Multi-item sales forecasting with total and split exponential smoothing

Efficient supply chain management relies on accurate demand forecasting. Typically, forecasts are required at frequent intervals for many items. Forecasting methods suitable for this application are those that can be relied upon to produce robust and accurate predictions when implemented within an automated procedure. Exponential smoothing methods are a common choice. In this empirical case study paper, we evaluate a recently proposed seasonal exponential smoothing method that has previously been considered only for forecasting daily supermarket sales. We term this method ‘total and split’ exponential smoothing, and apply it to monthly sales data from a publishing company. The resulting forecasts are compared against a variety of methods, including several available in the software currently used by the company. Our results show total and split exponential smoothing outperforming the other methods considered. The results were also impressive for a method that trims outliers and then applies simple exponential smoothing.     

Stochastic multi-site supply chain planning in textile and apparel industry under demand and price uncertainties with risk aversion

A multi-product, multi-period, multi-site supply chain production and transportation planning problem, in the textile and apparel industry, under demand and price uncertainties is considered in this paper. The problem is formulated using a two-stage stochastic programming model taking into account the production amount, the inventory and backorder levels as well as the amounts of products to be transported between the different plants and customers in each period. Risk management is addressed by incorporating a risk measure into the stochastic programming model as a second objective function, which leads to a multi-objective optimization model. The objectives aim to simultaneously maximize the expected net profit and minimize the financial risk measured. Two risk measures are compared: the conditional-value-at-risk and the downside risk. As the considered objective functions conflict with each other’s, the problem solution is a front of Pareto optimal robust alternatives, which represents the trade-off among the different objective functions. A case study using real data from textile and apparel industry in Tunisia is presented to illustrate the effectiveness of the proposed model and the robustness of the obtained solutions.     

Forecasting demand for mail order catalogue lines during the season

Most mail order catalogues include a large number of few lines. Forecasting demand is therefore not easy, and the forecasts for all lines are typically up-dated every week of the catalogue season. The forecasts for each line are usually obtained by determining how the demand for similar lines built up in the corresponding season of the previous year, and then grossing up the demands received accordingly. Using data for one particular mail order company, the sources of error in this trend profile method of forecasting are explored, and some simpl ways of improving its accuracy are suggested. An assessment of the proposed improvements is made by determining their likely effects on forecasting accuracy and stock control performance.     

Peak demand forecasting for a seasonal product using Bayesian approach

An actual demand-forecasting problem of the US apparel dealers is studied. Demand is highly fluctuating during the peak sale season and low prior to the peak season. The model is described by the continuous time stochastic process applying the Bayesian process. The standard gamma distribution is selected for the demand process and an inverse gamma distribution is chosen as the conjugate prior for the model. The choice is supported by the maximum likelihood estimate among a number of non-negative distribution models. The proposed Bayesian models predict the probability of the future demand expressed explicitly conditional on the observed demand prior to the peak season. The data set illustrates partial demand of a seasonal product procured by the US dealers from overseas. In recent years, hazard and operational risks due to weather disasters and equipment shutdowns were felt significantly. These caused supply chain disruption and unrecorded demand. The model is extended to contribute to forecast from an unrecorded data set due to supply disruption. Forecasts are compared with real data and a widely implemented adaptive Holt-Winters (H-W) seasonal forecasting model. Results show that the forecasts calculated by the proposed methods do better than those of the adaptive H-W model.     

Inventory rationing for the News-Vendor problem with a drop-shipping option

We consider a single-period inventory model for a bricks-and-clicks business. Store inventory can be used to fulfill both store demand and internet demand. Drop-shipping is used as an additional option for internet sale. We analyze two rationing policies for store inventory: a threshold policy and a fixed-portion policy. We formulate the expected profit for both and prove concavity. There exists an optimal order quantity for store inventory and an optimal stock rationing level below which the manager starts to use drop-shipping for internet demand. Numerical examples show that considering the rationing problem for the single-period inventory model, which is ignored in some earlier works, can result in remarkable differences.     

