Inventory management for stochastic lead times with order crossovers

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordWe study the impact of stochastic lead times with order crossover on inventory costs and safety stocks in the order-up-to (OUT) policy. To motivate our research we present global logistics data which violates the traditional assumption that lead time demand is normally distributed. We also observe that order crossover is a common and important phenomenon in real supply chains. We present a new method for determining the distribution of the number of open orders. Using this method we identify the distribution of inventory levels when orders and the work-in-process are correlated. This correlation is present when demand is auto-correlated, demand forecasts are generated with non-optimal methods, or when certain ordering policies are present. Our method allows us to obtain exact safety stock requirements for the so-called proportional order-up-to (POUT) policy, a popular, implementable, linear generalization of the OUT policy. We highlight that the OUT replenishment policy is not cost optimal in global supply chains, as we are able to demonstrate the POUT policy always outperforms it under order cross-over. We show that unlike the constant lead-time case, minimum safety stocks and minimal inventory variance do not always lead to minimum costs under stochastic lead-times with order crossover. We also highlight an interesting side effect of minimizing inventory costs under stochastic lead times with order crossover with the POUT policy - an often significant reduction in the order variance

Inventory management for stochastic lead times with order crossovers

We study the impact of stochastic lead times with order crossover on inventory costs and safety stocks in the order-up-to (OUT) policy. To motivate our research we present global logistics data which violates the traditional assumption that lead time demand is normally distributed. We also observe that order crossover is a common and important phenomenon in real supply chains. We present a new method for determining the distribution of the number of open orders. Using this method we identify the distribution of inventory levels when orders and the work-in-process are correlated. This correlation is present when demand is auto-correlated, demand forecasts are generated with non-optimal methods, or when certain ordering policies are present. Our method allows us to obtain exact safety stock requirements for the so-called proportional order-up-to (POUT) policy, a popular, implementable, linear generalization of the OUT policy. We highlight that the OUT replenishment policy is not cost optimal in global supply chains, as we are able to demonstrate the POUT policy always outperforms it under order cross-over. We show that unlike the constant lead-time case, minimum safety stocks and minimal inventory variance do not always lead to minimum costs under stochastic lead-times with order crossover. We also highlight an interesting side effect of minimizing inventory costs under stochastic lead times with order crossover with the POUT policy—an often significant reduction in the order variance

Inventory control with seasonality of lead times

The practical challenges posed by the seasonality of lead times have largely been ignored within the inventory control literature. The length of the seasons, as well as the length of the lead times during a season, may demonstrate cyclical patterns over time. This study examines whether inventory control policies that anticipate seasonal lead-time patterns can reduce costs. We design a framework for characterizing different seasonal lead-time inventory problems. Subsequently, we examine the effect of deterministic and stochastic seasonal lead times within periodic review inventory control systems. We conduct a base case analysis of a deterministic system, enabling two established and alternating lead-time lengths that remain valid through known intervals. We identify essential building blocks for developing solutions to seasonal lead-time problems. Lastly, we perform numerical experiments to evaluate the cost benefits of implementing an inventory control policy that incorporates seasonal lead-time lengths. The findings of the study indicate the potential for cost improvements. By incorporating seasonality in length of seasons and length of lead times within the season into the control models, inventory controllers can make more informed decisions when ordering their raw materials. They need smaller buffers against lead-time variations due to the cyclical nature of seasonality. Reductions in costs in our experiments range on average between 18.9 and 26.4% (depending on safety time and the probability of the occurrence of stock out). Therefore, inventory control methods that incorporate seasonality instead of applying large safety stock or safety time buffers can lead to substantial cost reductions

The impact of stochastic lead times on the bullwhip effect – An empirical insight

In this article, we review the research state of the bullwhip effect in supply chains with stochastic lead times. We analyze problems arising in a supply chain when lead times are not deterministic. Using real data from a supply chain, we confirm that lead times are stochastic and can be modeled by a sequence of independent identically distributed random variables. This underlines the need to further study supply chains with stochastic lead times and model the behavior of such chains

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

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordWe 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.National Science Centr

Modeling Stochastic Lead Times in Multi-Echelon Systems

In many multi-echelon inventory systems, the lead times are random variables. A common and reasonable assumption in most models is that replenishment orders do not cross, which implies that successive lead times are correlated. However, the process that generates such lead times is usually not well defined, which is especially a problem for simulation modeling. In this paper, we use results from queuing theory to define a set of simple lead time processes guaranteeing that (a) orders do not cross and (b) prespecified means and variances of all lead times in the multiechelon system are attained

On the Dynamics of Closed-Loop Supply Chains under Remanufacturing Lead Time Variability

Remanufacturing practices in closed-loop supply chains (CLSCs) are often characterised by highly variable lead times due to the uncertain quality of returns. However, the impact of such variability on the dynamic benefits derived from adopting circular economy models remains largely unknown in the closed-loop literature. To fill the gap, this work analyses the Bullwhip and inventory performance of a multi-echelon CLSC with variable remanufacturing lead times under different scenarios of return rate and information transparency in the remanufacturing process. Our results reveal that ignoring such variability generally leads to an overestimation of the dynamic performance of CLSCs. We observe that enabling information transparency generally reduces order and inventory variability, but it may have negative effects on average inventory if the duration of the remanufacturing process is highly variable. Our findings result in useful and innovative recommendations for companies wishing to mitigate the negative consequences of lead time variability in CLSCs

A Stochastic Product Priority Optimization Method for Remanufacturing System Based on Genetic Algorithm

Increasing number of manufacturers are developing remanufacturing facilities to recover end-of-life products for product/component reuse and material recycling while the high uncertainty pattern of returned products complicates the production planning. In this thesis a stochastic production priority optimization method, considering various priority concerns for remanufacturing systems is developed. Priority ranking and matching algorithm is developed to determine the priority rule, using thirteen weighting factors. Queueing models are developed to formulate the objective function, a genetic algorithm is then developed to search optimal solution under different business configurations. Result of this research will provide insights to priority assignment mechanism, which in turn provides support to manufacturers in decision-making in production planning thus improving the performance of remanufacturing systems