Safety Stock Determination with Serially Correlated Demand in a Periodic-Review Inventory System

We consider a periodic-review inventory replenishment model with an order-up-to-R operating doctrine for the case of deterministic lead times and a covariance-stationary stochastic demand process. A method is derived for setting the inventory safety stock to achieve an exact desired stockout probability when the autocovariance function for Gaussian demand is known. Because the method does not require that parametric time-series models be fit to the data, it is easily implemented in practice. Moreover, the method is shown to be asymptotically valid when the autocovariance function of demand is estimated from historical data. The effects on the stockout rate of various levels of autocorrelated demand are demonstrated for situations in which autocorrelation in demand goes undetected or is ignored by the inventory manager. Similarly, the changes to the required level of safety stock are demonstrated for varying levels of autocorrelation.     

Multi-echelon systems: A service measure perspective

This paper reviews the most important results on divergent multi-echelon systems. In particular, we concentrate on the interactions between the elements that constitute such a multi-echelon system, in order to determine several service measures (e.g. external customer service level and inventory holding costs). We distinguish between two types of policies: installation stock and echelon stock policies. A comparison between these two types of policies revealed that the complexity of the analysis is concentrated at different aspects, which are discussed by reveiwing the most important papers on both types. Special attention is given to the applicability of the models. Extensions to divergent multi-echelon systems with more than two stages are also treated.     

Inventory control under temporal demand heteroscedasticity

This paper studies an inventory control problem when the variance of demand is time-varying and exhibits temporal heteroscedasticity. We use a first-order autoregressive process to characterize the dynamic changes in the level of demand over time and a GARCH(1, 1) structure to describe the changes in the variance of demand. Under these demand settings, we quantify the effect of a temporal heterogeneous variance on inventory performance for a system controlled via an order-up-to-level policy. We show that the effect of temporal heteroscedasticity on the forecasting accuracy can be additively decomposed from the total forecasting error variance. The decomposition is used to derive the absolute and relative cost deviations when the temporal heteroscedasticity is ignored. The relationship of these cost deviations to demand autocorrelation and replenishment leadtime is investigated. Computational results show that ignoring temporal heteroscedasticity can increase firm’s inventory costs by as much as 30% when demand autocorrelation is highly positive.     

Finding the optimal CSP inventory level for multi-echelon system in Air Force using random effects regression model

Determining the optimal inventory level of CSP (concurrent spare parts) is crucial at the time of acquisition of new aircrafts. Most of the existing optimal CSP models do not take into account the time varying characteristics of CSP even though their demand rates are sensitive to such variation. In this paper, we introduce the CSP inventory model using a two stage approach. At the first stage, we use a random effects model to predict the expected demand of CSP in a multi-echelon system consisting of depot and bases based on CSPs varying characteristics with time. At the second stage, we find the optimal inventory level of CSP by using the optimization algorithm with various constraints under limited budget. The study is expected to contribute to the Air Force establishing the optimal national defense procurement policy for CSP of aircrafts.     

Multi-echelon multi-company inventory planning with limited information exchange

Supply chain planning concepts from multi-echelon inventory theory are generally based on some form of centralised planning of supply chains. Those multi-echelon models that do consider decentralised planning, assume complete information and/or a specific single objective function. This paper investigates how multi-echelon inventory theory can accommodate a setting with decentralised decision makers (a supplier and a number of retail groups) without complete information. We present a coordination procedure that does not require the retail groups to exchange demand information, but does allow using opportunities for demand pooling between them. We illustrate our ideas by way of a quantitative analysis of a two-echelon divergent supply chain, with both cooperative and non cooperative retail groups. We conclude that coordination across a supply chain with decentralised control and limited centralised information is feasible by using available algorithms with satisfactory service level and cost performance.     

Demand selection decisions for a multi-echelon inventory distribution system

In this paper, we study an integrated demand selection and multi-echelon inventory control problem that generalizes the classical deterministic single distribution centre (DC) multi-retailer model by incorporating demand selection decisions. In addition to the ordering and holding cost components, a concave operating cost of the DC and a capacity on the total market demand served are also considered. For given revenue and cost parameters, the problem is to determine which sets of demand to fulfill and which multi-echelon inventory control policy to implement so as to maximize the net profit. We show that the problem can be formulated as a nonlinear discrete optimization model. We analyse the structural properties of the model and, based on these, outline an approach to solve the model efficiently. We also present some interesting managerial insights obtained from the numerical experiments.     

