Demand Autocorrelation Research Articles

Supply chain cash-flow bullwhip effect: An analytical model for working capital variance propagation

This research article probes the cash-flow bullwhip effect (CFB), a phenomenon precipitating an increase in the fluctuations of working capital within supply chains. A novel analytical model is proposed to delve into the CFB within a multi-echelon, serial supply chain, taking factors into account, such as demand autocorrelation, procurement lead time, and payment lead times. Our study implies that extended procurement lead times contribute to a heightened CFB, and a substantial discrepancy between a firm’s payment lead time and that of its customers results in a more pronounced CFB. Importantly, adopting shorter payment lead times for customers and extending them for suppliers can inflate the cash-flow bullwhip for all three constituent entities: the echelon, its customers, and suppliers. Our quantitative analysis reveals that strategies, such as payment batching and divulging end-customer demand information can mitigate the cash-flow bullwhip by as much as 49.5 and 53.7%, respectively. Empirical inspection of the CFB experienced by a sample of 786 companies from 2010 to 2019 demonstrates that ∼65% of these companies intensify their working capital variance. This underscores the need for cautious management of working capital variance and the adoption of suitable inventory and payment strategies to forestall financial turmoil within the supply chain.

Supply chain cash-flow bullwhip effect: An empirical investigation

The cashflow bullwhip effect (CFB) is the amplification of working capital variance along a supply chain, analogous to the bullwhip effect (BWE) for order variance. High CFB is an indication of inefficiency in working capital management. This study investigates the occurrence of CFB and BWE in a sample of 763 U.S. public companies from 2010 to 2019. The results indicate that CFB is experienced by 37% of retailing, 43% of wholesaling, and 81% of manufacturing firms. Additionally, firms with conservative payment policies have smaller CFB and BWE, while high liquidity ratios are associated with smaller BWE. Predictability in demand seasonality is linked with smaller CFB and BWE, while high lead time is associated with larger CFB and BWE. Higher demand autocorrelation is associated with larger BWE. This new knowledge on the associations between CFB and BWE with firm attributes can help inform important decisions, including those made at the firm, industry, or government policy level.

Adoption of blockchain technology in a two-stage supply chain: Spillover effect on workforce

Although blockchain technology (BCT) has been applied to supply chain practices, the theoretical understanding of its impact is limited. Motivated by the practice of an apparel supply chain, we study the application of BCT in a supply chain model to enable the effective and efficient implementation of trade credit (called “smart credit”) and demand information transparency. In this model, a retailer (“she”) and a supplier (“he”) manage their own inventories to satisfy autocorrelated customer demands and fill downstream orders during a planning horizon; the supplier strategically plans the number of full-time workers for manufacturing workforce consumption before the horizon begins. By analyzing this model, we try to address BCT’s operational value to supply chain firms and the spillover effect on the supply chain workforce. The spillover effect is expected to be negative because the BCT will replace human workers. We find that BCT’s operational value to the retailer is positive because the smart credit benefits her; however, the value to the supplier may not be positive because the smart credit hurts him and information transparency improves. The condition for a positive value depends on the type of demand autocorrelation: when the demands are positively correlated, the condition is simple, namely, the autocorrelation coefficient is higher than a threshold; when the demands are negatively correlated, the condition becomes complicated. BCT’s spillover effect on the supply chain workforce also differs according to the type of demand autocorrelation. Contrary to intuition, we find that the spillover effect can be positive (i.e., more full-time workers are hired) when demand is negatively correlated. The underlying reason is that the supplier updates his manufacturing process under BCT and this updated process’ variability can be amplified when the demands are negatively correlated; this leads the supplier to hire more full-time workers to hedge against the increasing uncertainties in the manufacturing workforce consumption. Finally, we conduct a numerical study based on a dataset collected from the apparel supply chain to provide more managerial insights.

