Webinar Recordings Available Now

05/31/2016 : 0 Comments  

Every month, Invistics offers educational Webinars in a variety of supply chain topics. Typically, these Webinars include best practices, case studies, and lessons learned from our experience working with a industry leaders. We’re proud to now be able to offer our Webinar recordings to be viewed at anytime:


How Invistics Solutions can prevent Controlled Substance Diversion (4/4)

04/14/2016 : 0 Comments  

Invistics Controlled Substance Blog Series:

In our Controlled Substance blog series so far, we’ve detailed the epidemic of opioid abuse that has ravaged our nation, leading to annual death counts as high as 27,000 per year, which is more than car accident fatalities and rivals the damage done by the AIDS epidemic in the 1990’s.

Invistics’ background is in helping complex supply chains with advanced inventory analytics and visibility tools. In 2012, one our pharmaceutical customers asked us to develop software specifically designed to improve Controlled Substance Inventory Management; it needed to have real-time inventory accuracy and verification to pass Drug Enforcement Agency (DEA) inspections, electronic data entry for Research& Development and Analytical Lab environments who are still mostly using paper-based inventory tracking, smart reporting features to consolidate controlled substance inventory data and make Year-End reporting less burdensome, and the capability to track and manage quota for schedule II controlled substances.

We were surprised to learn, given the urgency of the national drug diversion problem, that there wasn’t another software on the market that provided these capabilities. Over the course of the next four years, we have learned all we could about our nation’s current controlled substance crisis. And we have made significant investments building out our software’s capabilities to help prevent controlled substance diversion.

So now we can offer our experience and our software solution to fight diversion:

  • FlowPath Health: Real-time visibility showing the location of all controlled substance inventory, with alerts to flag if any material is not properly secured in the appropriate vault, cage, or restricted access location:

Controlled Substance Inventory Tracker

  • DataVault: Electronic data entry screens that allow employees in analytical laboratories, product development, and research departments to convert paper-based log books into electronic, real-time tracking information:


  • Report Manager: Electronic reports that provide cradle-to-grave lot lineage, with audit trails for every movement of every gram or tablet or sample of controlled substances, and accurately compile the reports required by the DEA to prevent diversion or theft of controlled substances:


  • Quota Calculator: And assistance with requesting annual quota from the DEA for Schedule II controlled substances, the most additive and most dangerous controlled substances:

Quota Calculator

To see if our software solutions can help your company, please call us at 1-800-601-3456 for a free consultation, or download our Executive Brief for more information. Together we can turn the tide in the fight against Controlled Substance diversio


When Opioid Addiction Hits Home: Atlanta (3/4)

03/30/2016 : 0 Comments  

In first blog entry of our Controlled Substance Abuse series, we reviewed the widespread abuse of pharmaceutical opioids in America, and our second entry detailed how controlled substance abuse devastates families, and children in particular. Today we’re going to discuss the alarming trend of opioid abuse that really hits home for us because it’s occurring right in Invistics’ backyard: the greater Atlanta area. According to 11 Alive, the Atlanta News Channel:

“In the past six years, the number of heroin-related deaths has gone up by 3844% in Fulton, DeKalb, Cobb, and Gwinnett counties. The Georgia Bureau of Investigation (GBI) confirms the fastest growing rate of heroin-related deaths is in a cluster of Atlanta’s northern wealthy suburbs. That fact is hiding in state and county records.(For more information regarding this story, 11 Alive conducted a chilling 4 episode investigation “Inside the Triangle”.)”

Young people, in Atlanta suburbs, are dying from heroin overdose at an alarming rate. The problem has even captured the White House’s attention, and President Obama visited Atlanta last week as part his efforts to escalate the fight against the prescription opioid abuse and heroin epidemic in the area.

There is a direct correlation between opioid painkiller abuse and its much deadlier cousin, heroin. As government and health services continue to crack down on controlled substance diversion, people who abuse non-prescribed painkillers are turning to heroine due to increased accessibility, lower market price and high purity of heroin to achieve a stronger “high”. The National Institute of Drug Abuse estimates that 1 in 15 people who take non-medical prescription pain killers will try heroin in the next 10 years, and that heroin is almost 3x as addictive as pain killers, while being much more dangerous. The U.S. National Library of Medicine stated that “Painkillers [are] often gateway to Heroin for U.S. Teens.”