Copula-CVaR下考虑随机成本和需求的单周期订货决策研究

不确定环境下的单周期最优订货量决策具有重要且广泛的应用价值。与传统的仅考虑需求不确定性的报童模型不同,本文考虑市场价格恒定,但成本和需求随机变化且相关联下的报童决策问题。为此,采用Copula函数构建成本和需求之间的关联,考虑决策者可能具有的风险态度,建立了相应的Copula-CVaR模型,证明了模型解的存在性和唯一性,并将模型离散化为易求解的线性规划问题。最后,通过不同的风险水平和多种Copula函数下的仿真,分析了随机成本与需求的相关性和波动性对最优决策结果影响,并得到相关结论,为相关企业决策提供依据。     

Forecasting demand variation when there are stockouts

This paper addresses the common problem of forecasting demand when there are a large number of stockouts. The well-known single period stochastic inventory (or ‘newsboy’) problem provides the optimum, single period, stocking level for a product subject to stochastic demand. There are many situations where repetitive ‘newsboy’ solutions are implemented to guide stocking of repeat, but related, products, such as newspapers, magazines, or perishable groceries. Implementation of the ‘newsboy’ solution requires forecasts of the distribution of demand, although there are many plausible cost parameters that lead to optimum stocking policies where there is a high probability of a stockout. The company is, therefore, faced with the problem of attempting to forecast demand when a high percentage of the available sales data reflects the stock available for sale, rather than the true demand.A procedure has been developed¹ to improve estimates of the mean and variance of the distribution of demand when there are stockouts, but this procedure fails when the percentage of stockouts increases above 50%. A modified stockout adjustment procedure is presented in this paper, and it is shown that use of this new procedure can lead to greatly improved estimates of demand parameters, and greatly improved profitability, when there are a high percentage of stockouts.     

Bayesian decision-making in inventory modelling

The objective of this paper is to advocate the use of Bayesianmethods in tackling decision problems with limited past data.It is assumed that a Bayesian approach is least likely to besuccessful when there is no information on which to base a meaningfulprior. Here we use a limiting, invariant, form of the conjugateprior distribution to represent this ignorance. The resultsof decisions based on Bayesian methods with this ‘non-informative’prior are compared with those which result from deriving a pointestimate for the unknown parameter. The particular context consideredhere is that of a single-period inventory model with compoundPoisson demand made up of a known demand size distribution butan unknown demand rate. The demand rate is assumed to be highenough for a normal approximation to the compound Poisson distributionto be used, in which case it is possible to analyse the behaviourdirectly. An extension to the multi-period model with zero leadtime is considered briefly. The results lend support to theuse of Bayesian methods, with or without a meaningful prior,for which the analysis and computation are no more complex thanthose required by standard methods.     

Style goods pricing with demand learning

For many industries (e.g., apparel retailing) managing demand through price adjustments is often the only tool left to companies once the replenishment decisions are made. A significant amount of uncertainty about the magnitude and price sensitivity of demand can be resolved using the early sales information. In this study, a Bayesian model is developed to summarize sales information and pricing history in an efficient way. This model is incorporated into a periodic pricing model to optimize revenues for a given stock of items over a finite horizon. A computational study is carried out in order to find out the circumstances under which learning is most beneficial. The model is extended to allow for replenishments within the season, in order to understand global sourcing decisions made by apparel retailers. Some of the findings are empirically validated using data from U.S. apparel industry.     

Multi-source facility location–allocation and inventory problem

We consider a joint facility location–allocation and inventory problem that incorporates multiple sources of warehouses. The problem is motivated by a real situation faced by a multinational applied chemistry company. In this problem, multiple products are produced in several plants. Warehouse can be replenished by several plants together because of capabilities and capacities of plants. Each customer in this problem has stochastic demand and certain amount of safety stock must be maintained in warehouses so as to achieve certain customer service level. The problem is to determine number and locations of warehouses, allocation of customers demand and inventory levels of warehouses. The objective is to minimize the expected total cost with the satisfaction of desired demand weighted average customer lead time and desired cycle service level. The problem is formulated as a mixed integer nonlinear programming model. Utilizing approximation and transformation techniques, we develop an iterative heuristic method for the problem. An experiment study shows that the proposed procedure performs well in comparison with a lower bound.     