Forecasting of lead-time demand variance: Implications for safety stock calculations

Lead-time demand forecasting constitutes the backbone of inventory control. Although there has been a considerable amount of research on forecasting the mean lead-time demand, less has centered around forecasting lead-time demand variance, especially in the case of stochastic lead-times. This represents an important gap in the literature, given that safety stock calculations rely explicitly on the lead-time demand variance (or equivalently the variance of the lead-time demand forecast error for unbiased estimators). We bridge this gap by exploring the viability of three strategies to estimate the variance of the lead-time demand forecast error under stochastic lead-times: (1) aggregating the per period variance of forecast errors over the lead-time, which is the classical approach; (2) considering the variance of the aggregated (over the lead-time) forecast error; (3) considering the variance of the forecast errors resulting from temporally aggregated (over the lead-time length) demand. Analytical results are derived for a first order autoregressive moving average ARMA(1,1) demand process for both a single exponential smoothing and the minimum mean squared error forecasting method. A numerical investigation assesses the effects of demand autocorrelation and lead-time variability on the accuracy of each strategy, and the conditions under which one outperforms the others. The results show that the classical strategy presented in textbooks appears to be the least accurate one, except for cases with a high negative demand autocorrelation. An analysis of the inventory control performance also reveals that the classical strategy often leads to higher inventory costs and lower service levels for positive autocorrelation.

The impact of stochastic lead times on the bullwhip effect under correlated demand and moving average forecasts

We quantify the bullwhip effect (which measures how the variance of replenishment orders is amplified as the orders move up the supply chain) when both random demands and random lead times are estimated using the industrially popular moving average forecasting method. We assume that the lead times constitute a sequence of independent identically distributed random variables and the correlated demands are described by a first-order autoregressive process. We obtain an expression that reveals the impact of demand and lead time forecasting on the bullwhip effect. We draw a number of conclusions on the bullwhip behaviour with respect to the demand auto-correlation and the number of past lead times and demands used in the forecasts. We find maxima and minima in the bullwhip measure as a function of the demand auto-correlation.

The value of Vendor Managed Inventory in an autocorrelated demand environment

The Vendor Managed Inventory (VMI) is a coordination mechanism that aims to improve supply chain performance. This paper investigates a two-echelon supply chain composed of one manufacturer and one retailer. It studies the value of VMI where customer demand follows a first-order autoregressive process (AR(1)). Based on an analytical model from prior literature, we demonstrate that for some replenishment frequency ranges, the value of VMI decreases when the demand autocorrelation is very high, which is different from earlier results. The research findings are helpful for managers considering autocorrelated demand products.

Fill rate in a periodic review order-up-to policy under auto-correlated normally distributed, possibly negative, demand

We investigate the inventory service metric known as the fill rate—the proportion of demand that is immediately fulfilled from inventory. The task of finding analytical solutions for general cases is complicated by a range of factors including; correlation in demand, double counting of backlogs, and proper treatment of negative demand. In the literature, two approximate approaches are often proposed. Our contribution is to present a new fill rate measure for normally distributed, auto-correlated, and possibly negative demand. We treat negative demand as returns. Our approach also accounts for accumulated backlogs. The problem reduces to identifying the minimum of correlated normally distributed bivariate random variables. There exists an exact solution, but it has no closed form. However, the solution is amenable to numerical techniques, and we present a custom Microsoft Excel function for practical use. Numerical investigations reveal that the new fill rate is more robust than previous measures. Existing fill rate measures are likely to cause excessive inventory investment, especially when fill rate targets are modest, a strongly positive or negative autocorrelation in demand is present, or negative demands exist. Our fill rate calculation ensures that the target fill rate is achieved without excessive inventory investments.

