Revisiting rescheduling: MRP nervousness and the bullwhip effect

We study the material requirement planning (MRP) system nervousness problem from a dynamic, stochastic and economic perspective in a two-echelon supply chain under first order auto-regressive demand. MRP nervousness is an effect where the future order forecasts, given to suppliers so that they may plan production and organize their affairs, exhibits extreme period-to-period variability. We develop a measure of nervousness that weights future forecast errors geometrically over time. Near-term forecast errors are weighted higher than distant forecast errors. Focusing on replenishment policies for high volume items, we investigate two methods of generating order call-offs and two methods of creating order forecasts. For order call-offs, we consider the traditional order-up-to (OUT) policy and the proportional OUT policy (POUT). For order forecasts, we study both minimum mean square error (MMSE) forecasts of the demand process and MMSE forecasts coupled with a procedure that accounts for the known future influence of the POUT policy. We show that when retailers use the POUT policy and account for its predictable future behavior, they can reduce the bullwhip effect, supply chain inventory costs and the manufacturer’s MRP nervousness

Avoiding the bullwhip effect using Damped Trend forecasting and the Order-Up-To replenishment policy

We study the Damped Trend forecasting method and its bullwhip generating behaviour when used within the Order-Up-To (OUT) replenishment policy. Using z-transform transfer functions we determine complete stability criteria for the Damped Trend forecasting method. We show that this forecasting mechanism is stable for a much larger proportion of the parametrical space than is generally acknowledged in the literature. We provide a new proof to the known fact that the Naïve, Exponential Smoothing and Holts Method forecasting, when used inside the OUT policy, will always generate bullwhip for every possible demand process, for any lead-time. Further, we demonstrate the Damped Trend OUT system behaves differently. Sometimes it will generate bullwhip and sometimes it will not. Bullwhip avoidance occurs when demand is dominated by low frequency harmonics in some instances. In other instances bullwhip avoidance happens when demand is dominated by high frequency harmonics. We derive sufficient conditions for when bullwhip will definitely be generated and necessary conditions for when bullwhip may be avoided. We verify our analytical findings with a numerical investigation

The impact of product returns and remanufacturing uncertainties on the dynamic performance of a multi-echelon closed-loop supply chain

We investigate a three-echelon manufacturing and remanufacturing closed-loop supply chain (CLSC) constituting of a retailer, a manufacturer and a supplier. Each echelon, apart from its usual operations in the forward SC (FSC), has its own reverse logistics (RL) operations. We assume that RL information is transparent to the FSC, and the same replenishment policies are used throughout the supply chain. We focus on the impact on dynamic performance of uncertainties in the return yield, RL lead time and the product consumption lead time. Two outcomes are studied: order rate and serviceable inventory. The results suggest that higher return yield improves dynamic performance in terms of overshoot and risk of stock-out with a unit step response as input. However, when the return yield reaches a certain level, the classic bullwhip propagation normally associated with the FSC does not always hold. The longer remanufacturing and product consumption lead times result in a higher overshoot and a longer time to recover inventory, as well as more oscillation in the step response at the upstream echelons. We also study bullwhip and inventory variance when demand is a random variable. Our analysis suggests that higher return yield contributes to reduced bullwhip and inventory variance at the echelon level but for the CLSC as a whole the level of bullwhip may decrease as well as increase as it propagates along the supply chain. The reason for such behaviour is due to the interaction of the various model parameters and should be the subject of further analytical research. Furthermore, by studying the three-echelon CLSC, we produce a general equation for eliminating inventory offsets in an n-echelon CLSC. This is helpful to managers who wish to maintain inventory service levels in multi-echelon CLSCs

The inventory performance of forecasting methods::evidence from the M3-competition data

Forecasting competitions have been a major drive not only for improving the performance of forecasting methods but also for the development of new forecasting approaches. Despite the tremendous value and impact of these competitions, they suffer from the limitation is that performance is measured only in terms of forecast accuracy and bias, lacking utility metrics. Using the monthly industry series of the M3-competition, we empirically explore the inventory performance of widely used forecasting techniques, including exponential smoothing, ARIMA models, Theta method and approaches based on multiple temporal aggregation. We employ a rolling simulation approach and analyse the results for the order-up-to policy under various lead times. We find that methods based on combinations result in superior inventory performance, while Na¨ıve, Holt and Holt-Winters perform poorly

