Replenishment Point Research Articles

Prediction of Intermittent Demand Occurrence using Machine Learning

Demand forecasting plays a pivotal role in modern Supply Chain Management (SCM). It is an essential part of inventory planning and management and can be challenging at times. One of the major issues being faced in demand forecasting is insufficient forecast accuracy to predict the expected demand and fluctuation in actual vs. the predicted demand results in fore-casting errors. This problem is further exaggerated with slow-moving and intermittent demand items. Every organization encounters large proportions of items that have small ir-regular demand with long periods of zero demand, which are known as intermittent demand Items. Demand for such items occur sporadically and with considerable fluctuation in the size of the demand. Forecasting of the intermittent demand entails the prediction of demand series that is characterized by the time interval between demand being significantly greater than the unit forecast period. Because of this there are multiple periods of no demand in the intermittent demand time series. The challenge with these products with low irregular demand is that these items need to be stocked and replenished at regular interval irrespective of the demand cycle, thus adding to the cost of holding the inventory. Since the demand is not continuous, Traditional Forecasting models are unable to provide reliable estimate of required inventory level and replenishment point. Forecast errors would resulting in obsolescent stock or unfulfilled demand. The current paper presents a simple yet powerful approach for generating a demand forecasting and replenishment process for such low volume intermittent demand items to come up with a recommendation for dynamic re-order point, thus, improving the inventory performance of these items. Currently, the demand forecast is generally based on past usage patterns. The rise of Artificial Intelligence/Machine Learning (AI/ML) has provided a strong alternative to solve the problem of forecasting Intermittent Demand. The intention is to highlight that machine learning algorithm is more efficient and accurate than traditional forecasting method. As we move forward to industry 4.0, the digital supply chain is considered as the most essential com-ponent of the value chain wherein the inventory size is controlled, and the demand predicted.

Optimal Allocation of Water Reservoirs for Sustainable Wildfire Prevention Planning via AHP-TOPSIS and Forest Road Network Analysis

The sustainable management of forest ecosystems is directly linked to the management of forest fires. The increasing occurrence of wildfires has prompted the need for the establishment of infrastructure aimed at addressing them. The placement of anti-fire water reservoirs can address the lack of water intake points. This study introduces a decision support system (DSS) tailored for the optimal allocation of anti-fire water reservoirs in Mediterranean forest ecosystems, ensuring a reliable water supply for firefighting operations. The methodology integrates the analytical hierarchy process (AHP) and the technique of order of preference by similarity to ideal solutions (TOPSIS) methods, facilitating precise location determination through comprehensive criteria analysis. Additionally, the analysis of the forest road network is incorporated to optimize the placement of water reservoirs. In the forest complex of Taxiarchis, Chalkidiki, Greece, 100 potential reservoir sites were identified and prioritized based on factors such as fire risk, proximity to existing water sources, and coverage area using optimal pathways. The study’s findings demonstrate that by establishing 34 water reservoirs, firefighting forces can access a replenishment point within a 5-min travel time. The conclusions underscore the efficacy of this methodology as a valuable decision-making tool for sustainable wildfire prevention planning. This approach contributes to allocating resources judiciously, effectively mitigating the wildfire risk in Mediterranean forest ecosystems, and therefore promoting sustainability.

Simulation- optimisation approach to support management of blood components inventory

ABSTRACT Blood supply chains (BSCs) face challenges in managing the production and inventory of blood components. We developed a simulation-optimisation approach to address inventory of blood products in blood supply chains. This approach can determine inventory size and replenishment points for blood products that balances supply and demand, while maintaining acceptable levels of wastage and shortage. A simulation methodology is used to represent the complexities in the inventory management of blood components. An optimisation module, coupled with the simulation, is used to address constraints related to waste, shortages, and inventory levels. The approach was verified and validated using a case study conducted in a blood bank in Brazil managing a supply of Red Blood Cells (RBCs). The approach proved to be suitable for the case analyzed and results suggest that 120 units is adequate to meet the demand for RBCs, while maintaining acceptable levels of shortages and wastages.

