ARMA(1,1)需求条件下供应链需求提前承诺的影响效果分析

为了分析供应链需求提前承诺的影响效果,考虑供应链所面临的顾客需求满足ARMA（1,1）过程。首先从理论上建立正常顾客需求与顾客需求提前承诺时零售商订单量波动程度和平均库存的定量描述模型,通过两种情形下的比较分析,得出在顾客需求自回归系数大于零时,顾客需求提前承诺将减小牛鞭效应和平均库存水平;同时得出在顾客需求提前承诺时,如果顾客需求自回归系数大于零,顾客提前承诺的需求比例越高,则牛鞭效应和平均库存水平越低;顾客需求提前承诺的时间跨度越长,则牛鞭效应和平均库存水平也越低。反之亦然。其次运用仿真方法分析了顾客需求提前承诺对零售商平均库存成本的影响,得出在顾客需求自回归系数大于零时,顾客需求提前承诺将有效降低零售商的平均库存成本。     

Stability analysis and optimization of an inventory system with bounded orders

This paper addresses the control of a one-item inventory system subject to random order lead time and random demand. The key parameter of the control policy is the objective inventory. In each period, the order to be placed brings the inventory position as close as possible to the objective inventory. The order of each period is kept between a lower bound and an upper bound. We show that the distribution of the inventory level converges to its stationary distribution provided that the lower bound is smaller than the average demand, the upper bound is greater than the average demand and some regularity conditions hold. The average inventory cost is shown to be a convex function of the objective inventory level. A simulation-based approach is proposed for the determination of the optimal objective inventory. A method of bisection with derivative is then used to determine the optimal objective inventory. The derivatives needed in various iterations of this method are estimated using a single sample path with respect to a given objective inventory. Numerical results are provided.     

Inventory rationing in an (<Emphasis Type="Italic">s,Q</Emphasis>) inventory model with lost sales and two demand classes

Whenever demand for a single item can be categorised into classes of different priority, an inventory rationing policy should be considered. In this paper we analyse a continuous review (s, Q) model with lost sales and two demand classes. A so-called critical level policy is applied to ration the inventory among the two demand classes. With this policy, low-priority demand is rejected in anticipation of future high-priority demand whenever the inventory level is at or below a prespecified critical level. For Poisson demand and deterministic lead times, we present an exact formulation of the average inventory cost. A simple optimisation procedure is presented, and in a numerical study we compare the optimal rationing policy with a policy where no distinction between the demand classes is made. The benefit of the rationing policy is investigated for various cases and the results show that significant cost reductions can be obtained.     

Periodic control of intermittent demand items: theory and empirical analysis

In this paper we propose a modification to the standard forecasting, periodic order-up-to-level inventory control approach to dealing with intermittent demand items, when the lead-time length is shorter than the average inter-demand interval. In particular, we develop an approach that relies upon the employment of separate estimates of the inter-demand intervals and demand sizes, when demand occurs, directly for stock control purposes rather than first estimating mean demand and then feeding the results in the stock control procedure. The empirical performance of our approach is assessed by means of analysis on a large demand data set from the Royal Air Force (RAF, UK). Our work allows insights to be gained on the interactions between forecasting and stock control as well as on demand categorization-related issues for forecasting and inventory management purposes.     

Base stock policies for production/inventory problems with uncertain capacity levels

In this paper we consider a single item, stochastic demand production/inventory problem where the maximum amount that can be produced (or ordered) in any given period is assumed to be uncertain. Inventory levels are reviewed periodically. The system operates under a stationary modified base stock policy. The intent of our paper is to present a procedure for computing the optimal base stocl level of this policy under expected average cost per period criterion. This procedure would provide guidance as to the appropriate amount of capacity to store in the form of inventory in the face of stochastic demand and uncertain capacity. In achieving this goal, our main contribution is to establish the analogy between the class of base stock production/inventory policies that operate under demand/capacity uncertainty, and the G/G/1 queues and their associated random walks. We also present example derivations for some important capacity distributions.     

Taming the bullwhip effect whilst watching customer service in a single supply chain echelon

We study a generalised order-up-to policy that has highly desirable properties in terms of order and inventory variance and customer service levels it generates. We quantify exactly the variance amplification in replenishment orders, i.e. the bullwhip effect, and the variance of inventory levels over time, for i.i.d. and the weakly stationary auto regressive (AR), moving average (MA) and auto regressive moving average (ARMA) demand processes. We demonstrate that high customer service as measured by fill-rate, and smooth replenishments need not increase inventory cost substantially. We observe that in some instances of the ARMA demand pattern this comes at the expense of a relatively small increase in safety stock, whilst in other instances inventory levels can actually be reduced.     