On March 10 2016, The Atlanta Journal Constitution reported that a criminal scheme that burglarized close to 2 million doses of addictive prescription drugs ($40 million worth of narcotics) from Emory University Hospital Midtown, including 1.2 million doses of hydrocodone and 110 gallons of promethazine with codeine, has been shut down after running for 5 years.

Emory Midtown’s case is yet another example of how prescription drugs can be put to illegal uses at top brand-name hospitals, even when administrators think they’re following the rules. There are no statistics on how often these kinds of cases happen, in part because the hospitals hush them up, said Kimberly New, founder of Diversion Specialists, which advises hospitals on how to prevent prescription drug theft, which is often called drug diversion.”

The article states the problem stemmed from a “lack of control” by hospital administrators that let the criminal operation run for over 5 years before discovery. “By the time Emory Midtown reported its suspicions to law enforcement in 2013, some 2 million doses of opiates and other addictive drugs had gone missing. The suspects — all hourly employees — were driving Mercedes Benz and BMW cars.”

We believe at Invistics the best way to prevent drug diversion is to stop it before it starts. The technology exists to provide accurate visibility and accountability in the form of diversion alerts for any institution that handles controlled substances— hospitals, drug manufacturers, R&D labs—to monitor and shut down diversion before it can occur. For every diversion scheme uncovered, there are many more that go undetected due to the lack of visibility and control of controlled substances along the supply chain. By spreading awareness of problem, as well as the technology advancements that can monitor and curb diversion, we hope to Invistics can make a difference starting with our own backyard.




Silent Victims of Opioid Addiction: The Children (2/4)

03/09/2016 : 0 Comments  

One of the devastating backdrops of America’s opioid epidemic is the impact it has on the children whose guardians are victims of the powerful addiction to opioids that renders them unfit to function as parents. Last week, we reviewed the widespread abuse of pharmaceutical opioids in America, and now we will turn our lens to the silent victims of the opioid addiction, the ones that won’t appear on any statistics but will have nevertheless had their life’s unrevokably altered by chemical addiction: the children.

The Wall Street Journal states in “Parents’ Drug Abuse Strains Child-Welfare Agencies”: “Abuse of opioids like heroin and prescription painkillers is straining child-welfare agencies across the U.S. and sending more children into foster care, officials say. Addiction treatment for opioids only occasionally succeeds, relapse is common and children often languish for years in the system. The number of children in foster care nationwide as of September 2014 rose 3.5% from a year earlier to 415,129, according to the latest data collected by the Administration for Children and Families, part of the U.S. Department of Health and Human Services.”

The epidemic’s reach is pervasive. The Wall Street Journal continues, “In Vermont, opioid use was a factor in 80% of cases in which a child under the age of 3 was taken into custody…The number of children under the custody of the Department for Children and Families as of last September grew 40% from two years earlier to 1,373, driven mainly by parental opioid addiction, according to Gov. Peter Shumlin.[…]

The Indiana Department of Child Services added 459 family case managers in the past two years to help handle a rising tide of cases. The agency estimates 2,600 children had to be removed from homes due to parental drug abuse in a six-month period that ended last March, a 71% jump from two years earlier.

It’s a double-edge sword for parents who are afflicted: on one hand, if they ignore the issue, they risk their children growing up in unfit environment where their needs come second; on the other hand, if they seek out treatment and admit to their problem, they risk losing their kids to the state anyways. Dr. Sarah Wakeman, a specialist in substance abuse treatment at Massachusetts General Hospital, states for the Boston Globe: “Right now, there’s an incentive not to talk about the fact that you have an addiction because you’re worried you’ll be punished and lose your kids.”

An even more disturbing trend: doctors are confronting the challenge of newborns being born with a dependency to painkillers, due to their parents abusing the drugs during pregnancy. According to The New York Times: “Infants […] may cry excessively and have stiff limbs, tremors, diarrhea and other problems that make their first days of life excruciating. Many have to stay in the hospital for weeks while they are weaned off the drugs, taxing neonatal units and driving the cost of their medical care into the tens of thousands of dollars.

Like the cocaine-exposed babies of the 1980s, those born dependent on prescription opiates — narcotics that contain opium or its derivatives — are entering a world in which little is known about the long-term effects on their development. Few doctors are even willing to treat pregnant opiate addicts, and there is no universally accepted standard of care for their babies, partly because of the difficulty of conducting research on pregnant women and newborns.

