On the effectiveness of top‐down strategy for forecasting autoregressive demands

We investigate the relative effectiveness of top‐down versus bottom‐up strategies for forecasting the demand of an item that belongs to a product family. The demand for each item in the family is assumed to follow a first‐order univariate autoregressive process. Under the top‐down strategy, the aggregate demand is forecasted by using the historical data of the family demand. The demand forecast for the items is then derived by proportional allocation of the aggregate forecast. Under the bottom‐up strategy, the demand forecast for each item is directly obtained by using the historical demand data of the particular item. In both strategies, the forecasting technique used is exponential smoothing. We analytically evaluate the condition under which one forecasting strategy is preferred over the other when the lag‐1 autocorrelation of the demand time series for all the items is identical. We show that when the lag‐1 autocorrelation is smaller than or equal to 1/3, the maximum difference in the performance of the two forecasting strategies is only 1%. However, if the lag‐1 autocorrelation of the demand for at least one of the items is greater than 1/3, then the bottom‐up strategy consistently outperforms the top‐down strategy, irrespective of the items' proportion in the family and the coefficient of correlation between the item demands. A simulation study reveals that the analytical findings hold even when the lag‐1 autocorrelation of the demand processes is not identical. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007.     

An application of servomechanisms to inventory

In recent years, some attention has been devoted to the application of techniques of control theory to inventory management. In particular, H. Vassian (1955) developed a model for a periodic review inventory system utilizing techniques of discrete variable servomechanisms to analyze the system in a cost-free structure. The resulting model is inherently deterministic, however, and emphasizes the control of inventory fluctuation about a safety level by selecting an appropriate order policy. Such an order policy is defined only up to an arbitrary method of forecasting customer demands. The present paper is a continuation of the model developed by Vassian in which exponential smoothing is used as a specific forecasting technique. Full recognition of the probabilistic nature of demand is taken into account and the requirement of minimizing expected inventory level is imposed. In addition, explicit formulas for the variance in inventory are derived as functions of the smoothing constant and the tradeoff between small variance and rapid system response is noted. Finally, in an attempt to remove the bias inherent in exponential smoothing, a modification of that technique is defined and discussed as an alternate forecasting method.     

A note on the forecast performance of temporal aggregation

Earlier research on the effects of nonoverlapping temporal aggregation on demand forecasting showed the benefits associated with such an approach under a stationary AR(1) or MA(1) processes for decision making conducted at the disaggregate level. The first objective of this note is to extend those important results by considering a more general underlying demand process. The second objective is to assess the conditions under which aggregation may be a preferable approach for improving decision making at the aggregate level as well. We confirm the validity of previous results under more general conditions, and we show the increased benefit resulting from forecasting by temporal aggregation at lower frequency time units. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 489–500, 2014     

Impact of transfer pricing methods for tax purposes on supply chain performance under demand uncertainty

Transfer pricing refers to the pricing of an intermediate product or service within a firm. This product or service is transferred between two divisions of the firm. Thus, transfer pricing is closely related to the allocation of profits in a supply chain. Motivated by the significant impact of transfer pricing methods for tax purposes on operational decisions and the corresponding profits of a supply chain, in this article, we study a decentralized supply chain of a multinational firm consisting of two divisions: a manufacturing division and a retail division. These two divisions are located in different countries under demand uncertainty. The retail division orders an intermediate product from the upstream manufacturing division and sets the retail price under random customer demand. The manufacturing division accepts or rejects the retail division's order. We specifically consider two commonly used transfer pricing methods for tax purposes: the cost‐plus method and the resale‐price method. We compare the supply chain profits under these two methods. Based on the newsvendor framework, our analysis shows that the cost‐plus method tends to allocate a higher percentage of profit to the retail division, whereas the resale‐price method tends to achieve a higher firm‐wide profit. However, as the variability of demand increases, our numerical study suggests that the firm‐wide and divisional profits tend to be higher under the cost‐plus method than they are under the resale‐price method. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Models for production planning under power interruptions

We present a robust optimization model for production planning under the assumption that electricity supply is subject to uncertain interruptions caused by participation in interruptible load contracts (ILCs). The objective is to minimize the cost of electricity used for production while providing a robust production plan which ensures demand satisfaction under all possible interruption scenarios. The combinatorial size of the set of interruption scenarios makes this a challenging problem. Furthermore, we assume that no probabilistic information is known about the supply uncertainty: we only use the information given in the ILC to identify an uncertainty set that captures the possible scenarios. We construct a general robust framework to handle this uncertainty and present a heuristic to compute a good feasible solution of the robust model. We provide computational experiments on a real‐world example and compare the performance of an exact solver applied to the robust model with that of the heuristic procedure. Finally, we include the operational impact of interruptions such as “recovery modes” in the definition of the uncertainty set. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Exploiting self‐canceling demand point aggregation error for some planar rectilinear median location problems