Digital twin-driven real-time planning, monitoring, and controlling in food supply chains

There needs to be more clarity about when and how the digital twin approach could benefit the food supply chains. In this study, we develop and solve an integrated problem of procurement, production, and distribution strategies (PPDs) in a medium-scale food processing company. Using the digital twin approach, the model considers the industrial symbiosis opportunities between the supplier, manufacturer, and customer using interval and sequence variables operating in a constrained environment using mixed-integer linear programming (MILP) and agent-based simulation (ABS) methodology. The study optimizes the make-span and lead time, simultaneously achieving a higher level of digitalization. The analysis demonstrates how digital twin accelerates supply chain productivity by improving makespan time, data redundancy (DR), optimal scheduling plan (OSP), overall operations effectiveness (OOE), overall equipment effectiveness (OEE), and capacity utilization. Our findings provide compelling evidence that the seamless integration PPDs enormously enhance production flexibility, resulting in an excellent service level of 94 %. Managers leverage real-time simulation to accurately estimate the replenishment point with minimal lead time, ensuring optimized operations.Furthermore, our results demonstrate that implementing PPDs has yielded considerable benefits. Specifically, we observed a remarkable 65 % utilization of the pasteurizer and aging vessel and an impressive 97 % utilization of the freezer. Moreover, by applying the DT model, the present model found a notable 6 % reduction in backlog, further streamlining operations and enhancing efficiency.

A Study of a Two Storage Single Product Inventory System with Ramp Type Demand, N-Phase Prepayment and Purchase for Exigency

This model considers a two-warehouse inventory system of deteriorated items with ramp-type demand and a constant rate of deterioration. It is maintained a rental warehouse (RW) of infinite capacity to load the excess items of replenished goods after filling the items of finite capacity in the own warehouse (OW). Retailers are encouraged to opt for the prepayment option of paying their purchase cost in equal installments prior to the delivery of the ordered items with a considerable discount, which will ensure the purchase guarantee of their orders. The slotted backlog interval of the stock out period is handled in two different ways to retain the customers and ease their impatience. Customers in the first slot of the stock out period are satisfied by the emergency purchases from local suppliers with high purchasing costs to avoid losing customers. Customers in the next slot are satisfied immediately after the next replenishment point. Essential measures of the system are derived: optimal ordering quantities from both regular and local suppliers; replenishment cycle length; and a partitioned backlog interval. A numerical example is given along with the optimal solutions for a particular environment with sensitive analysis in order to validate the model’s efficacy.

Effect of Inflation and Permitted Three-Slot Payment on Two-Warehouse Inventory System with Stock-Dependent Demand and Partial Backlogging

This study examines the effect of monetary inflation for a two-warehouse single-product inventory system, in which items are stored in a limited capacity Own Warehouse (OW) and an unlimited capacity Rental Warehouse (RW). Demand for an item is considered stock dependent. Items may deteriorate at a different constant rate in both warehouses. Shortages are allowed in the stock-out period and are partially backlogged and satisfied in the next replenishment point. The supplier permits flexible payment options for the retailer to pay the amount in three equal payments at different time points. The retailers’ preferred payment option is as follows: the first payment is prior to the replenishment point with some discount; the second payment is one-third of the total purchasing cost, which is paid at the time of the replenishment epoch; and the third payment is after the replenishment point and before the start of the next cycle, with some penalty. The influence of inflation on the cost calculation is considered, and an analytic expression for optimal minimal cost is explicitly derived from this. We performed arrived sensitivity analysis to discern the effects of the inflation and backlogging rates, as well as the effects of the discount rate on purchasing cost, and the effects of penalties upon the late payment of purchasing costs in optimizing the total cost.

