Forecasting and Stock Control for Intermittent Demands

Exponential smoothing is frequently used for the forecasts in stock control systems. The analysis given shows that intermittent demands almost always produce inappropriate stock levels. Demand for constant quantities at fixed intervals may generate stock levels of up to double the quantity really needed. A method of overcoming these difficulties is described, using separate estimates of the size of demand, and of the demand frequency. The rules for setting the safety stock levels have also to be adjusted before consistent protection can be obtained against being out of stock.     

A periodic-review inventory control policy for a two-level supply chain with multiple retailers and stochastic demand

We consider a time-based inventory control policy for a two-level supply chain with one warehouse and multiple retailers in this paper. Let the warehouse order in a fixed base replenishment interval. The retailers are required to order in intervals that are integer-ratio multiples of the base replenishment interval at the warehouse. The warehouse and the retailers each adopt an order-up-to policy, i.e. order the needed stock at a review point to raise the inventory position to a fixed order-up-to level. It is assumed that the retailers face independent Poisson demand processes and no transshipments between them are allowed. The contribution of the study is threefold. First, we assume that when facing a shortage the warehouse allocates the remaining stock to the retailers optimally to minimize system cost in the last minute before delivery and provide an approach to evaluate the exact system cost. Second, we characterize the structural properties and develop an exact optimal solution for the inventory control system. Finally, we demonstrate that the last minute optimal warehouse stock allocation rule we adopt dominates the virtual allocation rule in which warehouse stock is allocated to meet retailer demand on a first-come first-served basis with significant cost benefits. Moreover, the proposed time-based inventory control policy can perform equally well or better than the commonly used stock-based batch-ordering policy for distribution systems with multiple retailers.     

中国股指期现货市场间的非对称风险溢出效应——基于分位数Granger因果检验

为了揭示中国股指期现货市场之间风险溢出效应的非对称特征,本文利用已实现半方差将中国股指期现货市场的风险区分为下跌风险和上涨风险,并运用均值Granger因果检验和分位数Granger因果检验,考察两市场之间下跌风险溢出效应和上涨风险溢出效应的差异。研究发现,中国股指期现货市场之间不仅存在显著的下跌风险溢出,还存在显著的上涨风险溢出,而且溢出效应随着分位数区间不同而呈现出显著的非对称特征。一方面,期货市场对现货市场的下跌风险溢出在全部分位数区间均显著,而上涨风险溢出仅在分布的中间位置和上尾显著。另一方面,现货市场对期货市场的下跌风险溢出主要集中在尾部极端分位数区间,而上涨风险溢出主要集中在分布的中间位置和低分位数区间。     

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.     

Continuous-review,lost-sales inventory models with Poisson demand,a fixed lead time and no fixed order cost

This paper considers continuous-review lost-sales inventory models with no fixed order cost and a Poisson demand process. There is a holding cost per unit per unit time and a lost sales cost per unit. The objective is to minimise the long run total cost. Base stock policies are, in general, sub-optimal under lost sales. The optimal policy would have to take full account of the remaining lead times on all the orders currently outstanding and such a policy would be too complex to analyse, let alone implement. This paper considers policies which make use of the observation that, for lost sales models, base stock policies can be improved by imposing a delay between the placement of successive orders. The performance of these policies is compared with that of the corresponding base stock policy and also with the policy of ordering at fixed and regular intervals of time.     

Controlling pollution and environmental absorption capacity

This pollution accumulation model shows that the environmental absorption capacity is impacted by economic activity. The resulting optimal control problem has two inter-related state variables: the stock of pollution and the absorption capacity of the environment. The stock of pollution decreases with environmental absorption capacity and increases with the rate of current emissions, which is controlled by a production level as well as an emissions reduction effort. However, the environmental absorption capacity is positively affected by an absorption development effort, and negatively impacted by the stock of pollution. Under specific conditions, it is shown that an optimal path, which can be either monotonic or following transient oscillations, leads to a (nontrivial) saddle-point characterized by a positive environmental absorption capacity.     

Inventory models with lateral transshipments: A review

Lateral transshipments within an inventory system are stock movements between locations of the same echelon. These transshipments can be conducted periodically at predetermined points in time to proactively redistribute stock, or they can be used reactively as a method of meeting demand which cannot be satisfied from stock on hand. The elements of an inventory system considered, e.g. size, cost structures and service level definition, all influence the best method of transshipping. Models of many different systems have been considered. This paper provides a literature review which categorizes the research to date on lateral transshipments, so that these differences can be understood and gaps within the literature can be identified.     