Estimating the lead-time demand distribution when the daily demand is non-normal and autocorrelated Hon-Shiang LAU

This paper develops convenient formulas for estimating the probability distribution of lead time demand when the inventory item's daily demand follows a probability distribution of any arbitrary shape, and when simple univariate models can be found for the autocorrelated daily demand series. Numerical examples are presented to illustrate the use of these formulas. The numerical results also indicate that significant error may be incurred when inventory decisions are made without proper consideration of the autocorrelations or the arbitrary distribution shapes of daily demands.     

自相关对常规控制图影响的模拟研究与案例分析

常规统计控制图的基本假设前提是观测值独立同分布,而在实际生产过程中,质量指标值常表现出自相关现象,违背独立性假定。本文运用平均链长(ARL)研究自相关过程为AR(1)时对常规控制图的影响,并比较了常规控制图和残差控制图对序列相关过程的控制效果。模拟结果和实例分析表明:当过程序列相关时,使用常规作图法估计出的标准差是有偏的,致使控制限设置错误和常规控制图检测能力降低。因此,在一些统计过程控制中,须考虑自相关现象并采用适当的控制图方法。     

Evaluation of time-varying availability in multi-echelon spare parts systems with passivation

The popular models for repairable item inventory, both in the literature as well as practical applications, assume that the demands for items are independent of the number of working systems. However this assumption can introduce a serious underestimation of availability when the number of working systems is small, the failure rate is high or the repair time is long. In this paper, we study a multi-echelon repairable item inventory system under the phenomenon of passivation, i.e. serviceable items are passivated (“switched off”) upon system failure. This work is motivated by corrective maintenance of high-cost technical equipment in the miltary. We propose an efficient approximation model to compute time-varying availability. Experiments show that our analytical model agrees well with Monte Carlo simulation.     

The impact of data collection on fill rate performance in the (R,s, Q) inventory model

In this paper we consider the determination of the reorder point s in an (R, s, Q) inventory model subject to a fill rate service level constraint. We assume that the underlying demand process is a compound renewal process. We then derive an approximation method to compute the reorder level such that a target service level is achieved. Restrictions on the input parameters are given, within which this method is applicable. Moreover, we will investigate the effects on the fill rate performance in case the underlying demand process is indeed a compound renewal process, while the demand process is modelled as a discrete-time demand process. That is, the time axis is divided in time units (for example, days) and demands per time unit are independent and identically distributed random variables. It will be shown that smooth and erratic behaviour of the inter-arrival times have different impacts on the performance of the fill rate when demand is modelled as a discrete-time process and in case the underlying demand process is a compound renewal process.     

Designing multi-echelon service parts networks with finite repair capacity

We propose an approach to model and solve the joint problem of facility location, inventory allocation and capacity investment in a two echelon, single-item, service parts supply chain with stochastic demand. The objective of the decision problem is to minimize the total expected costs associated with (1) opening repair facilities, (2) assigning each field service location to an opened facility, (3) determining capacity levels of the opened repair facilities, and (4) optimizing inventory allocation among the locations. Due to the size of the problem, computational efficiency is essential. The accuracy of the approximations and effectiveness of the approach are analyzed with two numerical studies. The approach provides optimal results in 90% of scenarios tested and was within 2% of optimal when it did not.We explore the impact of capacity utilization, inventory availability, and lead times on the performance of the approach. We show that including tactical considerations jointly with strategic network design resulted in additional cost savings from 3% to 12%. Our contribution is the development of a practical model and approach to support the decision making process of joint facility location and multi-echelon inventory optimization.     

A multi-product multi-echelon inventory control model with joint replenishment strategy

On the basis of analyzing the shortages of present studies on multi-echelon inventory control, and considering some restrictions, this paper applies the joint replenishment strategy into the inventory system and builds a multi-product multi-echelon inventory control model. Then, an algorithm designed by Genetic Algorithm (GA) is used for solving the model. Finally, we respectively simulate the model under three different ordering strategies. The simulation result shows that the established model and the algorithm designed by GA have obvious superiority on reducing the total cost of the multi-product multi-echelon inventory system. Moreover, it illustrates the feasibility and the effectiveness of the model and the GA method.     

Supply chain inventory optimization with two customer classes in discrete time

In this paper we consider a single-item inventory system where two demand classes with different service requirements are satisfied from a common inventory. A critical level, reorder point, order quantity or (s, q, k) policy is in use. The time axis is divided into discrete time units, which is a common characteristic of many real-life supply-chain processes. The inventory process within the lead time of a replenishment order is modelled as a sequence of (1) an ordinary renewal process and (2) two alternating renewal processes. Approximations are developed for the demand class-specific fill rates and the probability distribution of the waiting time of low priority customer orders. This waiting time distribution is used for the inventory allocation in a two-stage supply chain.     