SHIP MOTIONS DURING REPLENISHMENT AT SEA OPERATIONS IN HEAD SEAS

During replenishment at sea operations the interaction between the two vessels travelling side by side can cause significant motions in the smaller vessel and affect the relative separation between their replenishment points. A study into these motions has been conducted including theoretical predictions and model experiments. The model tests investigated the influence of supply ship displacement and longitudinal separation on the ships’ motions. The data obtained from the experimental study has been used to validate a theoretical ship motion prediction method based on a 3-D zero-speed Green function with a forward speed correction in the frequency domain. The results were also used to estimate the expected extreme roll angle of the receiving vessel, and the relative motion between the vessels, during replenishment at sea operations in a typical irregular seaway. A significant increase in the frigate’s roll response was found to occur with an increase of the supply ship displacement, whilst a reduction in motion for the receiving vessel resulted from an increase in longitudinal separation between the vessels. It is proposed that to determine the optimal vessel separation it is vital that the motions of the vessels are not considered in isolation and all motions need to be considered for both vessels simultaneously.

Identifying optimal magnesium replenishment points based on risk of severe hypomagnesemia in colorectal cancer patients treated with cetuximab or panitumumab.

Cetuximab and panitumumab are monoclonal antibodies that target the epidermal growth factor receptor (EGFR). Treatment with cetuximab and panitumumab commonly causes hypomagnesemia, and optimal management of this adverse effect remains unclear. Here, we evaluated the optimal magnesium replacement points based on the risk of severe hypomagnesemia in colorectal cancer patients who received cetuximab or panitumumab. We retrospectively evaluated 184 patients who received cetuximab or panitumumab for colorectal cancer at Ogaki Municipal Hospital (Ogaki, Japan) between January 2010 and December 2019. Univariate analyses were conducted to evaluate the relationship between patient baseline characteristics and development of hypomagnesemia following cetuximab or panitumumab treatment. Variables that were significantly associated with hypomagnesemia in the univariate analyses as well as previously reported risk factors were entered into a multivariate logistic regression model. The incidence of hypomagnesemia was associated with panitumumab treatment, pre-replenishment serum magnesium concentration, treatment duration, and treatment line. Severe hypomagnesemia post-cetuximab or panitumumab treatment was significantly associated with low baseline magnesium concentrations (< 1.8mg/dL; odds ratio 18.100, 95% confidence interval 1.570-210.000; p = 0.020) and low serum magnesium concentrations during treatment (< 1.1mg/dL; odds ratio 93.800, 95% confidence interval 3.510-2510.000; p = 0.007). To minimize the risk of severe hypomagnesemia during anti-EGFR treatment, magnesium replenishment should be initiated in patients with pre-replenishment concentrations of < 1.8mg/dL, preferably before reaching intra-treatment concentrations of < 1.1mg/dL.

The residual time approach for (Q, r) model under perishability, general lead times, and lost sales

We consider a (Q, r) perishable inventory system with state-dependent compound Poisson demands with a random batch size, general lead times, exponential shelf times, and lost sales. We assume $$r<Q$$ and analyze the system using an embedded Markov process at the replenishment points. Using the queueing and Markov chain decomposition approach, we characterize the distribution of the residual lead time and derive the stationary distribution of the inventory level. We construct closed-form expressions for the expected total long-run average cost function. The closed form allows us to efficiently obtain, numerically, the optimal Q and r parameters. Numerical study provides several guidelines for the optimal control. For example, we show that approximating the lead time distribution by an exponential one only works when the optimal reorder point of the approximation is very small; in other cases the usage of the exact distribution can lead to substantial cost savings (up to 14%). We further provide intuition insight on the optimal controls and how they depend on different factors, e.g., the lead time variability, and the demand features (arrival rate, size and variability).