When solving location problems in practice it is quite common to aggregate demand points into centroids. Solving a location problem with aggregated demand data is computationally easier, but the aggregation process introduces error. We develop theory and algorithms for certain types of centroid aggregations for rectilinear 1‐median problems. The objective is to construct an aggregation that minimizes the maximum aggregation error. We focus on row‐column aggregations, and make use of aggregation results for 1‐median problems on the line to do aggregation for 1‐median problems in the plane. The aggregations developed for the 1‐median problem are then used to construct approximate n‐median problems. We test the theory computationally on n‐median problems (n ≥ 1) using both randomly generated, as well as real, data. Every error measure we consider can be well approximated by some power function in the number of aggregate demand points. Each such function exhibits decreasing returns to scale. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 614–637, 2003.     

基于备件需求预测的两步法理论?

在对备件需求时间序列研究的基础上,结合指数平滑法和Croston法的特点,分析了指数平滑法与两步法的原理,通过对指数平滑法和两步法方差的研究,得到两步法是指数平滑法的一般形式的结论,为两步法的进一步研究提供一定的理论支撑。     

A comparative study of demand forecasting techniques for military helicopter spare parts

This paper deals with techniques applicable to predicting spare parts demand for military helicopters. The military helicopter is a distinct weapons system, whose unique configuration may preclude the direct application of forecasting techniques which have proved successful for other weapon systems. Furthermore, although the military helicopter has become extremely important tactically in modern warfare, it has received scant attention in terms of research concerning its supply support. Specifically, this paper summarizes research done to measure and compare the forecasting accuracy of six mathematical models, as they were applied to three prominent military helicopters. In addition, the paper describes attempts that were made to define, where possible, the conditions under which a specific forecasting technique might be applicable. In general, it is shown that the most accurate set of helicopter spare parts demand forecasts are produced by a second order polynomial exponential smoothing model. This model is observed to have most accurately described the highly volatile, and upward-trended demand time series which were the subject of the study.     

A three‐stage procurement optimization problem under uncertainty

This article examines a problem faced by a firm procuring a material input or good from a set of suppliers. The cost to procure the material from any given supplier is concave in the amount ordered from the supplier, up to a supplier‐specific capacity limit. This NP‐hard problem is further complicated by the observation that capacities are often uncertain in practice, due for instance to production shortages at the suppliers, or competition from other firms. We accommodate this uncertainty in a worst‐case (robust) fashion by modeling an adversarial entity (which we call the “follower”) with a limited procurement budget. The follower reduces supplier capacity to maximize the minimum cost required for our firm to procure its required goods. To guard against uncertainty, the firm can “protect” any supplier at a cost (e.g., by signing a contract with the supplier that guarantees supply availability, or investing in machine upgrades that guarantee the supplier's ability to produce goods at a desired level), ensuring that the anticipated capacity of that supplier will indeed be available. The problem we consider is thus a three‐stage game in which the firm first chooses which suppliers' capacities to protect, the follower acts next to reduce capacity from unprotected suppliers, and the firm then satisfies its demand using the remaining capacity. We formulate a three‐stage mixed‐integer program that is well‐suited to decomposition techniques and develop an effective cutting‐plane algorithm for its solution. The corresponding algorithmic approach solves a sequence of scaled and relaxed problem instances, which enables solving problems having much larger data values when compared to standard techniques. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Technical note – operational statistics: Properties and the risk‐averse case

Consider a repeated newsvendor problem for managing the inventory of perishable products. When the parameter of the demand distribution is unknown, it has been shown that the traditional separated estimation and optimization (SEO) approach could lead to suboptimality. To address this issue, an integrated approach called operational statistics (OS) was developed by Chu et al., Oper Res Lett 36 (2008) 110–116. In this note, we first study the properties of this approach and compare its performance with that of the traditional SEO approach. It is shown that OS is consistent and superior to SEO. The benefit of using OS is larger when the demand variability is higher. We then generalize OS to the risk‐averse case under the conditional value‐at‐risk (CVaR) criterion. To model risk from both demand sampling and future demand uncertainty, we introduce a new criterion, called the total CVaR, and find the optimal OS under this new criterion. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 206–214, 2015     

An adaptive forecasting algorithm and inventory policy for products with short life cycles