Optimizing a Production System with a Fixed Delivery Schedule

This note considers a model in which a manufacturing company purchases a raw material, manufactures a product (at a finite rate) and ships a fixed quantity of the product to a single customer at fixed and regular intervals of time, as specified by the customer. In general there are several shipments made during each production run. The objective is to determine a purchasing and production schedule which minimises the total cost of purchasing, manufacturing and stockholding. It extends previously published work by considering the possibility that a single raw material purchase provides stock for several production runs or that several raw material purchases provide stock for a single production run.     

Using an Expert System to Monitor an Automatic Stock Control System

The theory of the control of stock is well understood, and a large number of firms use automatic stock control and ordering techniques as a major part of their inventory control systems. However, the effectiveness of such automatic stock control systems depends on the correct selection of system parameters for each item in the inventory and on the accurate reporting of information. It is not unusual for errors to be made in both the selection of parameters and the entry of data, and regular failures of either can cause severe problems in stock control. It is generally difficult for a human stock controller to discover errors quickly because of the large number of items that is usually found in a company inventory. This paper describes the use of an expert system to examine stock records and diagnose anomalies in the data provided or parameters applied to individual items in a stock control system. The expert system ‘reasons’ from symptoms such as reports from the forecasting system or high stock levels, to defects in the stock model used or data-collection processes, and from there to possible remedial action. Results are presented for runs of the expert system on a simulated stock control system.     

Pricing of general European options on discrete dividend-paying assets with jump-diffusion dynamics

Stocks regularly pay dividends at discrete intervals of time while statistical evidence indicates the existence of small “jumps” in the stock price dynamics. In this paper, we find closed-form solutions for the valuation of European options when the underlying asset is modeled by a jump-diffusion process and pays discrete or continuous dividends. The formula is very general and can be used with any specification on the distribution of the jump. Moreover, the formula is written in terms of the Black–Scholes formula with no jumps or dividends and thus indicates the effect of the jumps and the effect of the inclusion of discrete (or continuous) dividends on the price of the option.     

A Method of Fixing Desirable Stock Levels,and of Stock Control

The size of the stock of raw material kept by a company in the steel industry was such that it could not be kept in the main stockyard but had to be spread over two sites. This had an adverse effect on the cost of stockholding. Analysis showed that the stock was large because of the lack of a systematic method of stock control.A study of works records indicated the form that a stock control system should take, using all the available information concerning the present stock, the future production, and a forecast of what raw material was still likely to be delivered as a result of orders placed in the immediate past but as yet not completely fulfilled.A "simulation" technique, which is fully described in the paper, was used to determine the effect of using the method of stock control which had been devised. The results indicated that the stock could be reduced to about half its original size, so releasing about £100,000 of working capital and, by concentrating it in one stockyard, reducing the costs of transporting and handling.     

EQUILIBRIUM ABUNDANCE OF SALMON STOCKS IN A LIFE CYCLE MODEL WITH INTERACTING HATCHERY AND NATURAL SUBSTOCKS

This paper develops the equilibrium solutions for an age-structured life cycle model where spawning stock is split between natural and hatchery spawners. Mixing is allowed between the stocks through natural stock take by the hatchery and release of eggs or fry by the hatchery when its capacity is exceeded. The natural stock is assumed to have density-dependent egg-smolt survival while the hatchery stock has linear survival. The model can be applied to any hatchery reared fish stock but is most appropriate for salmon, where hatchery and naturally spawned fish mix completely later in life. Questions about the mix between the hatchery and natural stocks can be addressed by computing the fraction of naturally and hatchery derived stock among the natural and hatchery spawners as well as among the total adult run. Columbia River chinook stock are used as an example for which equilibria and mixing fractions are computed. A Monte Carlo sensitivity study on model parameters showed that the natural stock survival from smoltification to age 1 and the natural basin smolt carrying capacity are most important in controlling the equilibrium age-1 naturally spawned stock. Changing hatchery capacity over two orders of magnitude showed a 50 percent change in the fraction of naturally derived fish in the natural spawning stock, while the relative size of natural and hatchery stocks changed over two orders of magnitude. The model can serve as a tool for quickly assessing the effects of spawning habitat modification and hatchery supplementation practices on long-term stock mixing and stock abundance.     

Environmental safety stock: The impacts of regulatory and voluntary control policies on production planning,inventory control,and environmental performance

This paper analyzes the impacts of different pollution control policies on a firm’s decisions of production planning and inventory control. Based on a stochastic model with both demand and environmental uncertainties, we derive the optimal policies of production planning and inventory control under both regulatory and voluntary pollution control approaches, and investigate their operational and environmental effects. We establish that the conventional wisdom which suggests that reduction of environmental waste at the end of a production process also decreases the stock and throughput levels of a production system is not necessarily true. Rather, a regulatory environmental standard that limits the total amount of waste may induce the firm to raise its planned stock level, which would lead to a higher expected amount of environmental wastes before the standard is enforced as well as environmental risks at other stages of the production process. The additional planned stock level, which is termed “environmental safety stock,” can be reversed by using the voluntary control approach that provides the firm with the flexibility to occasionally exceed the environmental standard. We also conduct numerical experiments to analyze the effects of different values of model parameters under different control approaches. The analytical results provide new insights to the impacts of a firm’s production and inventory decisions on the natural environment as well as to the choices of pollution control approaches by decision makers in both the private and public sectors.     

