IMA Journal of Management Mathematics - recent issues

Editorial

Boylan, J. E., Syntetos, A. A. — 2008-03-18

Supply chain aperiodicity, bullwhip and stability analysis with Jury's inners

Disney, S. M. — 2008-03-18

Jury (1974, Inners and the Stability of Dynamic Systems. New York: John Wiley) presents a novel method for the analysis of dynamical systems based on matrices of the coefficients of the systems transfer function and its ‘inners’. Here, we exploit his procedure for an analysis of a supply chain replenishment or ordering decision known as the order-up-to policy. We study the discrete-time case and generalize the classical order-up-to policy by the addition of two independent proportional controllers in the policy's feedback loops. The addition of the proportional controllers is well known to allow the order-up-to policy to eliminate the bullwhip problem and we quantify this herein using Jury's inners approach. However, care has to be taken with the use of independent controllers as they can introduce stability problems. This is because the roots of the characteristic equation become complex, and they may even move out of the unit circle in the z-plane. We identify the conditions of stability using Jury's inners approach. We also investigate further the root distribution in the characteristic equation to identify the conditions under which the order-up-to policy is aperiodic. An aperiodic system has only a limited number of maxima and minima in its dynamic response. Thus, aperiodicity is an important characteristic of a supply chain replenishment policy as it will not induce rogue seasonality.

Investigation of rolling horizon flexibility contracts in a supply chain under highly variable stochastic demand

Walsh, P. M., Williams, P. A., Heavey, C. — 2008-03-18

A discrete-event simulation model of a supply chain has been developed to evaluate operational performance of sharing uncertain information on upcoming demand between an original equipment manufacturer (OEM) and a contract manufacturer under a formal rolling horizon flexibility (RHF) contract in a four-node supply chain. There are two types of RHF contracts evaluated, i.e. RHF contract with constant flexibility and decreasing flexibility bounds. The demand is externalized (i.e. the OEM receives the demand), stochastic and generated according to a gamma distribution. This paper reports on the analysis of RHF contracts operating with coefficients of variation of demand up to 2.00. Analysis of the interaction of RHF contracts with forecasting and the impact an RHF contract has on the transmission of the bullwhip effect are reported here.

Characterizing the frequency of orders received by a stockist

Shale, E. A., Boylan, J. E., Johnston, F. R. — 2008-03-18

It is regularly asserted that the frequency of orders received by a stockist can be represented as a Poisson process, but very little corroborative evidence has been published. This paper presents some results supporting the assumption. An adaptation to the standard testing methodology is presented which overcomes the complications arising from the necessity of sampling from time series data. The new approach is applied to a large range of stock-keeping units. Except for the extreme tail of the distribution, which is of little interest for most inventory applications, it is found that the frequency of orders is well represented by a Poisson process.

An inventory control project in a major Danish company using compound renewal demand models

Larsen, C., Seiding, C. H., Teller, C., Thorstenson, A. — 2008-03-18

We describe the development of a framework to compute the optimal inventory policy for a large spare parts distribution centre operation in the refrigeration and air conditioning (RA) division of the Danfoss Group in Denmark. The RA division distributes spare parts worldwide for cooling and air-conditioning systems. The warehouse logistics operation is highly automated. However, the procedures for estimating demands and the policies for the inventory control system that were in use at the beginning of the project did not fully match the sophisticated technological standard of the physical system. During the initial phase of the project development, we focussed on the fitting of suitable demand distributions for spare parts and on the estimation of demand parameters. Demand distributions were chosen from a class of compound renewal distributions. In the next phase, we designed models and algorithmic procedures for determining suitable inventory control variables based on the fitted demand distributions and a service-level requirement stated in terms of an order fill rate. Finally, we validated the results of our models against the procedures that had been in use in the company. It was concluded that the new procedures provided a better fit with the actual demand processes and were more consistent with the stated objectives for the distribution centre. We also initiated the implementation and integration of the new procedures into the company's inventory management system.

Using imperfect advance demand information in forecasting

Tan, T. — 2008-03-18

In this paper, we consider the demand-forecasting problem of a make-to-stock system operating in a business-to-business environment where some customers provide information on their future orders, which are subject to changes in time, hence constituting imperfect advance demand information (ADI). The demand is highly volatile and non-stationary not only because it is subject to seasonality and changing trends but also because some individual client demands have significant influence on the total demand. In such an environment, traditional forecasting methods may result in highly inaccurate forecasts, since they are mostly developed for the total demand based only on the demand history, not making use of demand information and ignoring the effects of individual order patterns of the customers. We propose a forecasting methodology that makes use of individual ordering pattern histories of the product–customer combinations and the current build up of orders. Moreover, we propose making use of limited judgemental updates on the statistical forecasts prior to the use of ADI.