A two-echelon base-stock inventory model with Poisson demand and the sequential processing of orders at the upper echelon

We consider a two-echelon inventory system with a number of non-identical, independent ‘retailers’ at the lower echelon and a single ‘supplier’ at the upper echelon. Each retailer experiences Poisson demand and operates a base stock policy with backorders. The supplier manufactures to order and holds no stock. Orders are produced, in first-come first-served sequence, with a fixed production time. The supplier therefore functions as an M/D/1 queue. We are interested in the performance characteristics (average inventory, average backorder level) at each retailer. By finding the distribution of order lead time and hence the distribution of demand during order lead time, we find the steady state inventory and backorder levels based on the assumption that order lead times are independent of demand during order lead time at a retailer. We also propose two alternative approximation procedures based on assumed forms for the order lead time distribution. Finally we provide a derivation of the steady state inventory and backorder levels which will be exact as long as there is no transportation time on orders between the supplier and retailers. A numerical comparison is made between the exact and approximate measures. We conclude by recommending an approach which is intuitive and computationally straightforward.     

A partial replenishment model for an inventory with constant demand

An inventory with constant demand is considered. The inventory is checked according to a Poisson process and replenished either fully or partially when the stock is below a threshold. We obtained the stationary distribution of the level of the inventory. After assigning several costs to the inventory, we also derived the long-run average cost per unit time. A numerical example is studied to find the optimal values of the checking rate and threshold, which minimize the long-run average cost.     

Performance analysis for assemble-to-order systems with general renewal arrivals and random batch demands

We study multi-product and multi-item assemble-to-order systems under general assumptions on demand patterns and replenish leadtime distributions. We only assume that the demand process of each product being a renewal process, and the replenish leadtimes follow general distributions. Based upon techniques from renewal theory, we developed procedures for approximating key performance measures of these inventory systems, such as average inventory and immediate order fill rate. We also obtain qualitative results that reveal the impacts of changes in demand patterns and leadtime variability upon the performance of the systems.     

Mathematical programming for network revenue management revisited

Mathematical programming models for airline seat inventory control provide booking limits and bid-prices for all itineraries and fare classes. E.L. Williamson [Airline network seat inventory control: methodologies and revenue impacts, Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA, 1992] finds that simple deterministic approximation methods based on average demand often outperform more advanced probabilistic heuristics. We argue that this phenomenon is due to a booking process that includes nesting of the fare classes, which is ignored in the modeling phase. The differences in the performance between these approximations are studied using a stochastic programming model that includes the deterministic model as a special case. Our study carefully examines the trade-off between computation time and the aggregation level of demand uncertainty with examples of a multi-leg flight and a single-hub network.     

历史订单信息对牛鞭效应的影响分析

客户需求信息的失真是导致牛鞭效应存在的原因,基于零售商的历史订单数据对其需求进行预测可以部分消除牛鞭效应。论文基于零售商-分销商二级供应链视角,分析了在零售商的需求为线性自回归模式的二级供应链中,分销商利用零售商历史订单数据和现有订单数据进行需求预测时自身库存成本的变更以及整个供应链的牛鞭效应的缓解程度。结果表明:分销商利用历史订单数据进行库存的决策可以显著地降低自己的平均库存和需求的波动,这种降低程度在零售商的订货提前期较大的情况下比较明显,但是零售商的需求预测相关系数对它影响不大。     

Dynamic inventory system with pricing adjustment for price-comparison shoppers

With numerous price-comparison websites and applications, consumers today are frequently conducting price-comparison shopping. As a result, retailers face an increasing challenge in predicting consumer demand and determining the optimal product price and inventory level accordingly. To address this issue, this paper proposes an inventory model with joint decisions of price and inventory to optimize the retailer's long-run average profit under price-comparison consumer shopping. We first formulate the demand arrival process for a retailer under price-comparison shopping to be affected by not only its own price but also its competitors'. Based on this demand arrival process, we then formulate the retailer's long-run average profit and derive properties of its optimal solution. Our model focuses on capturing the impact of price-comparison consumers on a retailer's optimal price and inventory decisions. In particular, we allow competitors' prices to affect the retailer's demand via two key factors: the manufacturer's suggested price and the variability of the outside lowest price. According to our results, when the suggested price increases, the retailer should lower its price to obtain more price-comparison customers from competitors, whereas when the variability of outside lowest price increases, the retailer should raise its price to increase per unit profit from nonprice-comparison customers.     

Forecasting sales of slow and fast moving inventories

Traditional computerised inventory control systems usually rely on exponential smoothing to forecast the demand for fast moving inventories. Practices in relation to slow moving inventories are more varied, but the Croston method is often used. It is an adaptation of exponential smoothing that (1) incorporates a Bernoulli process to capture the sporadic nature of demand and (2) allows the average variability to change over time. The Croston approach is critically appraised in this paper. Corrections are made to underlying theory and modifications are proposed to overcome certain implementation difficulties. A parametric bootstrap approach is outlined that integrates demand forecasting with inventory control. The approach is illustrated on real demand data for car parts.     

