results clearly show the benefit of using the proposed hybrid inventory model. The model and solution approach could help healthcare providers or humanitarian logistics providers in managing their emergency supplies in responding to surge demands.     

A New Two‐Bin Policy for Inventory Systems with Differentiated Demand Classes

We consider an inventory system under continuous review with two demand classes that are different in terms of service level required (or penalty cost incurred for backordering of demand). Prior literature has proposed the critical level rationing (CLR) policy under which the demand from the lower priority class is backordered once inventory falls below the critical level. While this reduces the penalty cost for the higher demand class, the fill rate achieved for the lower priority demand class gets compromised. In this study, we propose a new class of two‐bin (2B) policy for the problem. The proposed 2B policy assigns separate bins of inventory for the two demand classes. The demand for each class is fulfilled from its assigned bin. However, when the bin intended for the higher demand class is empty, the demand from the higher class can still be fulfilled with the inventory from the other bin. The advantage of the 2B policy is that better fill rates are achieved, especially for the lower demand class. Computational results show that the proposed policy is able to provide a much higher service level for the lower priority class demand without increasing the total cost too much and without affecting the service level for the higher priority class. When a service level constrained optimization problem is considered, the 2B policy dominates the CLR policy when the service level difference for the two classes is not too high or the service levels required for both the classes are relatively lower.     

Assessing Service Level Targets in Production and Inventory Planning*

In production and stock planning, the relationship between customer service, defined as the ability to meet demand for finished goods from in-stock inventory, and expected profits or expected costs can be represented by a simple reliability curve. The shape of this curve depends upon the parameters of the demand process, specifically the expected level of demand, standard deviation and correlation structure, as well as upon the capacities and initial state of the production and inventory system. A model is presented which explicitly determines this trade-off curve for a firm. The model is intended both as an operational model to aid managers in setting revenue and service targets which are compatible with the capacities and resources of the firm, and as a tool for exploring relationships between the parameters of the demand process and the constraints of the physical production and inventory system. The results illustrate that the level of risk depends strongly on the variability of the demand process, the cost structure, the capacities and initial state of the system and, to a lesser extent, the correlation in demand between succeeding periods. Results suggest that establishing service level targets consistent with the firm's strategic orientation must be done in consideration of both the characteristics of the demand process and the capacities of the production and inventory system. The model provides a tool for estimating the premium above unit cost which must be paid to provide a designated service level.     

需求替代情形下反应能力的价值分析

本文通过对竞争报童模型加以拓展以研究需求替代情形下企业运用反应能力产生的价值。文中考虑了两种不同的需求结构:第一种中企业总需求是竞争双方库存量的分段线性函数,第二种中企业总需求的均值是双方库存水平任意形式的函数。根据需求结构的不同,建立了不同的库存竞争模型并提出了相应的均衡库存策略。基于这些均衡结论,进一步探讨了反应能力的价值。分析表明运用反应能力能在降低企业库存水平的同时提高顾客服务水平。此外,在不同的需求结构下,运用反应能力产生的价值均随可用反应能力以及缺货惩罚成本递增,而随单位反应能力的使用成本递减。     

The impact of distributions of uncertain lumpy demand on inventories

Most studies on inventory management under demand uncertainty analyse the detrimental effects of demand variability (i.e. its coefficient of variation). In contrast, the consequences of the shape of demand distribution (e.g. its multi-modality and asymmetry) have received only minor attention. The aim of the present paper is to assess the impact of the shape of demand distribution on inventories. In particular, it considers contexts in which demand distributions have more than one 'mode' and are asymmetric, thus making requirements lumpy. The analysis is based on a simulation model which, in order to ensure comparable conditions, keeps all the other factors constant (i.e. ceteris paribus), and compares different demand distributions with the same mean and coefficient of variation. Results show that that demand shape is a key driver of inventory investment. Specifically: (i) the magnitude of the impact of multi-modality and asymmetry is comparable to that of variability; (ii) multi-modality and asymmetry can have either a negative or positive effect depending on the target service level sought. The managerial implications of these findings are addressed in the conclusions.     

Strategic supply network planning with vendor selection under consideration of risk and demand uncertainty

We present a stochastic version of a three-layer supply network planning problem that includes the selection of vendors that must be equipped with company-specific tools. The configuration of a supply network must be determined by using demand forecasts for a long planning horizon to meet a given service level. The risk induced by the uncertain demand is explicitly considered by incorporating the conditional value at risk. The objective is to maximize the weighted sum of the expected net present value of discounted cash flows and the conditional value at risk. This would lead to a non-linear model formulation that is approximated by a mixed-integer linear model. This approximation is realized by a piecewise linearization of the expected backlogs and physical inventory as non-linear functions of cumulative production quantities. A two-stage stochastic programming approach is proposed. Our numerical analysis of generic test instances indicates that solving the linearized model formulation yields a robust and stable supply network configuration when demand is uncertain.     