Products with short life cycles are becoming increasingly common in many industries, such as the personal computer (PC) and mobile phone industries. Traditional forecasting methods and inventory policies can be inappropriate for forecasting demand and managing inventory for a product with a short life cycle because they usually do not take into account the characteristics of the product life cycle. This can result in inaccurate forecasts, high inventory cost, and low service levels. Besides, many forecasting methods require a significant demand history, which is available only after the product has been sold for some time. In this paper, we present an adaptive forecasting algorithm with two characteristics. First, it uses structural knowledge on the product life cycle to model the demand. Second, it combines knowledge on the demand that is available prior to the launch of the product with actual demand data that become available after the introduction of the product to generate and update demand forecasts. Based on the forecasting algorithm, we develop an optimal inventory policy. Since the optimal inventory policy is computationally expensive, we propose three heuristics and show in a numerical study that one of the heuristics generates near‐optimal solutions. The evaluation of our approach is based on demand data from a leading PC manufacturer in the United States, where the forecasting algorithm has been implemented. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

The impact of demand uncertainty on product line design under endogenous substitution

The existing product line design literature devotes little attention to the effect of demand uncertainty. Due to demand uncertainty, the supply‐demand mismatch is inevitable which leads to different degrees of lost sales depending on the configuration of product lines. In this article, we adopt a stylized two‐segment setup with uncertain market sizes and illustrate the interplay between two effects: risk pooling that mitigates the impact of demand uncertainty and market segmentation that facilitates consumer differentiation. Compared to downward substitution, inducing bidirectional substitution through product line decisions including quality levels and prices can yield greater risk pooling effects. However, we show that the additional benefit from the risk pooling effect cannot compensate for the reduced market segmentation effect. We demonstrate that the presence of demand uncertainty can reduce the benefit of market segmentation and therefore the length of product lines in terms of the difference between products. We also propose three heuristics that separate product line and production decisions; each of these heuristics corresponds to one particular form of demand substitution. Our numerical studies indicate that the best of the three heuristics yields performance that is close to optimality. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 143–157, 2015     

Call center arrival modeling: A Bayesian state‐space approach

In this article, we introduce three discrete time Bayesian state‐space models with Poisson measurements, each aiming to address different issues in call center arrival modeling. We present the properties of the models and develop their Bayesian inference. In so doing, we provide sequential updating and smoothing for call arrival rates and discuss how the models can be used for intra‐day, inter‐day, and inter‐week forecasts. We illustrate the implementation of the models by using actual arrival data from a US commercial bank's call center and provide forecasting comparisons. © 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 28–42, 2011     

Expansion planning for waste‐to‐energy systems using waste forecast prediction sets

We consider an expansion planning problem for Waste‐to‐Energy (WtE) systems facing uncertainty in future waste supplies. The WtE expansion plans are regarded as strategic, long term decisions, while the waste distribution and treatment are medium to short term operational decisions which can adapt to the actual waste collected. We propose a prediction set uncertainty model which integrates a set of waste generation forecasts and is constructed based on user‐specified levels of forecasting errors. Next, we use the prediction sets for WtE expansion scenario analysis. More specifically, for a given WtE expansion plan, the guaranteed net present value (NPV) is evaluated by computing an extreme value forecast trajectory of future waste generation from the prediction set that minimizes the maximum NPV of the WtE project. This problem is essentially a multiple stage min‐max dynamic optimization problem. By exploiting the structure of the WtE problem, we show this is equivalent to a simpler min‐max optimization problem, which can be further transformed into a single mixed‐integer linear program. Furthermore, we extend the model to optimize the guaranteed NPV by searching over the set of all feasible expansion scenarios, and show that this can be solved by an exact cutting plane approach. We also propose a heuristic based on a constant proportion distribution rule for the WtE expansion optimization model, which reduces the problem into a moderate size mixed‐integer program. Finally, our computational studies demonstrate that our proposed expansion model solutions are very stable and competitive in performance compared to scenario tree approaches. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 47–70, 2016     

Augmented nested sampling for stochastic programs with recourse and endogenous uncertainty

We propose a novel simulation‐based approach for solving two‐stage stochastic programs with recourse and endogenous (decision dependent) uncertainty. The proposed augmented nested sampling approach recasts the stochastic optimization problem as a simulation problem by treating the decision variables as random. The optimal decision is obtained via the mode of the augmented probability model. We illustrate our methodology on a newsvendor problem with stock‐dependent uncertain demand both in single and multi‐item (news‐stand) cases. We provide performance comparisons with Markov chain Monte Carlo and traditional Monte Carlo simulation‐based optimization schemes. Finally, we conclude with directions for future research.     