There is already some relief on the way. Just Last month, President Obama proposed $1.1 billion in new funding to address the prescription opioid abuse and heroin use epidemic. Additionally, many states are proposing new legislation to help the children of addicted parents by sponsoring programs where the state will temporarily remove the children out of their parents care, but rather than settle them into a state home, they will approach close family as a temporary asylum for the children as their parents seek treatment.

One reason the epidemic has spread to its current state is due to the ease-of-access of getting these drugs from a prescription or from an illegal source which allow addiction to fester. At Invistics, we believe the best response is to prevent diversion before it happens. By spreading awareness and assisting pharmaceutical manufactures and developers with tracking and alerts for their controlled substances, we can hope to curb addiction & abuse before it occurs. Join us in the fight against opioid addiction and ensure that our nation’s children are afforded the opportunity to grow up in healthy homes, free from suffering.


Invistics Joins the Fight against CS Diversion (1/4)

02/11/2016 : 0 Comments  

Prescription painkillers are abused by more than two million Americans every year. Each day, 7000 people are treated in emergency rooms across the country for abusing opioids such as Hydrocodone, Oxycodone, and Methadone, and the number of fatalities in the US alone has reached 44 people a day, higher than the number of car collision fatalities. Most of these are people are unaware of the addictive nature of these drugs, and have too-easy access to them via a prescription or from illegal sources. Recently, the New England Journal of Medicine has established a direct link between nonmedical prescription-opioid use and their more potent street counterpart, heroine. The statistics have looked bad for years, and recent overdoses continue to grow.

The rates of overdose deaths are rising particularly for women (up 400% from 1999 to 2010) and middle-aged Caucasian Americans. The New York Times, states in “Drug Overdoses Propel Rise in Mortality Rates of Young Whites”:

The drug overdose numbers were stark. In 2014, the overdose death rate for whites ages 25 to 34 was five times its level in 1999, and the rate for 35- to 44-year-old whites tripled during that period. The numbers cover both illegal and prescription drugs.

“That is startling,” said Dr. Wilson Compton, the deputy director of the National Institute on Drug Abuse. “Those are tremendous increases.”

Rising rates of overdose deaths and suicide appear to have erased the benefits from advances in medical treatment for most age groups of whites. Death rates for drug overdoses and suicides “are running counter to those of chronic diseases,” like heart disease, said Ian Rockett, an epidemiologist at West Virginia University.

Just last week, President Obama has proposed $1.1 billion in new funding to address the prescription opioid abuse and heroin use epidemic. So we at Invistics have decided to join our nation’s fight against the diversion of Controlled Substances.  What is diversion?  “Any criminal act involving a prescription drug.

Our initial exposure to Controlled Substance compliance came in 2012, when one of our pharmaceutical customers approached us to modify our supply chain software to have specific capabilities to manage Controlled Substance inventory across their supply chain. Specifically, we built software for them with the following capabilities:

  1. Real-time visibility showing the location of all their controlled substance inventories, with alerts to flag if any material is not properly secured in the appropriate vault, cage, or restricted access location
  2. Electronic data entry screens that allow their employees in their analytical laboratories, product development, and research departments to convert paper-based log books into electronic, real-time tracking information
  3. Electronic reports that provide cradle-to-grave lot lineage, with audit trails for every movement of every gram or tablet or sample of controlled substances, and accurately compile the reports required by the DEA to prevent diversion or theft of controlled substances
  4. And assistance with requesting annual quota from the DEA for Schedule II controlled substances, the most additive and most dangerous controlled substances.

Since then, Invistics has spoken with hundreds of individuals who manufacture, distribute, prescribe, or administer Controlled Substances. We have talked with, and learned from, people working in every link of our nation’s Controlled Substance supply chain: drug manufacturing companies, wholesalers and distributors, hospitals and their doctors & nurses, retail pharmacists, and law enforcement agencies to learn the role we can play in helping prevent Controlled Substance diversion and accidental overdoses. This blog entry is the first in a series of five, detailing what we have learned, and why we are joining the fight to prevent Controlled Substance diversion. We will be posting four more articles on this topic over the coming weeks, with additional details about the problem, and the new approach we are taking to join our nation’s fight against this epidemic.