Buffer stock under the effect of fluctuating demand

This paper deals with an inventory situation where the rate of demand for units stocked is known, but fluctuating over time. The focus of attention is on reserve stock. In an ideal world, where demand is known well in advance and where suppliers maintain scheduled shipping dates, there would be little need to hold any form of inventory other than a limited in-process stock. In practice however, supply interruptions are likely to occur. In this case an inventory acts as buffer to withstand variations between supply and demand. A mathematical model to determine the optimum reserve stock needed to minimize the expected total inventory cost of carrying the reserve inventory and cost of stockouts is developed.     

LR型模糊需求下连续盘点库存策略研究

本文研究了LR型模糊需求下缺货需补的连续盘点库存优化问题。基于可信性理论,建立了成本最小化的库存模型和两种服务水平下的库存分析模型,给出了其求解方法,并将成本和服务水平两方面进行综合获得最优库存策略。最后的算例分析,数值比较了不同模型下的库存策略。     

Economic order quantity model with trade credit financing for non-decreasing demand

Researchers in the past have established their inventory lot-size models under trade credit financing by assuming that the demand rate is constant. However, from a product life cycle perspective, it is only in the maturity stage that demand is near constant. During the growth stage of a product life cycle (especially for high-tech products), the demand function increases with time. To obtain robust and generalized results, we extend the constant demand to a linear non-decreasing demand function of time. As a result, the fundamental theoretical results obtained here are suitable for both the growth and maturity stages of a product life cycle. In addition, we characterize the optimal solutions and obtain conclusions on important and relevant managerial phenomena. Lastly, we provide several numerical examples to illustrate the proposed model and its optimal solution.     

区分仓库与货架库存需求影响效应的零售商库存决策

既往有关库存水平影响需求条件下的库存问题研究中,通常对终端库存水平是否存在货架与零售商仓库库存水平的区别未作深入探讨。本文的研究认为,现实中许多零售商拥有仓库,其现有库存水平包括仓库库存和货架库存两部分,而影响需求的仅为与货架展示能力相关的库存,因此有必要对二者的需求影响效应进行区分。在明确这一区别的前提下,本文首先建立了供应商管理库存情况下库存水平影响需求问题的一般库存模型,给出零售商的最优订货策略;并考虑货架的容量限制,给出零售商启用仓库的判断条件。由于仓库库存仅在能够影响货架展示能力的条件下才能够影响消费需求,本文还进一步讨论了在零售商拥有仓库时,区分货架与仓库的库存水平影响需求条件下的最优库存与订货决策。这对于经营不同特征商品的零售商在进行是否需要拥有仓库,以及拥有仓库条件下的库存决策具有很好的参考价值。     

COMPONENT COMMONALITY: MODELS WITH PRODUCT‐SPECIFIC SERVICE CONSTRAINTS*

Common components are used extensively for reasons including product postponement and expediting new product development. We consider a two‐stage assemble‐to‐order system with two products having uniformly distributed demand, one common component, and product‐specific components. We develop optimization models in which the cost‐minimizing inventory of the components must be determined and allocated to products in order to meet product‐specific service level constraints. We compare two different commonality models based on whether or not the products are prioritized. A distinctive feature of our study is the use of product‐specific service levels. We compare our results with models using aggregate service levels.     

面向批量订货和多需求类的生产与库存配给

针对一个面向两个需求类的生产企业,根据客户每次订货是否可分批交货,提出了当客户订货可分割和不可分割时供应商的最优生产和库存配给策略.分析表明,供应商的最优生产控制策略可用一个取决于系统状态的基准库存水平表示,最优的库存配给策略则用一个多层的取决于状态的配给水平向量表示.随后,该结论被推广至包含任意多个需求类的生产系统.数值分析验证了文中最优策略的有效性.     

Managing stochastic demand in an Inventory Routing Problem with transportation procurement

We study an Inventory Routing Problem in which the supplier has a limited production capacity and the stochastic demand of the retailers is satisfied with procurement of transportation services. The aim is to minimize the total expected cost over a planning horizon, given by the sum of the inventory cost at the supplier, the inventory cost at the retailers, the penalty cost for stock-out at the retailers and the transportation cost. First, we show that a policy based just on the average demand can have a total expected cost infinitely worse than the one obtained by taking into account the overall probability distribution of the demand in the decision process. Therefore, we introduce a stochastic dynamic programming formulation of the problem that allows us to find an optimal policy in small size instances. Finally, we design and implement a matheuristic approach, integrating a rollout algorithm and an optimal solution of mixed-integer linear programming models, which is able to solve realistic size problem instances. Computational results allow us to provide managerial insights concerning the management of stochastic demand.     

Updating Inventories of Substitutable Resources in Response to Forecast Updates

We show simple yet optimal results to update the inventory/capacity levels, expected profit, fill rates, and service levels of substitutable resources in response to an updating of the mean demand forecasts for the resources. We find that a change in the mean demand of one resource does not affect the optimal inventory level of any other resource. The results are obtained for demands with location‐scale distribution, and for a revenue structure satisfying a triangle property such that the manager will always use the inventory of a resource to meet her own demand first before using it for substitution. The results for updating the performance measures also extend to managers who maintain non‐optimal inventory/capacity levels. Implications for procurement, sales and operational planning, and multi‐store operations are discussed.     