Demand forecasting adjustments for service-level achievement

Syntetos, A. A., Boylan, J. E. — 2008-03-18

Demand forecasting and stock control are traditionally examined as independent of each other. Even though this weakness has been highlighted in the academic literature, little empirical work has been conducted on forecasting adjustments addressing the interaction between forecasting and stock control. In this paper, the relevant literature is critically reviewed. Subsequently, the empirical performance of some modifications and adjustments, on slow-moving items, is examined in detail. The data set consists of the individual demand histories of 753 intermittent line items from the Royal Air Force (UK). Overall, the results indicate that there is a scope for improving the performance of parametric stock control systems, and adjustments are indeed required in order to account for the interaction between forecasting and stock control.

Hierarchical estimation as a basis for hierarchical forecasting

Strijbosch, L. W. G., Heuts, R. M. J., Moors, J. J. A. — 2008-03-18

In inventory management, hierarchical forecasting (HF) is a hot issue: families of items are formed for which total demand is forecasted; total forecast then is broken up to produce forecasts for the individual items. Since HF is a complicated procedure, analytical results are hard to obtain; consequently, most literature is based on simulations and case studies. This paper succeeds in following a more theoretical approach by simplifying the problem: we consider estimation instead of forecasting. So, from a random sample we estimate both the total demand and the fraction of this total that individual items take; multiplying these two quantities gives a new estimate of the individual demand. Then, our research question is: Can aggregation of items, followed by fractioning, lead to more accurate estimates of individual demand? We consider two simple situations that can be analysed fully theoretically. Thirdly, a more practical situation is investigated by means of simulation.

Forecasting item-level demands: an analytical evaluation of top-down versus bottom-up forecasting in a production-planning framework

Widiarta, H., Viswanathan, S., Piplani, R. — 2008-03-18

We compare the performance of top–down (TD) and bottom–up (BU) strategies for forecasting the demand of an item that belongs to a product family. The TD strategy forecasts the sum of the item demands and distributes it to the individual item based upon the historical demand proportion of each item in the family. The BU strategy forecasts each item demand individually using the historical demand data for the particular item. All the item demands, which may be correlated with each other, are assumed to follow a first-order univariate moving average process. As is common in a production-planning environment, the forecasting under both strategies is carried out using the exponential smoothing technique. We show that the performance of the two forecasting strategies is nearly identical, regardless of the coefficient of correlation between the item demands, the items' proportion in the family and the coefficient of the serial correlation term of the demand process. We further investigate the relative performance of the two strategies when a fixed (rather than the optimal) smoothing constant is used for forecasting the demand under both strategies.

Acknowledgement

Darby-Dowman, K. — 2007-12-04

Towards integration: a revenue-sharing contract in a supply chain

Qin, Z. — 2007-12-04

This paper deals with the problem of a revenue-sharing contract adopted in a supply chain involving one supplier and one retailer with short life-cycle products. Under this contract, the retailer can obtain the product from the supplier at a discounted price while as a compensation, the retailer must share his revenue with the supplier at a certain revenue-sharing rate, say r (0 ≤ r ≤ 1), where r represents the portion of the revenue to be kept by the retailer. We use a two-stage (Stackelberg) game to model the problem, where one player is the game's leader and the other the game's follower. Our ultimate objective is to maximize the overall supply chain's total profit, and to show the effects of salvage revenue and the revenue-sharing rate on transfer cost rate, profit of the supplier and retailer and the overall supply chain's total profit while upholding the individual components’ incentives. Our analysis exhibits that the case in which salvage revenue is not shared is preferred and the computational results to explore the effects of the revenue-sharing rate lead to many managerial insights regarding the leader of the game.