Forecasting Leads to Improved Inventory?

12/14/2015 : 0 Comments  

Lora Cecerce, founder of Supply Chain Insights, posted a very insightful article in Forbes called “Does Better Forecasting Improve Inventory? Why I Don’t Think so Anymore”.

Inventory has always been necessary in supply chain management to buffer against supply and demand variability. With the advent of high-mix manufacturing and the need to produce a longer tail of SKUs with more equipment changeover, this is more true than ever before. Lora, in her recent analysis of planning benchmarking for large mult-nationals, states:

“A mistake that I see companies making over and over again is improving forecasting, but not improving inventory levels because of the lack of a holistic focus. After the implementation of a forecasting system, and getting basic functionality in place and providing a reliable forecast with minimal bias and accuracy, there is only minimal value in continuing to refine the forecast. Most companies do not have a forecasting problem. Instead, they do not know how to use the forecast to drive inventory strategies.

Why do I state this so boldly? The forecast is always wrong. This is true by definition. Improving it by a few percentage points on forecast accuracy is not going to drive the improvements in inventory that most people think. While most companies focus on the numbers, it is understanding the probability of demand and translating it to supply strategies that makes a difference.”

Lora counted four trends that lead her to rethink how inventory should be managed.

Cycle Stock is the Opportunity for Most Manufacturers

“Cycle stock is most effectively managed through the successful implementation of production planning. (Cycle stock is the management of stock required to cycle through production runs and procurement buys effectively. It involves complex logic on batch size, change-overs and production sequencing.) With the rise of item complexity, improving production planning becomes more important. This planning technology is tricky to implement and many of the technologies are not up to the task; but doing it well is essential.”

One of the cornerstone of Invistics’ solution is to view Inventory holistically as a combination of Cycle Stock and Safety Stock. It’s very common for companies to order materials in large quantities, often to meet a bulk discount, but then to skip the next step of figuring out bulk discount savings vs cycle stock inventory management costs. Even if you save 20% by ordering a years worth of product X in bulk, you must account for the holding, movement, and obsolescence risk of that left over inventory as it sits in your warehouse for the next year.

Download our Whitepaper to Learn More: Optimizing Cycle Stock, Lot Sizes, and Rhythm Wheels in High-Mix Manufacturing

Inventory is the Most Important Supply Chain Buffer, but Requires Design

“The most important buffers–shock absorber for volatility– in the supply chain is inventory and manufacturing capacity. The reduction of cost and improving asset utilization is usually the charter of the supply chain team. As assets become more and more utilized, manufacturing loses the ability to buffer volatility through manufacturing capacity optimization. In parallel, with more and more manufacturing outsourcing, companies lose the capability to buffer through the use of manufacturing capacity. As a result, inventory becomes the critical buffer to absorb demand and supply volatility. Designing the supply chain and making conscious choice about push-pull decoupling points, cycles, and late-stage postponement helps.”

At Invistics, we also stress the design before the implementation for three reasons. 1.) It builds consensus. 2.) It develops a relevant business case to get stakeholders invested, and 3.) it identifies processes and tools that are require to support the new approach. Our workshops begins with sketching out the “As-Is” value streams vs the future “Should-be” value streams, and discusses many of the items Lora mentions such as when to use Push vs Pull.

Technology can Help

“More and more companies are purchasing inventory technologies, but failing to give planners time to plan. This is a mistake. With the rise of the global multi-national. There is more and more need for an inventory planning role to manage the form and function of inventory and develop inventory strategies. Buying the technology and not having clear processes and accountability does not help. We are still in our infancy in the use of multi-tier inventory optimization technologies, but as shown in Figure 2, there is a strong impact when implemented correctly.”

Most high-mix environments will require technology due to sheer numbers. Traditional “rule of thumbs” approaches to inventory management such as “let’s hold 4 weeks of supply for product X” are becoming more and more outdated in a world where demand and supply rates fluctuate quickly. Often times you need a tool that can drill down into the just the items you are managing, to pull data from multiple computer systems, and can give you an accurate solution without tying up IT resources to sustain. If interested, here is a demo of a multi-tier inventory optimization technology called the Inventory Advsior:

Executive Understanding

“One of the surprises for me in the benchmark data is the gap in understanding of inventory strategies by the supply chain executive team. The concepts of planning and the management of form and function of inventory are not well understood. Most executives believe that the answer lies in having a better forecast. They are not able to have a discussion on the form and function of inventory. It takes training. The strategy requires careful definition with finance. However, it is worth it. Inventory turns correlate to market capitalization, and who can argue with improving market capitalization?”