An interactive method for inventory control with fuzzy lead-time and dynamic demand

Normally, the real-world inventory control problems are imprecisely defined and human interventions are often required to solve these decision-making problems. In this paper, a realistic inventory model with imprecise demand, lead-time and inventory costs have been formulated and an inventory policy is proposed to minimize the cost using man–machine interaction. Here, demand increases with time at a decreasing rate. The imprecise parameters of lead-time, inventory costs and demand are expressed through linear/non-linear membership functions. These are represented by different types of membership functions, linear or quadratic, depending upon the prevailing supply condition and marketing environment. The imprecise parameters are first transformed into corresponding interval numbers and then following the interval mathematics, the objective function for average cost is changed into respective multi-objective functions. These functions are minimized and solved for a Pareto-optimum solution by interactive fuzzy decision-making procedure. This process leads to man–machine interaction for optimum and appropriate decision acceptable to the decision maker’s firm. The model is illustrated numerically and the results are presented in tabular forms.     

Impacts of inventory shortage policies on transportation requirements in two-stage distribution systems

This paper investigates the impacts inventory shortage policies have on transportation costs in base-stock distribution systems under uncertain demand. The model proposed demonstrates how backlogging arrangements can serve to decrease the variability of transportation capacity requirements, and hence the magnitude of transportation costs, when compared with policies that expedite demand shortages. The model shows how inventory policy decisions directly impact expected transportation costs and provides a new method for setting stock levels that jointly minimizes inventory and transportation costs. The model and solution method provide insights into the relationship between inventory decisions and transportation costs and can serve to support delivery policy negotiations between a supplier and customer that must choose between expediting and backlogging demand shortages.     

Inventory management for dual sales channels with inventory-level-dependent demand

This paper studies the inventory management problem of dual channels operated by one vendor. Demands of dual channels are inventory-level-dependent. We propose a multi-period stochastic dynamic programming model which shows that under mild conditions, the myopic inventory policy is optimal for the infinite horizon problem. To investigate the importance of capturing demand dependency on inventory levels, we consider a heuristic where the vendor ignores demand dependency on inventory levels, and compare the optimal inventory levels with those recommended by the heuristic. Through numerical examples, we show that the vendor may order less for dual channels than those recommended by the heuristic, and the difference between the inventory levels in the two cases can be so large that the demand dependency on inventory levels cannot be neglected. In the end, we numerically examine the impact of different ways to treat unmet demand and obtain some managerial insights.     

Inventory sharing in integrated network design and inventory optimization with low-demand parts

Service Parts Logistics (SPL) problems induce strong interaction between network design and inventory stocking due to high costs and low demands of parts and response time based service requirements. These pressures motivate the inventory sharing practice among stocking facilities. We incorporate inventory sharing effects within a simplified version of the integrated SPL problem, capturing the sharing fill rates in 2-facility inventory sharing pools. The problem decides which facilities in which pools should be stocked and how the demand should be allocated to stocked facilities, given full inventory sharing between the facilities within each pool so as to minimize the total facility, inventory and transportation costs subject to a time-based service level constraint. Our analysis for the single pool problem leads us to model this otherwise non-linear integer optimization problem as a modified version of the binary knapsack problem. Our numerical results show that a greedy heuristic for a network of 100 facilities is on average within 0.12% of the optimal solution. Furthermore, we observe that a greater degree of sharing occurs when a large amount of customer demands are located in the area overlapping the time windows of both facilities in 2-facility pools.     

A Nomogram for Stock Control

A well-known replenishment policy for an inventory subject to probabilistic demand gives rise to the problem of determining an order quantity and a reorder level which minimize the average cost of keeping inventory. If the problem can be expressed in terms of a simple approximative model which includes a restriction on back-orders and represents demand in the replenishment lead time as normally distributed, it is possible to construct a "set-square index" nomogram which accomplishes a major part of the necessary computations. The procedure for using the nomogram and the principles of its construction are described.     

Capacity and Production Managment in a Single Product Manufacturing System

In planning and managing production systems, manufacturers have two main strategies for responding to uncertainty: they build inventory to hedge against periods in which the production capacity is not sufficient to satisfy demand, or they temporarily increase the production capacity by “purchasing” extra capacity. We consider the problem of minimizing the long-run average cost of holding inventory and/or purchasing extra capacity for a single facility producing a single part-type and assume that the driving uncertainty is demand fluctuation. We show that the optimal production policy is of a hedging point policy type where two hedging levels are associated with each discrete state of the system: a positive hedging level (inventory target) and a negative one (backlog level below which extra capacity should be purchased). We establish some ordering of the hedging levels, derive equations satisfied by the steady-state probability distribution of the inventory/backlog, and give a more detailed analysis of the optimal control policy in a two state (high and low demand rate) model.     

On Approximating Lead Time Demand Distributions Using the Generalised λ-type Distribution

In this paper the use of the generalised λ-type distribution (GLD) is proposed for the analysis of standard inventory problems. Using this distribution to approximate the lead time demand distribution we analyse the generalised newsboy problem and a (Q, r) policy. The standard inventory measures like optimal order size, reorder level, average demand lost, etc. are obtained under the GLD and are compared with those given by Shore's approximation and also under exact distributional assumptions. Through a numerical study the various inventory measures are compared using the GLD and Shore's approximation with the exact distributions. The comparison reveals that the GLD approximation is better suited than Shore's approximation to model the lead time demand.