A fuzzy stochastic single-period model for cash management

The major purpose of this paper is to apply a stochastic single-period inventory management approach to analyze optimal cash management policies with fuzzy cash demand based on fuzzy integral method so that total cost is minimized. We will find that, after defuzzification, the cash-raising amounts and the total costs between the fuzzy case and the crisp case are slightly different when the variation of cash demand is small. As a result, we point out that the fuzzy stochastic single-period model is one extension of the crisp models. In any case, one may conclude that a conscientious analysis in fuzzy mathematics like that presented in this paper provides a financial decision maker with a deeper insight into the more real cash management problem.     

Real options approach-based demand forecasting method for a range of products with highly volatile and correlated demand

To achieve a competitive edge needed for marketing highly competitive products, modern enterprises have actively sought to provide the marketplace with an expansive range of products with high random volatility of demand and correlations between demands of product. Consequently, traditional forecasting methods for separately forecasting demand for these products are likely to yield significant deviations. Therefore, this study develops a real options approach-based forecasting model to accurately predict future demand for a given range of products with highly volatile and correlated demand. Additionally, this study also proposes using Monte Carlo simulation to solve the demand forecasting model. The real options approach associated with Monte Carlo simulation not only deals effectively with random variation involving a particular demand stochastic diffusion process, but can handle the correlations in product demand.     

Alleviating supplier’s capital restriction by two-order arrangement

Consider a manufacturer that offers an advance payment to pre-order a quantity that must be satisfied by the production of a supplier before actual demand arises, and can order more after demand arises. We study the effectiveness of such two-order arrangement in alleviating the supplier’s capital restriction on channel performance.     

One day ahead demand forecasting in the utility industries: Two case studies

This paper describes two case studies of short-term demand forecasting for the utilities, water and gas, linked to earlier research in similar contexts. In both cases the forecast of demand has important consequences for the operations and control of productive capacity. It is shown that in these two cases extrapolative methods based on the past data history alone are outperformed by more complex multivariate approaches that include information on the effects of weather. The paper concludes with a discussion of how an organization with an important short-term forecasting problem should go about selecting an appropriate forecasting method.     

Formation of seasonal groups and application of seasonal indices

Estimating seasonal variations in demand is a challenging task faced by many organisations. There may be many stock-keeping units (SKUs) to forecast, but often data histories are short, with very few complete seasonal cycles. It has been suggested in the literature that group seasonal indices (GSI) methods should be used to take advantage of information on similar SKUs. This paper addresses two research questions: (1) how should groups be formed in order to use the GSI methods? and (2) when should the GSI methods and the individual seasonal indices (ISI) method be used? Theoretical results are presented, showing that seasonal grouping and forecasting may be unified, based on a Mean Square Error criterion, and K-means clustering. A heuristic K-means method is presented, which is competitive with the Average Linkage method. It offers a viable alternative to a company's own grouping method or may be used with confidence if a company lacks a grouping method. The paper gives empirical findings that confirm earlier theoretical results that greater accuracy may be obtained by employing a rule that assigns the GSI method to some SKUs and the ISI method to the remainder.     

An Optimization Model to Determine Master Designs and Runs for Advertisement Printing

In this paper we consider a common optimization problem faced by a printing company while designing masters for advertisement material. A printing company may receive from various customers, advertisements for their products and services and their demand is for a specified number of copies to be printed. In a particular case, the printer receives these orders to be delivered next week from the customers, until the Thursday of a week. By Monday the printed copies have to be delivered to the customers. These advertisement items of the various customers are to be printed on large sheets of papers of specified standard sizes. The size is called a k-up if k items can be printed on one sheet. It is a given constraint that only items of the same size can be loaded on a master. This constraint results in a decomposition of the original problem of designing masters into many sub-problems, one for each size. The objective is to minimize the number of masters required while meeting the requirements of the customers. We formulate this optimization problem mathematically, discuss the computational issues and present some heuristic approaches for solving the problem.     