The Pricing of a Supply Contract under Uncertainty with Long-Range Dependence

This paper aims to address a contracting problem between upstream and downstream agents in a supply chain using a stochastic demand process with autocorrelation properties. For example, the quarterly global sales volumes of Apple's iPhone are highly autocorrelated over time although the time lag is as long as 10 quarters. Based on such empirical evidence, an autocorrelated demand process referred to as fractional Brownian motion is adopted in this paper. It is assumed that there are two echelons in the supply chain: business and consumer markets. The information flows fall into four categories: demand flow, marketing info flow, uncertainty flow, and premium charge flow. The downstream agent can transfer demand uncertainty to the upstream firm (uncertainty flow) by signing a supply contract (contracting agent). The demand in the consumer market is assumed to follow a fractional Brownian motion. Based on the fractional Ito formula for the real option model, the result demonstrates that the real option value can be an increasing or decreasing function of the degree of autocorrelation in which the real option value reaches its maximum at the critical point. As a consequence, the trading price determined in the supply contract without considering the autocorrelation of demand could be significantly undervalued or overvalued. In other words, to ensure a fair game in a contracting activity, the upstream agent should charge more for the trading price depending on the degree of autocorrelation in demand.

Coordinating lead times and safety stocks under autocorrelated demand

We consider a supply chain in which orders and lead times are linked endogenously, as opposed to assuming lead times are exogenous. This assumption is relevant when a retailer’s orders are produced by a supplier with finite capacity and replenished when the order is completed. The retailer faces demands that are correlated over time – either positively or negatively – which may, for example, be induced by a pricing or promotion policy. The auto-correlation in demand affects the order stream placed by the retailer onto the supplier, and this in turn influences the resulting lead times seen by the retailer. Since these lead times also determine the retailer’s orders and its safety stocks (which the retailer must set to cover lead time demand), there is a mutual dependency between orders and lead times. The inclusion of endogenous lead times and autocorrelated demand represents a better fit with real-life situations. However, it poses some additional methodological issues, compared to assuming exogenous lead times or stationary demand processes that are independent over time. By means of a Markov chain analysis and matrix analytic methods, we develop a procedure to determine the distribution of lead times and inventories, that takes into account the correlation between orders and lead times. Our analysis shows that negative autocorrelation in demand, although more erratic, improves both lead time and inventory performance relative to IID demand. Positive correlation makes matters worse than IID demand. Due to the endogeneity of lead times, these effects are much more pronounced and substantial error may be incurred if this endogeneity is ignored.

Analysis of compound bullwhip effect causes

This research investigates compound causes of the bullwhip effect (BWE) by considering an inventory system with multiple price-sensitive demand streams. Joint price and demand dynamics are captured by a vector time-series process that incorporates the stochastic co-movements in price and demand. We study two BWE measures, one for each demand stream individually and one for the aggregated demand. We show that demand parameters including demand autocorrelation, cross-correlation, and price sensitivity serve as root causes of the BWE. We prove that the impact of these parameters on the BWE can be additively decomposed. Conditions are established under which a pair of simultaneous compound causes may attenuate or dampen the BWE. When demand streams are aggregated, we derive a pooling factor that quantifies the impact of demand aggregation on order stability. When positive, the pooling factor corresponds to a synergy effect that captures the gain in the stability of the pooled orders. Conditions for the existence of the synergy effect are obtained for several special cases involving a zero leadtime. We also discuss how our analytical findings can be managerially applied to bullwhip mitigation strategies.

Allocation of Cost Savings in a Three-Level Supply Chain with Demand Information Sharing: A Cooperative-Game Approach

We analyze the problem of allocating cost savings from sharing demand information in a three-level supply chain with a manufacturer, a distributor, and a retailer. To find a unique allocation scheme, we use concepts from cooperative game theory. First, we analytically compute the expected cost incurred by the manufacturer and then use simulation to obtain expected costs for the distributor and the retailer. We construct a three-person cooperative game in characteristic-function form and derive necessary conditions for the stability of each of five possible coalitions. To divide the cost savings between two members, or among three supply chain members, we use various allocation schemes. We present numerical analyses to investigate the impacts of the demand autocorrelation coefficient, ρ, and the unit holding and shortage costs on the allocation scheme.

