IMA Journal of Management Mathematics - current issue

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.