Sensitivity analysis on responsive pricing and production under imperfect demand updating

This paper examines three types of sensitivity analysis on a firm's responsive pricing and responsive production strategies under imperfect demand updating. Demand has a multiplicative form where the market size updates according to a bivariate normal model. First, we show that both responsive production and responsive pricing resemble the classical pricing newsvendor with posterior demand uncertainty in terms of the optimal performance and first‐stage decision. Second, we show that the performance of responsive production is sensitive to the first‐stage decision, but responsive pricing is insensitive. This suggests that a “posterior rationale” (ie, using the optimal production decision from the classical pricing newsvendor with expected posterior uncertainty) allows a simple and near‐optimal first‐stage production heuristic for responsive pricing. However, responsive production obtains higher expected profits than responsive pricing under certain conditions. This implies that the firm's ability to calculate the first‐stage decision correctly can help determine which responsive strategy to use. Lastly, we find that the firm's performance is not sensitive to the parameter uncertainty coming from the market size, total uncertainty level and information quality, but is sensitive to uncertainty originating from the procurement cost and price‐elasticity.     

To wait or not to wait: Optimal ordering under lead time uncertainty and forecast updating

There has been a dramatic increase over the past decade in the number of firms that source finished product from overseas. Although this has reduced procurement costs, it has increased supply risk; procurement lead times are longer and are often unreliable. In deciding when and how much to order, firms must consider the lead time risk and the demand risk, i.e., the accuracy of their demand forecast. To improve the accuracy of its demand forecast, a firm may update its forecast as the selling season approaches. In this article we consider both forecast updating and lead time uncertainty. We characterize the firm's optimal procurement policy, and we prove that, with multiplicative forecast revisions, the firm's optimal procurement time is independent of the demand forecast evolution but that the optimal procurement quantity is not. This leads to a number of important managerial insights into the firm's planning process. We show that the firm becomes less sensitive to lead time variability as the forecast updating process becomes more efficient. Interestingly, a forecast‐updating firm might procure earlier than a firm with no forecast updating. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

The cost impact of using simple forecasting techniques in a supply chain

In this paper we consider an inventory model in which the retailer does not know the exact distribution of demand and thus must use some observed demand data to forecast demand. We present an extension of the basic newsvendor model that allows us to quantify the value of the observed demand data and the impact of suboptimal forecasting on the expected costs at the retailer. We demonstrate the approach through an example in which the retailer employs a commonly used forecasting technique, exponential smoothing. The model is also used to quantify the value of information and information sharing for a decoupled supply chain in which both the retailer and the manufacturer must forecast demand. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 388–411, 2003     

Single‐commodity stochastic network design under demand and topological uncertainties with insufficient data

Stochastic network design is fundamental to transportation and logistic problems in practice, yet faces new modeling and computational challenges resulted from heterogeneous sources of uncertainties and their unknown distributions given limited data. In this article, we design arcs in a network to optimize the cost of single‐commodity flows under random demand and arc disruptions. We minimize the network design cost plus cost associated with network performance under uncertainty evaluated by two schemes. The first scheme restricts demand and arc capacities in budgeted uncertainty sets and minimizes the worst‐case cost of supply generation and network flows for any possible realizations. The second scheme generates a finite set of samples from statistical information (e.g., moments) of data and minimizes the expected cost of supplies and flows, for which we bound the worst‐case cost using budgeted uncertainty sets. We develop cutting‐plane algorithms for solving the mixed‐integer nonlinear programming reformulations of the problem under the two schemes. We compare the computational efficacy of different approaches and analyze the results by testing diverse instances of random and real‐world networks. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 154–173, 2017     

Dynamic capacity reservation and due date quoting in a make‐to‐order system

We consider a make‐to‐order manufacturer facing random demand from two classes of customers. We develop an integrated model for reserving capacity in anticipation of future order arrivals from high priority customers and setting due dates for incoming orders. Our research exhibits two distinct features: (1) we explicitly model the manufacturer's uncertainty about the customers' due date preferences for future orders; and (2) we utilize a service level measure for reserving capacity rather than estimating short and long term implications of due date quoting with a penalty cost function. We identify an interesting effect (“t‐pooling”) that arises when the (partial) knowledge of customer due date preferences is utilized in making capacity reservation and order allocation decisions. We characterize the relationship between the customer due date preferences and the required reservation quantities and show that not considering the t‐pooling effect (as done in traditional capacity and inventory rationing literature) leads to excessive capacity reservations. Numerical analyses are conducted to investigate the behavior and performance of our capacity reservation and due date quoting approach in a dynamic setting with multiple planning horizons and roll‐overs. One interesting and seemingly counterintuitive finding of our analyses is that under certain conditions reserving capacity for high priority customers not only improves high priority fulfillment, but also increases the overall system fill rate. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008