Synchronizing pricing and replenishment to serve forward‐looking customers

AbstractWe incorporate strategic customer waiting behavior in the classical economic order quantity (EOQ) setting. The seller determines not only the timing and quantities of the inventory replenishment, but also the selling prices over time. While similar ideas of market segmentation and intertemporal price discrimination can be carried over from the travel industries to other industries, inventory replenishment considerations common to retail outlets and supermarkets introduce additional features to the optimal pricing scheme. Specifically, our study provides concrete managerial recommendations that are against the conventional wisdom on “everyday low price” (EDLP) versus “high‐low pricing” (Hi‐Lo). We show that in the presence of inventory costs and strategic customers, Hi‐Lo instead of EDLP is optimal when customers have homogeneous valuations. This result suggests that because of strategic customer behavior, the seller obtains a new source of flexibility—the ability to induce customers to wait—which always leads to a strictly positive increase of the seller's profit. Moreover, the optimal inventory policy may feature a dry period with zero inventory, but this period does not necessarily result in a loss of sales as customers strategically wait for the upcoming promotion. Furthermore, we derive the solution approach for the optimal policy under heterogeneous customer valuation setting. Under the optimal policy, the replenishments and price promotions are synchronized, and the seller adopts high selling prices when the inventory level is low and plans a discontinuous price discount at the replenishment point when inventory is the highest.

A simulation-optimisation genetic algorithm approach to product allocation in vending machine systems

In recent years, vending machines have seen increasing levels of popularity. In a fast-paced world where convenience and accessibility of products is highly sought after the vending industry has provided a suitable solution. Although the economic impact of the vending industry is indisputable, it is not without challenges, especially when it comes to the efficiency of the vending logistics operations.The optimisation of logistic vending machine systems is decidedly complex. Product allocation to columns in a vending machine, replenishment points of products, product thresholds at vending machines, and vehicle routes for inventory replenishments are all essential challenges in vending machine system management and operation. If all facets of the problem were to be addressed, it would require techniques such as forecasting, machine learning, data mining, combinatorial optimization and vehicle routing, among others. In the past, these approaches have been explored individually despite their intrinsic interdependence within the problem. This paper aims to help to fill in this gap and proposes a model for the optimisation of product allocation within a vending machine under the constraint of fixed restocking instances. The optimal product allocation is based on the definition of product profitability which accounts for the net revenue earned after the cost of restock, as opposed to the revenue earned until first stock-out to prevent arbitrary extension of the stock-out period. The whole approach is encompassed in the simulation-optimisation framework that utilises a Genetic Algorithm, with fitness evaluated as simulated revenue, to determine the optimal product allocation. The acceptable threshold of missed sales for a machine is also determined as a means to make intelligent restocking decisions. Overall, the proposed approach allows the strengths of mathematically robust optimization algorithms and the implementation of analytic solutions to be combined and applied to realistic scenarios where uncertainty may rule out some high quality analytic solutions. It respects problem intricacies proper to vending and addresses the interdependence between routing and portfolio optimisation.The proposal is application-driven and stems from a collaboration with an industry partner. The model is validated against an authentic data set supplied by the partner. The case study results revealed a network-wide improvement in net revenue of approximately 3.4%, with varied efficacy based on machine popularity. The method of optimisation was found to be significantly more effective for higher performing machines, with median improvements as high as 6%.Our framework based on the optimization-simulation model yields clear benefits to vending logistics operations management. The simulation component provides the decision maker with a more comprehensive view on the actual implementation of the solution. Effectively, the joint use of simulation and optimization methods provides managers with enhanced information to help decide on both: (i) the most beneficial product portfolio, and (ii) the quality of the proposed restocking schedules. Simulation-optimisation based approach is a powerful technique used to address stochastic problems. However, it was yet to be applied specifically to logistic vending machine systems.

Optimal stocking strategies for inventory mechanism with a stochastic short-term price discount and partial backordering

Price discount is an important research topic in the field of inventory management. The existing research on this topic mainly considers fixed price discount, but ignores the situation in which stochastic short-term price discount may be involved. In this paper, we study an inventory problem considering stochastic short-term price discount and partial backordering. To address this problem, we propose an optimal replenishment and stocking model to maximise the retailers' profit. After that, a cost–benefit analysis-based heuristic method for solving the developed model is presented by considering two scenarios depending on whether a replenishment point belongs to a discount period or not. Furthermore, an algorithm is provided to elicit an optimal ordering policy from multiple solutions derived from the given heuristic solution method. Finally, a real case is offered to demonstrate the application of the proposed model, followed by a sensitivity analysis. The results indicate that a retailer can identify the optimal replenishment policy with the aim of achieving maximal profit in situations where stochastic short-term price discount and partial backordering are considered for certain inventory problems at hand. In addition, sensitivity analysis illustrates a fact that different values of the introduced parameters may influence the optimal replenishment policy.