Mitigating variance amplification under stochastic lead-time: the proportional control approach

Logistic volatility is a significant contributor to supply chain inefficiency. In this paper we investigate the amplification of order and inventory fluctuations in a state-space supply chain model with stochastic lead-time, general auto-correlated demand and a proportional order-up-to replenishment policy. We identify the exact distribution functions of the orders and the inventory levels. We give conditions for the ability of proportional control mechanism to simultaneously reduce inventory and order variances. For AR(2) and ARMA(1,1) demand, we show that both variances can be lowered together under the proportional order-up-to policy. Simulation with real demand and lead-time data also confirms a cost benefit exists

A unified theory of the dynamics of closed-loop supply chains

We investigate the dynamics of a closed-loop supply chain with first-order auto-regressive (AR(1)) demand and return processes. We assume these two processes are cross-correlated. The remanufacturing process is subject to a random triage yield. Remanufactured products are considered as-goodas- new and used to partially satisfy market demand; newly manufactured products make up the remainder. We derive the optimal linear policy in our closed-loop supply chain setting to minimise the manufacturer’s inventory costs. We show that the lead-time paradox can emerge in many cases. In particular, the auto- and cross-correlation parameters and variances of the error terms in the demand and the returns, as well as the remanufacturing lead time, all influence the existence of the lead-time paradox. Finally, we propose managerial recommendations for manufacturers

The impact of information sharing, random yield, correlation, and lead times in closed loop supply chains

We investigate the impact of advance notice of product returns on the performance of a decentralised closed loop supply chain. The market demands and the product returns are stochastic and are correlated with each other. The returned products are converted into “as-good-as-new” products and used, together with new products, to satisfy the market demand. The remanufacturing process takes time and is subject to a random yield. We investigate the benefit of the manufacturer obtaining advance notice of product returns from the remanufacturer. We demonstrate that lead times, random yields and the parameters describing the returns play a significant role in the benefit of the advance notice scheme. Our mathematical results offer insights into the benefits of lead time reduction and the adoption of information sharing schemes

Avoiding the capacity cost trap: Three means of smoothing under cyclical production planning

Companies tend to set their master production schedule weekly, even when producing and shipping on a daily basis—the term for this is staggered deliveries. This practice is common even when there is no marginal cost of setting a new schedule. We argue that the practice is sound for companies that use the ubiquitous order-up-to (OUT) policy to control production of products with a significant capacity cost. Under these conditions, the length of the order cycle (time between schedule updates) has a damping effect on production, while a unit (daily) order cycle can cause significant capacity costs. We call this the capacity cost trap. Developing an analytical model based on industrial evidence, we derive capacity and inventory costs under the staggered OUT policy, showing that for this policy there is an optimal order cycle possibly greater than unity. To improve on this solution, we consider three approaches to smoothing: either levelling within the cycle, deferring excess production or idling to future cycles via a proportional OUT policy, or increasing the length of the cycle. By deriving exact cost expressions we compare these approaches, finding that smoothing by employing the proportional OUT policy is sufficient to avoid the capacity cost trap

Exploring the oscillatory dynamics of a forbidden returns inventory system

We present an analytical investigation of the intrinsic oscillations in a nonlinear inventory system where excessive inventory cannot be returned to the supplier. Mathematically this is captured by a non-negative constraint on the replenishment order. By studying the eigenvalues of the characteristic matrices of the system, the criteria for different types of dynamic behaviour (including convergence, periodicity, quasi-periodicity, chaos, and divergence) are derived. The upper and lower bounds of the order and inventory oscillations are found via a time-domain analysis. Our results are verified by bifurcation diagrams. We find that the closer the replenishment rule feedback parameters are to the convergence area, the milder the intrinsic oscillation of the system