Delivery delay variation in multi-echelon inventory problems

Mathematical models for controlling multi-echelon inventory and production levels have been developed for entire interconnected systems rather than myopically for each point in the inventory or production system. With such models come the additional burden of considering the lead times and delays associated with the movement of items through the network. The delays develop when a backorder state occurs and are often considered in models by approximating the mean delay by an application of Little's Law and without consideration of the delay variation. In this article a general methodology for incorporating the variation of the delay is derived and incorporated into a backorders optimisation model. The result of incorporating delay variation into the model is a tolerance interval for order quantities that may be utilised for tighter inventory control.     

Coordinating lead times and safety stocks under autocorrelated demand

We consider a supply chain in which orders and lead times are linked endogenously, as opposed to assuming lead times are exogenous. This assumption is relevant when a retailer’s orders are produced by a supplier with finite capacity and replenished when the order is completed. The retailer faces demands that are correlated over time – either positively or negatively – which may, for example, be induced by a pricing or promotion policy. The auto-correlation in demand affects the order stream placed by the retailer onto the supplier, and this in turn influences the resulting lead times seen by the retailer. Since these lead times also determine the retailer’s orders and its safety stocks (which the retailer must set to cover lead time demand), there is a mutual dependency between orders and lead times. The inclusion of endogenous lead times and autocorrelated demand represents a better fit with real-life situations. However, it poses some additional methodological issues, compared to assuming exogenous lead times or stationary demand processes that are independent over time. By means of a Markov chain analysis and matrix analytic methods, we develop a procedure to determine the distribution of lead times and inventories, that takes into account the correlation between orders and lead times. Our analysis shows that negative autocorrelation in demand, although more erratic, improves both lead time and inventory performance relative to IID demand. Positive correlation makes matters worse than IID demand. Due to the endogeneity of lead times, these effects are much more pronounced and substantial error may be incurred if this endogeneity is ignored.     

A simulation optimization approach for a two-echelon inventory system with service level constraints

In this paper, we present a simulation optimization algorithm for solving the two-echelon constrained inventory problem. The goal is to determine the optimal setting of stocking levels to minimize the total inventory investment costs while satisfying the expected response time targets for each field depot. The proposed algorithm is more adaptive than ordinary optimization algorithms, and can be applied to any multi-item multi-echelon inventory system, where the cost structure and service level function resemble what we assume. Empirical studies are performed to compare the efficiency of the proposed algorithms with other existing simulation algorithms.     

Customer differentiated end-of-life inventory problem

This paper deals with the service parts end-of-life inventory problem in a circumstance that demands for service parts are differentiated. Customer differentiation might be due to criticality of the demand or based on various service contracts. In both cases, we model the problem as a finite horizon stochastic dynamic program and characterize the structure of the optimal inventory policy. We show that when customers are differentiated based on the demand criticality then the optimal structure consists of time and state dependent threshold levels for inventory rationing. In case of differentiation based on service contracts, we show that in addition to rationing thresholds we also need contract extension thresholds by which the system decides whether to offer an extension to an expiring contract or not. By numerical experiments in both cases, we identify the value of incorporating such decisions in service parts end-of-life inventory management with customer differentiation. Moreover, we show that these decisions not only result in cost efficiency but also decrease the risk of part obsolescence drastically.     

需求离散的变质性物品库存补充策略优化研究

研究了在不允许缺货情况下需求为离散的变质性物品的库存补充策略问题.在假定变质率为常数的情况下,建立了有限时域内变质性物品的补充策略模型,并给出了求最优补充策略的方法.     

An algorithm for repairable item inventory system with depot spares and general repair time distribution

We consider the problem of determining the initial spare inventory level for a multi-echelon repairable item inventory system. We extend the previous results to the system, which has an inventory at the central depot as well as at bases and with a general repair time distribution. We propose an algorithm which finds spare inventory level to minimize the total expected cost and simultaneously to satisfy a specified minimum service rate. Extensive computational experiments show that the algorithm is accurate and efficient.     

The stochastic guaranteed service model with recourse for multi-echelon warehouse management

The guaranteed service model (GSM) computes optimal order-points in multi-echelon inventory control under the assumptions that delivery times can be guaranteed and the demand is bounded. Our new stochastic guaranteed service model (SGSM) with Recourse covers also scenarios that violate these assumptions. Simulation experiments on real-world data of a large German car manufacturer show that policies based on the SGSM dominate GSM-policies.