Synchronizing Pricing and Replenishment to Serve Forward-Looking Customers with Lost Sales

[Problem Definition] We incorporate heterogeneous customer valuation and the strategic customer behavior in the classical economic order quantity (EOQ) setting. The seller incurs setup costs when replenishing inventory, and can set the prices differently over time and implement capacity rationing. [Academic/ Practical Relevance] While similar ideas of market segmentation and intertemporal price discrimination can be carried over from the travel industries to other industries, there are new aspects when applying these concepts to retail outlets and supermarkets, because they usually face inventory replenishment problems. This makes the joint inventory replenishment and revenue management problem imperative. [Methodology] We adopt the mechanism design and dynamic programming approaches. [Results] We establish the optimality of cyclic intertemporal price discrimination, even if the customers are endowed with homogeneous valuations. Under the optimal policy, the replenishments and price promotions are synchronized, and the seller adopts the highest selling price when the inventory level is the lowest and plans discontinuous price discount at the replenishment point when the inventory is the highest. We also show that, under inventory-based pricing there is a direct mapping between deterministic and stochastic arrivals scenarios, and randomness on the arrivals per se does not alter the structure of the optimal policy. [Managerial Implications] This cyclic pricing scheme offers a stark contrast to the low-price-every-day scheme and achieves overall higher profit because customer strategic behavior offers additional flexibility to the seller in managing his inventory. Furthermore, because strategic customers are willingly backlogged, this creates opportunities for the seller to work with the customers to achieve a lower operational cost and a higher overall profit.

Characterizing natural riparian vegetation for modeling of flow and suspended sediment transport

Riparian vegetation imposes a critical control on the transport and deposition of suspended sediment with important implications for water quality and channel maintenance. This paper contributes (1) to hydraulic and morphological modeling by examining the parameterization of natural riparian vegetation (trees, bushes, and grasses) and (2) to the design and management of environmental channels by determining how the properties of natural floodplain plant stands affect the erosion and deposition of suspended sediment. Laboratory and field data were employed for enhancing the physical description of flow–plant–sediment interactions with a consideration of practical applicability. A drag force parameterization that takes into account the flexibility-induced reconfiguration, and the complex structure of foliated plants was validated for small natural trees under laboratory conditions, while the data from a small vegetated compound channel demonstrated the approaches at the field scale. Based on the field data, we identified three key vegetative factors influencing the net deposition and erosion on the floodplain. The significance of these factors was evaluated for vegetative conditions ranging from almost bare soil to sparse willows and dense grasses. Overall, the investigated conditions covered flexible and rigid vegetation with seasonal differences represented by foliated and leafless states. The drag and reconfiguration of woody plants were reliably predicted under leafless and foliated conditions. Subsequently, we present a new easy-to-use methodology for predicting vegetative drag and flow resistance. The methodology is based on a physically solid parameterization for five widely used coefficients or terms (Eqs. (2)–(6)), with the necessary parameter values presented for common riparian species. The methodology was coupled with existing approaches at the field scale, revealing that increasing vegetation density and the associated decreasing flow velocity within vegetation significantly increased net deposition. Further, deposition increased with increasing cross-sectional vegetative blockage and decreasing distance from the suspended sediment replenishment point. Thus, longitudinal advection was the most important mechanism supplying fine sediment to the floodplain, but long continuous plant stands limited deposition. The proposed parameterization (Eqs. (2)–(6)) can be readily implemented into existing hydraulic and morphological models to improve the description of natural vegetation compared to the conventional rigid cylinder representation. The approach is advantageous for evaluating, for example, the effects of both natural succession and management interventions on floodplains. Finally, guidance is provided on how floodplain vegetation can be maintained to manage the erosion and deposition of suspended sediment in environmental channel designs.