SEQUENTIAL FISHING: COOPERATIVE AND NON-COOPERATIVE EQUILIBRIA

Two agents control the areas in which a migrating fish stock is located. The harvesting is sequential. The stock available to Agent 1 depends on the growth of the stock, which in turn depends on the amount left after harvesting by Agent 2. The stock available to Agent 2 is the quantity left after harvesting by Agent 1. Each agent fishes down the stock in each period to an “abandonment level” deemed appropriate. The problem is analyzed as a noncooperative versus cooperative, repeated game with an infinite time horizon. In the noncooperative solution, both agents will harvest the stock if the unit cost of Agent 2 is not too much higher than the unit cost of Agent 1. A cooperative solution supported by a threat to revert to the noncooperative solution if deviation occurs implies greater differences in unit costs at which both agents will harvest the stock. The problem is illustrated by a simple, numerical example.     

A matching approach for replenishing rectangular stock sizes

Consider a replenishment problem in which several different rectangular sizes of material are stocked. Customers order rectangles of the material, but the rectangles ordered have a range on specified width as well as on specified length. To satisfy the customer requirements, the stock material can be cut once longitudinally in order to satisfy two customer requirements or not cut at all, that is, an entire stock piece of material is used to satisfy one customer requirement. If an exact match is impossible in the current planning period, the unused material must be returned to stock— an expensive and undesirable situation. In this paper, a nonbipartite weighted matching problem formulation will be given for determining the replenishment requirements of rectangular stock sizes. Then, a hybrid solution approach, capable of solving real applications (typically up to 3000 nodes) efficiently, will be discussed. This solution was implemented in September 1998 and has operated successfully since then.     

基于误差理论的区间主成分分析及其应用

针对区间数样本,传统的主成分分析需进行拓展。首先讨论了区间样本数据的两种主要来源,即观测误差和符号数据分析。然后将区间数看作一个由中点和半径构成的具有一定误差的数,从误差理论出发,研究基于误差传递公式的区间主成分分析方法,并获得以区间数为表达形式的主成分。最后,结合我国2005年第四季度股票市场的数据进行了实证分析。结果表明,面对海量数据,区间PCA较传统PCA更容易从总体上把握样本的属性。     

A class of options with stochastic lives and an extension of the Black-Scholes formula

Certain options have a fixed date of maturity but may be cancelled prematurely. This can happen for a stock option in case of a merger or for an executive stock option in case the executive leaves his/her present job. The differential equation is given which governs the value of an option with a stochastic life. Solutions can be obtained through integration in certain cases. The main result is an extension of the Black-Scholes formula to options where the time to expiration is stochastic.     

The Effect of Transfer-Pack Size on Order Quantity

In many stock-control systems the policy is to place an order if the stock balance has fallen to or below a reorder level and to order enough stock to bring the stock balance up to a maximum stock level. It is often the case that stock is sold singly but is replenished in multiples of some pack size. This note considers how the actual order size depends on the pack size and the amount by which the stock balance has fallen below the reorder level at the time an order is placed.     

A STOCHASTIC FEEDBACK MODEL FOR OPTIMAL MANAGEMENT OF RENEWABLE RESOURCES

Analytical expressions for optimal harvest of a renewable resource stock which is subject to a stochastic process are found. These expressions give the optimal harvest as an explicit feedback control law. All relations in the model, including the stochastic process, may be arbitrary functions of the state variable (stock). The objective function, however, is at most a quadratic function in the control variable (yield). A quadratic objective function includes the cases of downward sloping demand and increasing marginal costs which are the most common sources for nonlinearities in the economic part of the model. When it is assumed that there is a moratorium on harvest for stock sizes below a certain level (biological barrier), it is shown that the barrier requirements influence the optimal harvest paths throughout.     

Joint Determination of Production Cycle and Inspection Intervals in a Deteriorating Production System

This paper considers production-maintenance policy for the deteriorating production system which can go ‘out of control’ while producing items. Once out of control, the production process produces some proportion of defective items. The defective items are reworked at some cost before being shipped, or, if passed to the customer, incur much larger warranty cost. Thus, to operate this system economically, periodic inspection and restoration of the process are needed. A mathematical model representing the expected annual cost is developed to determine the production cycle and process inspection intervals jointly. A case of equally spaced inspection intervals is solved by using an approximation to the cost function.