Leadership is the key to sustainability. All the planning and software tools in the world aren’t enough to effect change if your companies management isn’t on board with visible metrics and staff training to ensure the new processes are being implemented with care.

To share with you an example from Invistics past, we completed a new inventory management workshop at a large company where we “capped” inventory using Pull-driven methods. Later on, when we came back to audit the shop floor, planners were still relegating to their old habits and focused only on maximizing machine utilization even when there was no demand for more of the product. In the planner’s eyes, the waste was due to letting a machine sit “unused”, instead of the storage and handling cost of the piles of unnecessary inventory. Leadership is key to bridge such communication gaps.

We hope this blog article was educational. If you have any questions or would like a consultant with Invistics please contact us using the contact button at the top of the page. And oh, a Happy Holidays to all.


Screencast of our Safety Stock Optimization Software

12/03/2015 : 0 Comments  

High-mix companies are manufacturing and distributing a wider variety of products every year, with increased variability in both supply and demand.

These companies have a choice for inventory optimization:

  1. Continue to struggle with homegrown, spreadsheet approaches,
  2. Invest significant time and money building and maintaining tools from ERP vendors
  3. Quickly optimize inventory using cloud-based tools, such as the Inventory Advisor from Invistics

Our Invetory Advisor software uses advanced analytics to optimize inventory levels & safety stocks. Implementation is quick and requires a minimal amount of inputs and resources from IT. You can configure the software to optimizes all inventory: raw materials, WIP, and finished goods, across the supply chain, while slicing and dicing the dataset in whichever way makes sense for your business so that you can manage your “A” SKUs (also known as high runners) differently than your “B” and “C” SKUs

Below is a video demonstration of the Inventory Advisor in action:


Pull in Demand Driven Value Networks

03/23/2015 : 0 Comments  

Gartner posted an article detailing the benefits of pull replenishment in Demand Driven Value Networks:

Demand-driven value networks (DDVNs) integrate processes and data to translate demand signals into a supply response that creates value and mitigates risk.

The manufacturing, retail, high-tech, life science and healthcare industries with demand-driven capabilities perform better in the long term than peers with traditional, cost-focused supply chains. These companies grow revenue faster, achieve more than 15% higher perfect-order rates and reduce inventory levels by as much as one-third. They leverage an outside-in view based on insights about customer value. They apply this view to their product portfolios, supply networks and service processes to deliver customer value and profitable growth.

Orchestration of value networks includes selectively collaborating with customers, suppliers and partners, as well as effectively managing trade-offs internally through cross-functional processes that synchronize product, demand and supply decisions for maximized value. Critical capabilities for orchestration include supply chain visibility, agile decision making in response to volatility and demand shaping to optimize profitable balance.

Invistics has been helping high-mix manufacturers and distributors design and implement their Demand Driven Value Network for over 15 years. Our Pull Design Workshop is a great way to get started using three steps:

1.) Reaching consensus on the type of pull strategy to be adopted, the production planning parameters that will be impacted and the process and tools to be deployed to ensure a systemic and sustainable implementation.
2.) Developing a relevant business case.
3.) Identifying processes and tools that will support the new approach on an on-going basis.


Kingsman's Equation and Your Plant's Utilization

04/20/2014 : 0 Comments  

Our last blog post provided a general summary of Kingsman’s Equation and how it relates to your manufacturing operation. Today we’re going to delve a little deeper into the equation to prove that when it comes to lowering the Average Queue Time (or Average Wait Time) of your resources, Utilization is King.

For every system whether it’s a single machine or an entire factory, the time a resource spends as raw material or work-in-progress can be divided into two parts.

  1. -Process Time. This is value-added time it takes per machine or machines to process the resource and churn out a finished product.
  2. -Queue/Wait Time. This is non-value added time the resources are set aside to wait at the queue of machine or bottleneck, on a machine’s setup, etc

Lead Time = Queue Time + Process Time. In most manufacturing systems, the Queue time can comprise 80-85% of the lead time. This is all non-value added time that should be reduced in order to maintain a Lean operation.