POLLUTION LOAD AND ECOLOGICAL REPLENISHMENT PLAN OF LIJIANG RIVER, CHINA

Lijiang River is the link of Guilin landscape and the golden waterway of Guilin tourism. With the development of social economy, the pollution problem of Lijiang River in recent decades has become more and more serious, which has aroused widespread concern and attention. However, the study on the reduction of river pollution load is seldom found reported until now. In this paper, the pollutant load of Lijiang River is estimated by equal standard pollution load method and the water pollution model is used to simulate the reduction of river pollution load under different ecological water supply of upstream reservoir. The calculation results showed that the livestock and poultry breeding and rural life are the main sources of pollution, and the main pollutants are TN and TP, the pollution load ratio data of which is 30.30% and 29.39% respectively. The simulation results indicated that three kinds of upstream reservoir replenishment plans have obvious effect on the reduction in pollution load of Lijiang water. After being replenished by upstream reservoir, the concentration of water in downstream of the replenishment point decrease rapidly, the higher the water intensity is, the faster the concentration will decrease. Compared with the target year (S2), the 30m3/s water replenishment plan from the upstream reservoir can reduce about 20% of the annual average maximum concentration of CODMn and NH4-N in the river, and 60m3/s water replenishment can reduce about 40% in same rate. At the same time, by the comparison of annual average data and dry season average date simulation, we found that the constant replenishment in dry season improve water quality obviously.

Methods for Stochastic Collection and Replenishment (SCAR) optimisation for persistent autonomy

Consideration of resources such as fuel, battery charge, and storage space, is a crucial requirement for the successful persistent operation of autonomous systems. The Stochastic Collection and Replenishment (SCAR) scenario is motivated by mining and agricultural scenarios where a dedicated replenishment agent transports a resource between a centralised replenishment point to agents using the resource in the field. The agents in the field typically operate within fixed areas (for example, benches in mining applications, and fields or orchards in agricultural scenarios), and the motion of the replenishment agent may be restricted by a road network. Existing research has typically approached the problem of scheduling the actions of the dedicated replenishment agent from a short-term and deterministic angle. This paper introduces a method of incorporating uncertainty in the schedule optimisation through a novel prediction framework, and a branch and bound optimisation method which uses the prediction framework to minimise the downtime of the agents. The prediction framework makes use of several Gaussian approximations to quickly calculate the risk-weighted cost of a schedule. The anytime nature of the branch and bound method is exploited within an MPC-like framework to outperform existing optimisation methods while providing reasonable calculation times in large scenarios.

Smart vending machine systems: operation and performance

The operation of smart vending machine systems creates decision-making problems under vendor-managed inventory schemes involving product allocation to vending machine storage compartments, replenishment points of products and replenishment thresholds at vending machines, and vehicle routes for inventory replenishments, all of which have critical effects on system profit. This paper considers the operation of smart vending machine systems in which possible product substitutions occur when customers face stock-outs. A simple, intuitive procedure is presented to estimate substitution probabilities, construct an integrated optimisation mathematical model for the operation problem of smart vending machine systems, and develop a two-phase heuristic based on this mathematical model. The results of computational experiments demonstrate the substantial economic benefit of the smart vending machine system over the conventional system. Sensitivity analysis indicates that certain input variables significantly impact the effectiveness of the smart vending machine system. [Received 28 August 2013; Revised 26 December 2013; Accepted 11 March 2014]

A local search method for periodic inventory routing problem

Inventory routing problem considers inventory allocation and routing problems simultaneously, in which the replenishment policies and routing arrangement are determined by the supplier under the vendor managed inventory mode. What we consider here is a periodic inventory routing problem that once the delivery time, quantity and routing are determined, they will remain the same in the following periods. The problem is modeled concisely, and then it is decomposed into two subproblems, inventory problem and vehicle routing problem. The inventory problem is solved by proposing a local search method, which is achieved by four operators on delivery quantity and retailer’s demand. Insertion operator aims to insert a new replenishment point of a retailer while removal operator is to remove a replenishment point. Besides, addition operator is adopted as an assistant tool, and crossover operator is proposed for some special cases. We also propose a tabu search method to solve the routing problem. Finally, the computational results show that the method is efficient and stable.