Analysis of supply contracts from a supplier's perspective

Wang, W., Wang, H., Kobbacy, K. A. H. — 2007-12-04

Incentive structure and demand uncertainty may cause supply chains to operate at a low efficiency. Therefore, many supply contracts are employed in practice to improve the performance of supply chains, i.e. to benefit all members involved in the chain. Supply chain contracts provide mechanisms to change the incentive structures of the supply chain members so that their decisions can improve the supply chain efficiency, while also protect their own interests. It is important to understand the impacts of supply contracts and their differences from a supplier's perspective, since it is often the supplier who initiates a supply contract. This paper reports on a comprehensive analysis of supply contracts from a supplier's perspective. Six commonly used supply contracts are analysed and the contract parameters are optimized to maximize the supplier's expected profit with consideration to improve the retailer's profit. This case has not been thoroughly investigated in literature to date. The risk-sharing mechanism and the division of the increased profit between the retailer and supplier for some of the contracts are also investigated in detail.

Gearbox failure diagnosis based on vector autoregressive modelling of vibration data and dynamic principal component analysis

Liu, B., Makis, V. — 2007-12-04

An effective gearbox failure diagnosis helps prevent catastrophic gearbox failure and can contribute to significant economic benefits. This paper proposes a gear failure diagnosis method based on vector autoregressive modelling of high-frequency vibration data, dimensionality reduction applying dynamic principal component analysis (PCA) and condition monitoring using a multivariate control chart. After extracting useful information from the vibration data obtained from distinct directions via dynamic PCA, a failure diagnosis scheme is implemented and tested using real gearbox vibration data. It is shown that the failure diagnosis scheme can indicate the gear teeth failure pattern when the gear is damaged, which has not been demonstrated in the previous studies. For a comparison, PCA is applied to the same data set. The results show that the advantages of dynamic PCA over PCA for failure diagnosis using vibration data consist not only in indicating more accurately the occurrence of incipient fault and the actual gear condition, but also in a much lower false alarm rate.

An inventory model for stock with advertising sensitive demand

Sana, S. S., Chaudhuri, K. S. — 2007-12-04

The effect of advertising media and sales effort on future demand of merchandize is considered. In an oligopolistic marketing system, it is quite natural to boost sales by using advertising and sales effort to earn more money from a business sector. Determination of demand and costs due to advertising and sales effort is quite difficult. The approach in this paper is to concentrate on investment for the purpose of advertising and increasing sales effort in order to maximize profit. The paper extends an inventory model over finite and infinite time horizons where demand is influenced by the level of stock, advertising media and sales effort. The associated profit maximization problem is solved by the ‘Euler–Lagrange method’. The model is illustrated with a numerical example.

Maximin investment problems for discounted and total wealth

Dokuchaev, N. — 2007-12-04

We study an optimal investment problem for a continuous-time incomplete market model such that the risk-free rate, the appreciation rates and the volatility of the stocks are all random; they are not necessarily adapted to the driving Brownian motion, and their distributions are unknown, but they are supposed to be currently observable. The optimal investment problem is stated in ‘maximin’ setting which leads to maximization of the minimum of expected utility over all distributions of parameters. We found that the presence of the non-discounted wealth in the performance criterion (in addition to the discounted wealth) implies an additional condition for the saddle point of the maximin problem: the saddle point must include the minimum of the possible risk-free return. This is different from the case when the utility depends on the discounted wealth only. Using this result, the maximin problem is reduced to a linear parabolic equation and minimization over two scalar parameters. It is an important development of the results obtained in Dokuchaev (2002, Dynamic Portfolio Strategies: Quantitative Methods and Empirical Rules for Incomplete Information. Boston: Kluwer; 2006, IMA J. Manage. Math., 17, 257–276).

Estimation and decomposition of cost efficiency in the health care food service sector: an extended stochastic frontier approach

Assaf, A., Matawie, K. M. — 2007-12-04

This paper introduces and implements an extended stochastic frontier model to estimate and decompose cost efficiency (CE) in the health care foodservice sector. The interesting feature of this model is that it allows differentiation between the three different types of efficiency: technical efficiency (TE), allocative efficiency (AE) and their associated CE. A complete illustration of these efficiencies is presented using a cross-sectional sample of 101 hospital foodservice operations. Results showed that the model and all its parameter coefficients were plausible, significant and satisfy all theoretical requirements. It was also clear that the average efficiency scores were lower for TE (80%) than AE (88%), indicating that TE is the main source of CE and requires further attention.

Modelling history-dependent parameters in the SMPS format for stochastic programming

Gassmann, H. I., Infanger, G. — 2007-12-04

This paper proposes two extensions to the SMPS format for stochastic programs to permit modelling of autoregressive-moving average (ARMA) processes. Sampling-based algorithms can thus proceed independently of any underlying modelling system, increasing efficiency. An illustrative example demonstrates the power of the new constructs.

