A Guide to Implementing the Theory of Constraints (TOC)





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How Can We Characterize Distribution?

We are all familiar with distribution to some extent.  Whenever we go to buy something off-the-shelf and it isn’t immediately available then we are made aware of the existence, or in this case maybe the absence, of distribution.  Of course it is best of all when distribution is invisible to the end user.  Distribution systems are an integral part of many processes and present their own unique problems and attendant opportunities.

Let’s draw a generalized distribution system and examine its properties in more detail.

Distribution is characterized by a source of some kind that produces products that are on-sold through a diverging supply chain to end users/consumers.  We could easily extend the case to a supermarket warehousing operation for example which might be fed by other producers’ warehouses rather than a plant.  However, let’s display our manufacturing bias and assume that something is indeed produced at the source of this system.

Initially there may not be a plant warehouse, rather orders may be batched and produced periodically and then shipped directly to distributors or wholesalers.  Therefore the source node is often characterized for a particular product by periods supply with long intervals of non-supply in-between.

The other levels in the system, let’s call them nodes, don’t produce anything.  They may purchase and on-sell or they may simply reflect a change of mode of transportation.  Although they don’t have a manufacturing lead time, the do have a resupply lead time.  Broadly this can be characterized as the time taken to pick, pack, ship, unload, and enter the goods from one node to another.

The time taken between manufacturing at the source node and consumption/purchase by the end user from the last node can be quite considerable – multiples of months or quarters.

The system as it is drawn could be geographically local with production, wholesale and retail nodes.  Or it might be national with regional, as well as local warehouses involved, or for that matter international with national warehouses in addition to regional and local warehouses.  The distribution chain might be a part of a whole integrated manufacturing business – the New Zealand diary industry springs to mind – or it might be a stand-alone business itself making money from buying and on-selling.  In this instance the manufacturer might not own the stock once it leaves the premises, but until the end user has made a purchase the system hasn’t really made a sale at all.

A feature of traditional linear supply chains is that we sometimes have too much of the wrong material which we can’t sell.  At the same time we also have too little of other things that we can sell.    In addition, diverging supply chains – distribution systems – may have the right amount of the right material at the right time, but it is in the wrong place.  Consequently sometimes we miss sales even though we have the material in stock but not in the right place and at other times we miss sales because we don’t have the material at all.  In a system which is not internally constrained by production, missing a sale should be a crime.

We need to address this problem; we need a plan of attack.

Plan Of Attack

There is only one plan of attack, our 5 focusing steps which we have employed in manufacturing and will continue to employ here and in other places to develop simple and workable solutions to our problems – both physical and policy.

(1)  Identify the system’s constraints.

(2)  Decide how to Exploit the system’s constraints.

(3)  Subordinate everything else to the above decisions.

(4)  Elevate the system’s constraints.

(5)  If in the previous steps a constraint has been broken Go back to step 1, but do not allow inertia to cause a system constraint.  In other words; Don’t Stop.

What is the constraint in this system?  The limited number of customers who come in the door seeking to buy something from us.  That almost answers the second question – how to exploit the constraint?  We need to ensure that we can always meet our customers’ demands and not miss any sales, or not sell something of less value than our customers’ desires.  We will need to deduce how to best do this.  We will also need to develop how best to subordinate the system once the exploitation strategy is in place.

The results of these activities might indeed stimulate demand, and therefore also elevate the system.  If, however, demand is still less than desired we may have to resort to the next tool – the Mafia offer.  A description of the Mafia offer forms the last page to this section on supply chain.  We will limit ourselves here, however, to the first 3 steps; identify, exploit, and subordinate.

To enable us to determine the exploitation and subordination tactics we need to examine the properties of distribution networks in a little more detail.  Let’s do that.

The Beer Game!