Now let’s take another look at Kingsman’s equation:


AQT = Average Queue Time.
p = Utilization, expressed as decimal
Ca2 + Cs2 = arrival and process coefficient of variations.
τ = average process time

so what does this mean exactly? First let’s look at some examples where utilization(p) is at .25, .5, .7, .9, and .99. For these examples, we’ll just assume: (Ca2 + Cs2)/2 = 1 and process time(τ) = 60 minutes.

Case 1: If p = .25, Average Queue Time (AVQ) = (.25/(1-.25) * 60 = 20 mins
Case 2: If p = .5, Average Queue Time (AVQ) = (.5/(1-.5) * 60 = 60 mins
Case 3: If p = .7, Average Queue Time (AVQ) = (.7/(1-.7) * 60 = 140 mins
Case 4: If p = .9, Average Queue Time (AVQ) = (.9/(1-.9) * 60 = 520 mins
Case 5: If p = .99, Average Queue Time (AVQ) = (.99/(1-.99) * 60 = 5940 mins or 99 hours

In this example since (Ca2 + Cs2)/2 = 1, the STDEV of the respective variables would have to equal the mean to get 1. While such high variability does exist in the real world, it’s not very common. But regardless, this example is enough to illustrate two very important take-aways.

1.) Despite such high variability in both arrival and process times. If the utilization of the machine(s) is low, as it is in case 1 or case 2, the Average Queue Time is still manageable. This is because in terms of reducing your AQT, machine utilization is by far the most important factor.

2.) As you can see from the exponential increases in AQT over the cases, it is very, very wasteful to run your machines at such high utilization because your Average Queue Time goes through the roof. Can you imagine an 99 hour Average Queue Time for each of your products? And the screeching of your customers or sales reps? No thanks.

One final thing I should note is that the AQT in Kingsman is not the exact AQT, but more of a likely upper bound of your real AQT. Though it’s accurate enough to get the point across.


The King of Manufacturing Equations

04/10/2014 : 0 Comments  

In queueing theory, Kingman’s formula states that the mean waiting time is given by:


AQT = Average Queue Time.
p = Utilization, expressed as decimal
Ca2 + Cs2 = arrival and process coefficient of variations.
τ = average process time

So what are the practical, manufacturing take-aways?

  1. The longer the average process time is, the more important is the queue length. For example a process that takes a minute, with a queue of 5, is much better than a process that takes an hour with a queue of 5
  2. Utilization is king. If utilization is low (~50% or less), arrival variation and process variation will have a small impact. If utilization is high (80% or higher), arrival and process variation will matter much more.
  3. service, and assembly, extra capacity may not be as expensive compared to it’s manufacturing counterparts. This is because it is easy to move/add employees between functions.
  4. Since many service processes are longer than manufacturing processes, variation is generally more tolerable in service than in manufacturing. In other words, it is generally much more effective to focus on reducing failure demand than variation when it comes to service organizations.
  5. Reducing time variation is generally less critical than reducing utilization. Utilization is affected by errors which generate failure demand or rework.
  6. Arrival variation should not be ignored. It is just as important as process variation. Can your arrival variation be influenced through salesmen, incentives, informing customers or reducing supply chain amplifications?
  7. The work release behavior of processes upstream of bottleneck is important. The smoother (less lumpy) the orders come in at those work stations, the faster the bottleneck will process the orders.

Additionally, the Theory of Constraint advocates 5 steps of improvement: identify, exploit, subordinate, elevate, and repeat. Kingman’s equations gives these additional insights:

-To identify the constraint (bottleneck), it is easier to examine only the load and compare it with demonstrated capacity. Kingman shows that overload begins at less than 100% utilization, and that sensitivity variations is particularly important at high utilization.
-Exploiting constraints should include variation reduction in addition to other methods such as buffering with Inventory.
-Subordinating other resources should include looking upstream of the constraint to examine arrival variation coming into the bottleneck.

Kingman’s equation ties together Lean, 6 Sigma, TOC, and service systems to show that there’s not a one-size fit all when it comes to adding value to your operations. The key is in knowing when to apply each school of thought.

(Be sure to check out John Bicheno’s “The King of Equations” in the Lean Manufacturing Journal for more information and tips related to Kingman’s equation).


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