Effects of centralization on expected profits in a multi-location newsboy problem

This paper develops a single-period, single-product inventory model with several individual sources of demand. It is a multi-location problem with an opportunity for centralization. Both decentralized and centralized inventory systems are also examined to extend the Ravindram, Phillips and Solberg (RPS) model to constitute a new inventory model. Two theorems that include the results of the RPS model are proved in the new inventory model.     

信息共享程度对我国服装供应链库存成本的影响

我国服装行业库存水平近年逐渐恶化,库存问题成为该行业发展的重要瓶颈。信息共享被认为是有效解决该问题的方法之一。然而目前国内文献对我国服装行业信息共享的定量研究较为缺乏;同时国内外对信息共享的普适研究也多集中于比较共享与不共享信息的影响,鲜有文章研究信息共享程度对供应链绩效的影响。本文通过建立信息共享量化模型分析以下三种情况对服装行业供应商库存水平及成本的影响:(1)共享需求统计信息,(2)共享实时需求信息,(3)共享需求及市场信息。本文研究表明,共享实时需求信息比共享需求统计信息能有效降低供应商库存水平及成本;而额外共享市场信息,能增加供应链柔性,提高其应对市场不确定性的能力。本文研究信息共享程度对服装行业供应链的影响,旨在降低我国服装供应链高库存水平,并为我国服装企业信息化及品牌建设提供管理启示。     

Using shared sell-through data to forecast wholesaler demand in multi-echelon supply chains

Operational forecasting in supply chain management supports a variety of short-term planning decisions, such as production scheduling and inventory management. In this respect, improving short-term forecast accuracy is a way to build a more agile supply chain for manufacturing companies. Demand forecasting often relies on well-established univariate forecasting methods to extrapolate historical demand. Collaboration across the supply chain, including information sharing, is suggested in the literature to improve upon the forecast accuracy of such traditional methods. In this paper, we review empirical studies considering the use of downstream information in demand forecasting and investigate different modeling approaches and forecasting methods to incorporate such data. Where empirical findings on information sharing mainly focus on point-of-sale data in two-level supply chains, this research empirically investigates the added value of using sell-through data originating from intermediaries, next to historical demand figures, in a multi-echelon supply chain. In a case study concerning a US drug manufacturer, we evaluate different methods to incorporate this data and consider both time series methods and machine learning techniques to produce multi-step ahead weekly forecasts. The results show that the manufacturer can effectively improve its short-term forecast accuracy by integrating sell-through data into the forecasting process and provide useful insights as to the different modeling approaches used. The conclusion holds for all forecast horizons considered, though it is most pronounced for one-step ahead forecasts. Therefore, our research provides a clear incentive for manufacturers to assess the forecast accuracy that can be achieved by using sell-through data.     

Incorporating one-way substitution policy into the newsboy problem with imprecise customer demand

This paper presents an approach for solving an inventory model for single-period products with maximizing its expected profit in a fuzzy environment, in which the retailer has the opportunity for substitution. Though various structures of substitution arise in real life, in this study we consider the fuzzy model for two-item with one-way substitution policy. This one-way substitutability is reasonable when the products can be stored according to certain attribute levels such as quality, brand or package size. Again, to describe uncertainty usually probability density functions are being used. However, there are many situations in real world that utilize knowledge-based information to describe the uncertainty. The objective of this study is to provide an analysis of single-period inventory model in a fuzzy environment that enables us to compute the expected resultant profit under substitution. An efficient numerical search procedure is provided to identify the optimal order quantities, in which the utilization of imprecise demand and the use of one-way substitution policy increase the average expected profit. The benefit of product substitution is illustrated through numerical example.