Senge describes a game, the beer game, which he uses to illustrate and develop a number of points that are relevant to distribution (1).  This game isn’t difficult to perform and is well worth while investigating.  Essentially there are just 3 nodes, a retailer, a wholesaler, and a plant.  The retailer has a stock of a particular beer and receives a steady stream of orders from customers each week.  However, on one week only, a small jump in sales is introduced into the system.  There is a long feedback period between retailer and wholesaler, and wholesaler and plant, essentially the resupply time.  This is sufficient to introduce a major oscillation in the system that magnifies at each subsequent stage quite out of proportion to the original small and unique perturbation in sales.

Why does this happen?

The easy answer is human nature.  People with good dynamic understanding will resist the temptation and the system will remain stable.  Most people, however, will not resist the temptation.  Try it yourself with a group of people and you will see.  We tend to look at the detail complexity and almost immediately lose focus on the dynamic complexity.  Play this game with several groups and watch just how consistent the reaction is.  The title of the chapter that describes this game is called “Prisoners of the system, or prisoners of our own thinking?”  It is a learning exercise; it is designed to make people aware of their own reactions to dynamic situations.  In the beer game there are just 3 players, the retailer, the wholesaler and the plant.  So it is a very simple chain of events, and yet within this simple chain of events people wanting to do their very best quite soon produce a system way out of control.  If this is the normal response in this simple and protected situation then consider the ramifications in a multilayer distribution system in the real world.

The beer game wouldn’t be so frightening if long lead times weren’t endemic to most distribution systems.  But they are.  They are endemic because of the long signal times that arise from using min-max systems to activate resupply.  They are endemic because of the long manufacturing lead times in many industries.  And they are endemic because of the perceived “lumpy” demand.  We saw how this was so in the previous page on replenishment.  The long feedback times cause perturbations at the plant when no such perturbations exist at the retail nodes, this tends to cause the plant to chase peaks that don’t exist, the overall capacity is sufficient to meet demand but the peak capacity isn’t.  This tends to be viewed as insufficient internal capacity when in fact it isn’t.

Essentially the beer game exposes to us the vices of batching.


When we have batching and long lead times we tend to compensate by forecasting future demand so that we can make “intelligent” decisions about current production.  However, we need to test the validity of these forecasts.  Consider for a moment; what is the accuracy with which you can estimate next months’ total sales?  Is it of the order of plus or minus 5%?  Sure it’s probably padded for safety, but if you had to put money on it falling either way, would +/- 5% be sufficient?  Probably.  Now consider a product line within next months’ total sales, what would the accuracy be for a product line?  Twice the previous value perhaps – plus or minus 10%?  We might sell 90% of budget or maybe 110% for a particular line.  Alright, then how about a line item within a particular product line for next month?  Would you be surprised to see plus or minus 20%?  Customers, the economy, and everything else are just so fickle.

Let’s look at this same problem from another perspective.  If the accuracy of the estimate for next month’s total sales is of the order of plus or minus 5%, what is the accuracy for a quarter?  It would be more than 5%, maybe plus or minus 10%.  What then of the accuracy for 2 quarters out?  Maybe plus or minus 20%?  The actual numbers aren’t so important.  Making our intuition explicit is more important.

It seems that our intuition tells us that forecasting degrades as we increase the time span, and forecasting degrades as we disaggregate the production down into product lines and then line items.  There seems no doubt that the less aggregate the forecast the greater the potential for forecast error, and the further out that we push the forecast horizon, again the greater the potential for forecast error.

Long lead times cause us to compensate by forecasting.  Forecasting carries with it some uncertainty.

We will call this “forecasting error.”

The Distribution Network

So far all of these characteristics are similar to the problems that are generally experienced by make-to-stock and which we discussed briefly in the section on finished goods.  However a distribution system adds a further dimension to our forecasting error due to the disaggregation of the orders by geography.  Let’s look at this.

