A smoothing replenishment policy with endogenous lead times.

We consider a two echelon supply chain consisting of a single retailer and a single manufacturer. Inventory control policies at the retailer level often transmit customer demand variability to the manufacturer, sometimes even in an amplified form (known as the bullwhip effect). When the manufacturer produces in a make-to-order fashion though, he prefers a smooth order pattern. But dampening the variability in orders inflates the retailer's safety stock due to the increased variance of the retailers inventory levels. We can turn this issue of conflicting objectives into a win-win situation for both supply chain echelons when we treat the lead time as an endogenous variable. A less variable order pattern generates shorter and less variable (production/replenishment) lead times, introducing a compensating effect on the retailer's safety stock. We show that by including endogenous lead times, the order pattern can be smoothed to a considerable extent without increasing stock levels.Bullwhip effect; Demand; endogenous lead times; Fashion; Inventory; Inventory control; Markov processes; Order; Policy; Queueing; Research; Safety stock; Smoothing; Supply chain; Supply chain management; Time; Variability; Variance;

The value of coordination in a two echelon supply chain: Sharing information, policies and parameters.

We study a coordination scheme in a two echelon supply chain. It involves sharing details of replenishment rules, lead-times, demand patterns and tuning the replenishment rules to exploit the supply chain's cost structure. We examine four different coordination strategies; naïve operation, local optimisation, global optimisation and altruistic behaviour on behalf of the retailer. We assume the retailer and the manufacturer use the Order-Up-To policy to determine replenishment orders and end consumers demand is a stationary i.i.d. random variable. We derive the variance of the retailer's order rate and inventory levels and the variance of the manufacturer's order rate and inventory levels. We initially assume that costs in the supply chain are directly proportional to these variances (and later the standard deviations) and investigate the options available to the supply chain members for minimising costs. Our results show that if the retailer takes responsibility for supply chain cost reduction and acts altruistically by dampening his order variability, then the performance enhancement is robust to both the actual costs in the supply chain and to a naïve or uncooperative manufacturer. Superior performance is achievable if firms coordinate their actions and if they find ways to re-allocate the supply chain gain.Bullwhip; Global optimisation; Inventory variance; Local optimisation; Supply chains; Studies; Coordination; Supply chain; IT; Replenishment rule; Rules; Demand; Patterns; Cost; Structure; Strategy; Retailer; Policy; Order; Variance; Inventory; Costs; Options; Variability; Performance; Performance enhancement; Firms;

Smooth is smart: bullwhip, inventory, fill-rates and the golden ratio.

Inventory;

Dampening variability by using smoothing replenishment rules.

A major cause of supply chain deficiencies is the bullwhip effect which can be substantial even over a single echelon. This effect refers to the tendency of the variance of the replenishment orders to increase as it moves up a supply chain. Supply chain managers experience this variance amplification in both inventory levels and replenishment orders. As a result, companies face shortages or bloated inventories, run-away transportation and warehousing costs and major production adjustment costs. In this article we analyse a major cause of the bullwhip effect and suggest a remedy. We focus on a smoothing replenishment rule that is able to reduce the bullwhip effect across a single echelon. In general, dampening variability in orders may have a negative impact on customer service due to inventory variance increases. We therefore quantify the variance of the net stock and compute the required safety stock as a function of the smoothing required. Our analysis shows that bullwhip can be satisfactorily managed without unduly increasing stock levels to maintain target fill rates.Bullwhip effect; Companies; Cost; Costs; Impact; Inventory; Managers; Order; Replenishment rule; Rules; Safety stock; Supply chain; Supply chain management; Variability; Variance; Variance reduction;

Revisiting activity sampling: A fresh look at binomial proportion confidence intervals

This is the author accepted manuscript. The final version is available from Inderscience via the DOI in this recordThe Wald interval is typically used to assign confidence to the accuracy of activity sampling studies. It is known the performance of the Wald interval is poor, especially when the observed probability is near zero or one. The suitability of the Wald interval for activity sampling is not often discussed in the operations management literature; if it is, this is usually followed by inappropriate and incorrect advice. Herein, a range of alternative binominal confidence intervals for activity sampling is reviewed. A number of selection criteria are considered including achievement of the target nominal coverage probability, size of the interval, and ease of use and presentation. It is recommended that the Clopper-Pearson interval is used for activity sampling. A table of confidence intervals and sample sizes that is specifically designed to be used within a new activity sampling procedure based on the Clopper-Pearson interval is developed. Finally, pedagogical issues are considered

The bullwhip effect: Progress, trends and directions

This is the final version. Available on open access from Elsevier via the DOI in this recordThe bullwhip effect refers to the phenomenon where order variability increases as the orders move upstream in the supply chain. This paper provides a review of the bullwhip literature which adopts empirical, experimental and analytical methodologies. Early econometric evidence of bullwhip is highlighted. Findings from empirical and experimental research are compared with analytical and simulation results. Assumptions and approximations for modelling the bullwhip effect in terms of demand, forecast, delay, replenishment policy, and coordination strategy are considered. We identify recent research trends and future research directions concerned with supply chain structure, product type, price, competition and sustainability

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

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordLogistic 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

Revisiting rescheduling: MRP nervousness and the bullwhip effect

This is the author accepted manuscript. The final version is available from Taylor & Francis via the DOI in this recordWe study the material requirements 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 organise 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 behaviour, they can reduce the bullwhip effect, supply chain inventory costs and the manufacturer’s MRP nervousness

Inventory performance under staggered deliveries and autocorrelated demand

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordProduction plans often span a whole week or month, even when independent production lots are completed every day and service performance is tallied daily. Such policies are said to use staggered deliveries, meaning that the production rate for multiple days are determined at a single point in time. Assuming autocorrelated demand, and linear inventory holding and backlog costs, we identify the optimal replenishment policy for order cycles of length P. With the addition of a once-per-cycle audit cost, we optimize the order cycle length P∗ via an inverse-function approach. In addition, we characterize periodic inventory costs, availability, and fill rate. As a consequence of staggering deliveries, the inventory level becomes cyclically heteroskedastic. This manifests itself as ripples in the expected cost and service levels. Nevertheless, the cost-optimal replenishment policy achieves a constant availability by using time-varying safety stocks; this is not the case with suboptimal constant safety stock policies, where the availability fluctuates over the cycle