Inventory control under temporal demand heteroscedasticity

This paper studies an inventory control problem when the variance of demand is time-varying and exhibits temporal heteroscedasticity. We use a first-order autoregressive process to characterize the dynamic changes in the level of demand over time and a GARCH(1, 1) structure to describe the changes in the variance of demand. Under these demand settings, we quantify the effect of a temporal heterogeneous variance on inventory performance for a system controlled via an order-up-to-level policy. We show that the effect of temporal heteroscedasticity on the forecasting accuracy can be additively decomposed from the total forecasting error variance. The decomposition is used to derive the absolute and relative cost deviations when the temporal heteroscedasticity is ignored. The relationship of these cost deviations to demand autocorrelation and replenishment leadtime is investigated. Computational results show that ignoring temporal heteroscedasticity can increase firm’s inventory costs by as much as 30% when demand autocorrelation is highly positive.

Push, pull, or hybrid control in supply chain management

In this paper, a model of a supply chain system is constructed, and a mathematical model of three control mechanisms, push and pull controls, and a hybrid control of both controls, is formulated. For the three control mechanisms, the variance of processing quantities at each process and the variance of inventory levels at each inventory station are analysed as performance measures. The effects of the number of branches in each stage, the lead time of each transportation process, and the autocorrelation of demand, are numerically investigated. In addition, by comparing the totals of the variances for the three control mechanisms, it is identified and presented that the hybrid control is superior to the others.

The effect of autocorrelated demand in JIT production systems

As a system of production planning and inventory control for multi-stage production inventory systems, this paper deals with the Kanban system in the just-intime (JIT) concept. In this paper, the autocorrelation of demand is considered as an important factor affecting the performance of the Kanban system. Mathematical models of a Kanban system and its modified system are developed as sequential and concurrent ordering systems, respectively. By means of simulation experiments, the effects of the autocorrelation of demand upon the performances of the systems are investigated and compared with each other. Based on the results, the procedure to design a system of production planning and inventory control is shown.

Safety Stock Determination with Serially Correlated Demand in a Periodic-Review Inventory System

We consider a periodic-review inventory replenishment model with an order-up-to-R operating doctrine for the case of deterministic lead times and a covariance-stationary stochastic demand process. A method is derived for setting the inventory safety stock to achieve an exact desired stockout probability when the autocovariance function for Gaussian demand is known. Because the method does not require that parametric time-series models be fit to the data, it is easily implemented in practice. Moreover, the method is shown to be asymptotically valid when the autocovariance function of demand is estimated from historical data. The effects on the stockout rate of various levels of autocorrelated demand are demonstrated for situations in which autocorrelation in demand goes undetected or is ignored by the inventory manager. Similarly, the changes to the required level of safety stock are demonstrated for varying levels of autocorrelation.

An Experimental Comparison of MRP Purchase Discount Methods

This paper addresses the managerial issue of how best to order purchased materials in MRP environments when discounts are available from vendors. The least unit cost, least period cost, McLaren's order moment, revised part-period balancing, incremental part-period balancing, traditional discount order quantity, and an optimal algorithm are experimentally investigated under a variety of simulated scenarios. Other experimental factors include the coefficient of variation in demand, forecast uncertainty beyond the current period, the average time between orders, the ratio of the discount quantity to the EOQ, the attractiveness of the discount, the length of the planning horizon, inventory holding costs, and the autocorrelation of demand. All factors tested in this comprehensive experiment significantly affected the performance of the discount ordering procedures. Furthermore, the results from this study suggest that the least unit cost, McLaren's order moment, the traditional discount order quantity, and the optimal procedures significantly out-perform the others. A further choice among these alternative methods was found to be a function of the operating environment and limitations that may exist on available computing time.