What is the general accuracy of the estimate of sales at the plant warehouse level?  Plus or minus 5% maybe?  If could be better and it could be worse, but let’s leave it at that.  What then is the accuracy of the estimate of sale at an individual distributor or wholesaler, better or worse?  Worse of course.  Let’s assign a plus or minus 10% accuracy to line level volumes at these nodes.  What then is the accuracy of the sales estimate at an individual retailer, better or worse?  Worse of course.  Let’s assign a plus or minus 20% accuracy to line level volumes at these nodes.

We have forecasting error due to;

(1)  Very long lead times.

(2)  Disaggregation by item.

(3)  Disaggregation by location.

Moreover, if we look to manufacturing for an analogy then distribution is similar to a “V-plant” as described in production section.  In V-plants under the traditional approach expensive equipment must be utilized constantly to absorb overhead and to insure that adequate value is received, since each diverging point is an opportunity to misallocate material the V-plant is dominated by this problem (2).

Thus in addition to forecasting there is the chance that the wrong material will go to the wrong place at the wrong time.  It is misallocated.

We will call this “allocation error.”

Allocation error leads us to a number of undesirable outcomes; there is channel stuffing, there is dead stock, and there are stock-outs.  In each case we are failing to fully exploit the constraint, our consumer who wishes to make a purchase.  Let’s look at each of these in turn.

Channel Stuffing

It would be nice to believe that in this day and age of lean production and integrated logistics that channel stuffing no longer occurs, but it does.  Especially in these times of very low interest rates and high liquidity when it is possible for distributors to borrow against new inventory at very low cost.  Moreover, in some industries a cash rebate is offered for these “sales” to distributors, so in effect taking inventory generates a small cash flow for the distributor even though the distributors are yet to make a sale to their own customers.  Moreover, the rebates cause “hockey stick” production and the plants that service the process will have large quarterly or 6 monthly swings in production demand as a consequence (depending upon whether their financial reporting is quarterly or 6 monthly).  Once again production plants feel the pinch as they try to chase artificially induced peaks even though there overall capacity is more than enough to meet demand.

A specific example comes from the automotive industry in the U.S.A., (3).  At least in the early 1990’s this mode of operation, channel stuffing, was still endemic in the automotive industry; “… dealers are small, individually owned businesses.  Some 11,700 of them, or 47 percent, are still single-site operations.  In many cases they still pay cash up front for their cars and still complain about the assemblers forcing them to take cars they don’t want.  Inventories are still large – averaging sixty-six days’ stock on hand over the last decade.”

Of course channel stuffing also causes lead times to increase providing a nice negative reinforcement loop to our forecasting error.

Dead Stock

In this situation we might also expect to see quite a bit of dead stock, however, this data is usually buried in the averages that are presented to top management.  Management may become concerned when they see average months-of-supply move from 3 to 4 months or from 6 to 7 months or whatever the figure might be.  However, within this story there will be a tail, a long tail of months-of-supply that for some line items will extend out to years.  If we go through our stock list item by item and divide it by recent demand, be that annual or quarterly or 6 monthly, we will soon see the extent of the tail in the stock.  Consider how much capacity we used to generate that stock.  Go figure out if we will sell it any time soon.

Womack et al., quote an example where they visited a divisional automotive headquarters facing the problem of how to sell 10,000 already built cars that no dealer wanted (3).  The company had built the cars based upon forecast of market demand rather than actual orders from dealers or consumers.  The market had change however and no one wanted the cars.  A dead stock problem of monumental proportions.


The above example is also a good indication of why companies that have dead-stock will also have stock-outs; their valuable manufacturing capacity was occupied building other things.

But, why use automotive examples?  Well, production/distribution chains in the automotive industry don’t come much larger, tie up more money, or appear more complex.  Thus it makes a good reference environment.  All distribution and allocation environments will share the same characteristics however.  We seem to be able to characterize the problem without too much difficulty, let’s see if we can characterize a solution with similar ease.


We have been describing the supply chain here as distribution.  However, a more accurate description would be distribution and allocation.  The allocation is according to manufacturing production-push.  The production-push is signaled by a forecast about the future based upon recent past trends and intuition about the future.