基于似然估计的零售商库存鲁棒均值-风险模型

针对具有风险厌恶的零售商,建立了权衡期望利润和条件风险值（CVaR）的均值-风险库存优化模型,给出了离散需求分布不确定条件下能实现帕累托最优但具有较高保守性和非帕累托最优但具有较低保守性的两种鲁棒对应。针对不确定需求分布,在仅知历史需求样本数据情况下,应用统计推断理论构建了满足一定置信水平的基于似然估计的需求概率分布不确定集。在此基础上,运用拉格朗日对偶理论,将上述两种鲁棒对应模型转化为易于求解的凹优化问题,并证明了其与原问题的等价性。最后,针对实际案例进行了数值计算,分析了不同系统参数和样本规模对零售商最优库存决策及其运作绩效的影响,并给出了零售商期望利润和条件风险值两个目标权衡的帕累托有效前沿。结果表明,采用基于似然估计的鲁棒优化方法得到的零售商库存策略具有良好鲁棒性,能够有效抑制需求分布不确定性对零售商库存绩效的影响。而且,历史需求样本规模越大,鲁棒库存策略下的零售商运作绩效越接近最优情况。进一步,通过对比发现,两种鲁棒对应模型虽然保守性不同,但在最终库存策略上保持一致。     

Impact of temporal aggregation on stock control performance of intermittent demand estimators: Empirical analysis

Intermittent demand is characterized by occasional demand arrivals interspersed by time intervals during which no demand occurs. These demand patterns pose considerable difficulties in terms of forecasting and stock control due to their compound nature, which implies variability both in terms of demand arrivals and demand sizes. An intuitively appealing strategy to deal with such patterns from a forecasting and stock control perspective is to aggregate demand in lower-frequency ‘time buckets’, thereby reducing the presence of zero observations. In this paper, we investigate the impact of forecasting aggregation on the stock control performance of intermittent demand patterns. The benefit of the forecasting aggregation approach is empirically assessed by means of analysis on a large demand dataset from the Royal Air Force (UK). The results show that the aggregation forecasting approach results in higher achieved service levels as compared to the classical forecasting approach. Moreover, when the combined service-cost performance is considered, the results also show that the former approach is more efficient than the latter, especially for high target service levels.     

短生命周期产品的三种库存模型的比较

讨论短生命周期产品库存模型,考虑无形变质因素,并假定无形变质率与需求率成反比关系.在线性需求和常数生产率的条件下,假设,若需求率为1,则视作产品的市场生命周期结束.并且,在产品生命周期的前期不存在缺货的情况下,给出了短生命周期产品分别在理想状态、允许缺货以及价格折扣导致需求率变化等3种状态下的库存模型,最后在相同参数条件下对这3种模型进行比较,找出了单位时间内平均总成本最小的最优库存模型,厂商可以根据自身的情况选择合适的库存策略.     

Optimal design of supply chain networks under uncertain transient demand variations

We consider a detailed mathematical formulation for the problem of designing supply chain networks comprising multiproduct production facilities with shared production resources, warehouses, distribution centers and customer zones and operating under time varying demand uncertainty. Uncertainty is captured in terms of a number of likely scenarios possible to materialize during the lifetime of the network. The problem is formulated as a mixed-integer linear programming problem and solved to global optimality using standard branch-and-bound techniques. A case study concerned with the establishment of Europe-wide supply chain is used to illustrate the applicability and efficiency of the proposed approach. The results obtained provide a good indication of the value of having a model that takes into account the complex interactions that exist in such networks and the effect of inventory levels to the design and operation.     

Testing for Nonlinear Dependence in Inventory Data

This paper describes the properties of nonlinear dynamical systems in demand data and assesses the implications for inventory management. A test from Brock, Dechert, and Scheinkman (BDS) [6] for detecting nonlinearities is presented. This test assists inventory managers with two issues. First, it can be used to detect departures from the independence and stationarity assumptions of particular inventory models, thereby identifying the need for more suitable models. Second, the BDS test can determine whether forecasting model improvements are possible, and can measure improvements in the forecasting model process. The corresponding reductions in forecast errors improve inventory management and lead to reduced inventory costs. Using actual weekly demand for oil filters, this paper demonstrates the use of the BDS test and the effects of nonlinearities in demand data on inventory model performance.     

Location of Inventories in an MRP Environment

Previous research on MRP systems has rarely considered at what level in a modular sub-assembly product structure to hold inventories. Based on a simulation study of an MRP environment, we show that the correct decision concerning where to hold inventory depends on the variance in end-item demand, the amount of inventory investment, and concomitantly, the desired level of customer service. In particular, for small investment in inventories and moderate end-item demand variance, it is equally effective to hold inventories at the subassembly level or the end-item level. But when end-item demand variance is high, subassembly level inventories are better. As inventory investment grows, however, it is best to use a diversified approach of holding both subassembly and end-item inventories, irrespective of end-item demand variance. The robustness of these conclusions is validated by simulating a hypothetical firm that also uses safety time to hedge against uncertainties.