Editorial

Mamon, R. S., Date, P. M. — 2007-09-04

Pricing vulnerable European options with stochastic default barriers

Hui, C., Lo, C., Ku, K. — 2007-09-04

This paper develops a valuation model of European options incorporating a stochastic default barrier, which extends a constant default barrier proposed in the Hull–White model. The default barrier is considered as an option writer's liability. Closed-form solutions of vulnerable European option values based on the model are derived to study the impact of the stochastic default barriers on option values. The numerical results show that negative correlation between the firm values and the stochastic default barriers of option writers gives material reductions in option values where the options are written by firms with leverage ratios corresponding to BBB or BB ratings.

Optimal hedging and parameter uncertainty

Monoyios, M. — 2007-09-04

We explore the impact of drift parameter uncertainty in a basis risk model, an incomplete market in which a claim on a nontraded asset is optimally hedged using a correlated traded stock. Using analytic expansions for indifference prices and hedging strategies, we develop an efficient procedure to generate terminal hedging error distributions when the hedger has erroneous estimates of the drift parameters. These show that the effect of parameter uncertainty is occasionally benign, but often very destructive. In light of this, we develop a filtering approach in which the hedger updates her parameter estimates from observations of the asset prices, and we find an analytic solution to the hedger's combined filtering and control problem in the case that the drift of the traded asset is known with certainty.

Gaussian factor models futures and forward prices

Hyndman, C. B. — 2007-09-04

We completely characterize the futures price and forward price of a risky asset (commodity) paying a stochastic dividend yield (convenience yield). The asset (commodity) price is modelled as an exponential affine function of a Gaussian factors process, while the interest rate and dividend yield are affine functions of the factors process. The characterization we provide is based on the method of stochastic flows. We believe this method leads to simpler and more clear-cut derivations of the futures price and forward price formulae than alternative methods. Hedging a long-term forward contract with shorter term futures contracts and bonds is also examined.

A calibration algorithm for simulation-based pricing models

Reesor, R. M., McLeish, D. L. — 2007-09-04

Derivative pricing models require calibration to market conditions in order to determine quantities such as hedging positions and the prices of other instruments. For stochastic models and/or complex derivatives whose prices are not of an analytic form, prices must be computed via simulation and the calibration is more difficult. A method to facilitate the calibration of simulation-based pricing models is proposed. The algorithm uses a statistically designed experiment to select the points at which simulations are performed. The method is quite general as it is independent of the stochastic model for the underlying and allows for different objective functions that can incorporate information such as open interest and volume. Furthermore, market prices from European- and/or American-style derivatives covering a range of strike prices and maturities can be handled by this technique. Examples show the procedure is successful at calibrating well-known asset pricing models to both simulated and market data.

Modelling financial time series with SEMIFAR GARCH model

Feng, Y., Beran, J., Yu, K. — 2007-09-04

A class of semiparametric fractional autoregressive models with generalized autoregressive conditional heteroskedastic (GARCH) errors, which includes deterministic trends, difference stationarity and stationarity with short- and long-range dependence and heteroskedastic model errors, is very powerful for modelling financial time series. This paper discusses the model fitting, including an efficient algorithm and parameter estimation of GARCH error term, so that the model can be applied in practice. We then illustrate the model and estimation methods with a few of different finance data sets.

Predicting stock returns and assessing prediction performance

Baker, R., Belgorodskiy, A. — 2007-09-04

We use regression methods to predict the expected monthly return on stocks and the covariance matrix of returns, the predictor variables being a company's ‘fundamentals’, such as dividend yield and the history of previous returns. Predictions are evaluated out of sample for shares traded on the London Stock Exchange from 1976 to 2005. We explore and evaluate many modelling and inferential approaches, including the use of weighted regression, discounted regression, shrinkage of regression coefficients and the transformation to normality of predictor variables. We also investigate alternative covariance matrix models, such as a two-index model and a shrinkage model. Using suitable statistics to enable the out-of-sample performance of competing methodologies to be compared is crucial, and we develop some new statistics and a graphical aid for this purpose. What is original in this paper is an evaluation of many modelling and inferential procedures for which conflicting claims have been made in the literature and the development of new measures of portfolio performance.