In the Theory of Constraints manufacturing application – drum-buffer-rope – we saw how work is pulled by the constraint schedules through the system.  The constraint schedules in turn are linked to actual customer demand.  In the same manner, the kanban in just-in-time also pull work through the system.  We need to invoke the same principles here in our distribution system; we need consumer, or customer, or end user demand-pull.  That way we only make what is required by the system to satisfy demand, no more and no less.

How can we do this however when we have such long lead times from the source to end user?  Well, what if we were to consider just the next layer of nodes in the chain rather than the whole chain from beginning to end?  What if we were to consider resupply to just the next level?  Then lead times would be much, much, shorter.  Surely that would help.

In fact, isn’t this exactly what we did with our replenishment buffers in the previous page?  Sure, there we only really considered one or two nodes at a time.  But is there any reason why we can’t repeat this – cut and paste it – from layer to layer in our distribution system?  Each node in the supply chain pulls from the node above according to the signal that it receives from the nodes that it supplies below.  This will enable us to invoke a pull-to-replenish system based upon demand by the end user.  Let’s try it.

We are going to move from manufacturing production push-to-forecast to customer demand pull-to-replenish.

Let’s have a look at this solution.

General Solution – Distribution With Replenishment

So far we have identified the constraint or the leverage point – our limited number of customers.  We have also now deduced an exploitation strategy to overcome the current problems of our distribution system.  We are going to use replenishment and buffer management to make sure that we can always have the right material in the right place at the right time – every time.  So what do we need to do and where do we start?

Replenishment as you will recall from the previous page is frequency driven, the more often we can replenish the smaller the buffer that we will need to maintain at each node.  What drives the frequency overall?  The frequency that we manufacture at.  It is no coincidence that supply chain follows production on these pages because ultimately we must reduce the production lead time, the batch size, and finished goods stock if we are to increase production frequency in order to substantially improve the supply chain.

Indeed, we have assumed that since we have an external sales or marketing constraint that we have already implemented drum-buffer-rope in the manufacturing or processing stage.  However, if we are looking at this as a free-standing distribution situation – the processing stage is beyond our span of control or sphere of influence – then we must treat that stage as an external (and maybe less than reliable) vendor.  We saw in the previous page how we can use replenishment buffers to protect our sales under such conditions.  In this situation we may not be able to reduce supply chain stock levels as we would have if production was under control.  However, that is not the objective, the objective is to increase throughput by not missing sales.

In order to not miss sales where is the place where we have the least allocation error and the least forecast error?  Surely the finished goods stock of the plant.  This is then the place where we must start.  We must size the finished goods stock buffers to adequately supply the downstream nodes while waiting for upstream resupply from the plant.  We have moved safety to the place where it best protects the whole system.  Let’s draw this.

In fact the whole solution to the distribution problem is simply to implement appropriately sized replenishment buffers at each node at each level.  In fact each node is the replenishment buffer.  Big deal?  You are absolutely right, it’s not a big deal, but the effects are profound.  We minimize allocation error and we avoid forecasting error.  Let’s summarize this;

Introducing replenishment buffers and increasing resupply frequency automatically
 aligns the process with the goal

Once again the aim is to increase throughput, but very often a consequence of that is a reduction in inventory locally, or even within the whole system.  If we aggregate inventory at the plant warehouse and we can reduce the plant lead time by half then we can also reduce finished goods at the plant warehouse by half and in other parts of the system by much, much, more.  Inventory reduction is a consequence of meeting the objective of increasing throughput via increased resupply frequency.

In essence we have synchronized the whole supply chain by buffering each node against the supply and variation in supply leading into it and the demand and variation in demand leading out of it.

Replenishment is the exploitation step, or the motor, for supply chain solutions.  We need now to consider how to subordinate this particular supply chain in order to ensure that we fully support the exploitation of the constraint.  Let’s have a look at that.