A heuristic for the inventory management of smart vending machine systems

Purpose: The purpose of this paper is to propose a heuristic for the inventory management of smart vending machine systems with product substitution under the replenishment point, order-up-to level policy and to evaluate its performance. Design/methodology/approach: The heuristic is developed on the basis of the decoupled approach. An integer linear mathematical model is built to determine the number of product storage compartments and replenishment threshold for each smart vending machine in the system and the Clarke and Wright’s savings algorithm is applied to route vehicles for inventory replenishments of smart vending machines that share the same delivery days. Computational experiments are conducted on several small-size test problems to compare the proposed heuristic with the integrated optimization mathematical model with respect to system profit. Furthermore, a sensitivity analysis is carried out on a medium-size test problem to evaluate the effect of the customer service level on system profit using a computer simulation. Findings: The results show that the proposed heuristic yielded pretty good solutions with 5.7% error rate on average compared to the optimal solutions. The proposed heuristic took about 3 CPU minutes on average in the test problems being consisted of 10 five-product smart vending machines. It was confirmed that the system profit is significantly affected by the customer service level.

Flash Crash Forensics

ast spring, investors were jittery over negative economic news from Europe, specifically the debt crisis in Greece. And on the afternoon of 6 May, the major U.S. equity indices in both the futures and securities markets were already down more than 4 percent from their prior-day close when something freakish occurred. Suddenly, the indices plunged a further 5–6 percent but then rebounded to close down about 3 percent from the previous day. In the interim, more than 20,000 trades involving more than 300 securities were executed at prices more than 60 percent away from what their values had been only moments before. Many were executed at prices of a penny or less and some as high as US$100,000. Since then, the U.S. Securities and Exchange Commission (SEC) and the U.S. Commodities Futures Trading Commission (CFTC) have been plowing through volumes of market data to figure out what happened. Their final report released on 4 October explains the events leading up to what is now known as the Flash Crash. According to the report, at around 1:00 p.m. (EST) there was an above-average increase in the number of volatility pauses known as liquidity replenishment points (LRPs) that were triggered for individual stocks on the NYSE. By 2:30 p.m., the S&P 500 volatility index (VIX) had skyrocketed and buy-side liquidity in the E-mini S&P 500 futures contracts and the S&P 500 SPDR exchangetraded fund (SPY) fell 55 percent and 20 percent, respectively. At 2:32 p.m., a fundamental trading firm (not named in the report but subsequently identified by the Wall Street Journal and others as Waddell & Reed) initiated an automated program to sell 75,000 E-mini contracts to hedge an existing equity position. The algorithm was programmed to feed orders into the June 2010 E-mini market to target an execution rate set to 9 percent of the trading volume calculated over the previous minute but without regard to price or time. The firm’s strategy was executed in 20 minutes. On a previous occasion, Waddell & Reed combined manual trading with several algorithms to execute the strategy over the course of more than five hours, taking into account price, time, and volume. High-frequency traders (HFTs), fundamental buyers, and crossmarket arbitrageurs initially absorbed the selling, but liquidity soon vanished. At 2:45 p.m., the Chicago Mercantile Exchange Stop Logic Functionality was triggered, and the E-mini was paused for five seconds. Prices stabilized. Large market makers and liquidity providers use automated systems that are programmed with predefined trading parameters and thresholds. During the flash crash, many of these temporarily shut down as traders paused to assess market conditions and the associated risks. Some continued with manual trading in specific securities, which was a challenge because of the spike in volume. The HFTs were net sellers in the cash market for a time and then they disappeared altogether. Meanwhile, the internalizers (firms that cross trades internally) began routing orders directly to the public exchanges where liquidity was shallow. Market makers posted “stub quotes”—prices far away from the current market— to meet their continuous quoting obligations, and orders were executed against them. After the market closed, the exchanges and FINRA agreed to cancel all erroneous trades. These events highlight the extent to which automated sell orders can trigger extreme volatility and erode liquidity in stressed market conditions. The interconnectedness of the securities and derivatives markets requires a harmonized regulatory approach, particularly for recalibrating marketwide circuit breakers.