Local Performance Measures

In our discussion of replenishment we described buffer sizing, re-order duration, and resupply duration as the planning functions which determine the characteristics of the system.  Much earlier we also used the word “plan” to describe how to exploit a system.  It was suggested that a plan was really is just a set of instructions that provides for a timely and appropriate output.  In distribution supply chains the instructions, the plan, is embedded in the way we construct the system.

In the replenishment section we also described buffer management as the control function once the buffers, our plan, are correctly sized and put in place.  And again much earlier we described subordination as deviation from our plan.  Thus the buffer management is our control system and our means of determining deviation from our plan.  Buffer management ensures correct subordination.

Goldratt considers that there are two ways in which we can deviate from our plan (4);

(1)  Not doing what was supposed to be done.

(2)  Doing what was not supposed to be done.

Let’s see how we can relate this to buffering in replenishment.

Generally we can view not doing what was supposed to be done as generating lateness.  We have ample protection at each stage of our distribution supply chain and therefore if something is late to the next step it is most likely to have arisen from something not having been done when it should have been done.  We can give this lateness a value of throughput-dollar-days late.

We calculate this by taking the sales value less any totally variable costs and multiplying that by the number of days late in the system or the subsystem.  Thus the later it is the greater the value of the throughput-dollar-days, and the more valuable it is the greater the value of the throughput-dollar-days.  Throughput-dollar-days should be attached to zone 1 buffer penetrations for internal measurements within a subsystem.  We don’t want things to progress so far as to affect the next node in the chain.  In this respect supply chain buffers behave like stock buffers in a make-to-stock environment.  For a more detailed description of these concepts see the page on implementation details in production.

The complement of guarding against what hasn’t been done, is guarding against what has been done that shouldn’t have been done.  Generally we can view this as having too much inventory sitting around for too long.  We can give this waiting process a value of inventory-dollar-days waiting.  We calculate this by taking the raw material cost only and multiplying by the number of days resident in the system or subsystem.  Material that sits around for too long rapidly gains inventory-dollar-days.

We can use these two measures to ensure that subsystems are adequately aligned with the whole system.  Throughput-dollar-days late to the next node should be zero, and inventory-dollar-days waiting at each node should be static or reducing.  These measures are the control system for distribution.  They ensure that the parts of the system are correctly subordinated to the whole.

Distribution Is Not Simple Replenishment

Distribution is not simple replenishment, by replacing forecasting with simple replenishment using buffers we avoid one source of error – forecasting error.  Therefore, why can’t we just treat distribution as a simple replenishment system through a linear supply chain of dependent vendors or dependent nodes?  Well, there are a number of reasons for this;

(1)  We must consolidate demand from numerous points of sale.

(2)  We must currently subordinate the source nodes to the points of sale.

(3)  We must position the protection in the place that best protects the whole system.

Of these; positioning the protection for the system in the place that does the most good is the most important; this avoids the other major source of error – allocation error.  The best place for the protection is where the aggregate volumes are greatest, closest to the plant.   We can limit the overall inventory in the plants finished goods stock and elsewhere by increasing the overall frequency of reorder and decreasing the duration of resupply.  Because distribution deals with a divergent supply chain it is not a case of simple replenishment.

Let’s Think It Through

We begin to determine the replenishment buffers for individual line items at the point where we know the demand with the greatest degree of certainty – at the plant warehouse.  The plant warehouse “sees” the aggregate demand of the whole system, the peaks and the toughs smoothed out to the largest extent.  Then we work through the individual nodes in the next layer, and the next layer after that until we reach the point of sale.  Wherever possible, increasing the reorder frequency and decreasing the resupply duration will allow us to hold less stock while maintaining or improving customer service levels.

We avoid forecasting error.

We avoid allocation error.

First-class distribution is predicated upon good buffer management at the plant – because this is where most of the protection is. The unavoidable outcomes are that we no longer have too little of the right material in the right place in the right time because our plant capacity is now “smoothed” and not wasted making unnecessary “emergency” jobs.

What Are The Unavoidable Outcomes?

The unavoidable outcomes are;

(1)  Increased throughput at the point of sale.

(2)  Decreased total inventory.

(3)  No stock-outs.

(4)  No over-stock.

(5)  Sufficient plant capacity

In fact we should have just the right amount of just the right material in just the right place – always.

But Wait, Reality Isn’t This Simple!

If this explanation seems quite simple and straightforward then that is excellent; then we know that we have developed an understanding of replenishment as applied to distribution.  If experience tells us that reality is more complicated than this generalized case, then that too is excellent.  Now we are in a position to better understand how to apply this methodology to our own particular situations.

Let’s see then what have been the results in specific implementations

Give Us Some Examples

We used several examples from the U.S. automotive industry earlier to show the magnitude of the problems faced by one of the largest business distribution systems in commerce today.  Automotive is important because it is a hugely significant and competitive industry for many economies both nationally and internationally.  What if we could provide a simple solution to distribution in that particular environment using replenishment and buffer management?  Well, the truth is that this has already been done.  Let’s have a look.

The Cadillac division of General Motors successfully implemented replenishment in the early 1990’s using the Florida region as the testing ground.  Instead of immediately forcing finished cars onto dealers from the plant they placed them in a regional buffer of 1400 cars at Orlando for delivery to the state’s 42 dealerships within 24 hours of an order – more than 95% of the time.  Special orders can now be filled in 14 days rather than taking several months as in the past (5).

As a consequence of the success in Florida the scheme was expanded to other major Cadillac regions in the country.  In 1996 General Motors took the concept nationally for Cadillac and expanded testing into the Chevrolet and GMC sport-utility vehicles (6).  A dealer was reported to be happy “that they no longer have to stock ’10 versions of the same car because if we had only one and sold it, it would take us six to 10 weeks to get another from the factory.  Now if we can sell one we can pull another one’ immediately from the regional distribution center.”

Overall then, popular model configuration delivery time decreased from 6-10 weeks to 24 hours, special order configurations can now be filled in 19 days guaranteed down from 10-12 weeks.  Turnover at the regional distribution centers was expected to of the order of 3 to 7 days (5, 6).

Replenishment and buffer management brought substantial and rapid improvement to General Motor’s Cadillac division’s distribution system.  It would be difficult to imagine a more substantial or difficult environment to undertake this type of exercise in.  Think about it.


The distribution supply chain historically has been one where goods have been produced and immediately pushed into the distribution network as close to the customer as possible.  This has lead to large inventories but none the less not always the right things in the right place at the right time.  This arises from misallocation in the divergent supply network and also forecasting error due to the large work-in-process and hence long lead times.

The Theory of Constraints supply chain solution, replenishment, provides a motor to exploit the constraint – the customer – by treating each node as a buffer and maintaining most goods where they will protect the overall system best – at the plant warehouse.  Reduced batch size in manufacturing leads to more frequent resupply to the whole supply chain.  More frequent reordering in the supply chain itself and reduced resupply duration from node to node means that substantially better levels of customer service can be maintained with less overall inventory.  Forecasting is no longer required.


(1) Senge, P. M., (1990) The fifth discipline: the art and practice of the learning organization.  Random House, pp 26-54.

(2) Stein, R. E., (1994) The next phase of total quality management: TQM II and the focus on profitability.  Marcel Dekker, pg 37.

(3) Womack, J. P., Jones, D. T., and Roos, D., (1990) The machine that changed the world.  Simon & Schuster Inc., pp 170-175.

(4) Goldratt, E. M., (1990) The haystack syndrome: sifting information out of the data ocean.  North River Press, pp 144-155.

(5) Gabriella Stern, "GM expands its experiment to improve Cadillac's distribution, cut inefficiency," The Wall Street Journal (February 8, 1995).

(6) Gabriella Stern and Rebecca Blumenstein, "GM expands plans to speed cars to buyers," The Wall Street Journal (October 21, 1996).

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