J E Beasley

OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). They were originally used by me in an introductory OR course I give at Imperial College. They are now available for use by any students and teachers interested in OR subject to the following conditions.

A full list of the topics available in OR-Notes can be found here.

Just-in-time (JIT)


Just-in-time (JIT) is easy to grasp conceptually, everything happens just-in-time. For example consider my journey to work this morning, I could have left my house, just-in-time to catch a bus to the train station, just-in-time to catch the train, just-in-time to arrive at my office, just-in-time to pick up my lecture notes, just-in-time to walk into this lecture theatre to start the lecture. Conceptually there is no problem about this, however achieving it in practice is likely to be difficult!

So too in a manufacturing operation component parts could conceptually arrive just-in-time to be picked up by a worker and used. So we would at a stroke eliminate any inventory of parts, they would simply arrive just-in-time! Similarly we could produce finished goods just-in-time to be handed to a customer who wants them. So, at a conceptual extreme, JIT has no need for inventory or stock, either of raw materials or work in progress or finished goods.

Obviously any sensible person will appreciate that achieving the conceptual extreme outlined above might well be difficult, or impossible, or extremely expensive, in real-life. However that extreme does illustrate that, perhaps, we could move an existing system towards a system with more of a JIT element than it currently contains. For example, consider a manufacturing process - whilst we might not be able to have a JIT process in terms of handing finished goods to customers, so we would still need some inventory of finished goods, perhaps it might be possible to arrange raw material deliveries so that, for example, materials needed for one day's production arrive at the start of the day and are consumed during the day - effectively reducing/eliminating raw material inventory.

Adopting a JIT system is also sometimes referred to as adopting a lean production system. More about JIT can be found here, here, here and here.


JIT originated in Japan. Its introduction as a recognised technique/philosophy/way of working is generally associated with the Toyota motor company, JIT being initially known as the "Toyota Production System". Note the emphasis here - JIT is very much a mindset/way of looking at a production system that is distinctly different from what (traditionally) had been done previous to its conception.

Within Toyota Taiichi Ohno is most commonly credited as the father/originator of this way of working. The beginnings of this production system are rooted in the historical situation that Toyota faced. After the Second World War the president of Toyota said "Catch up with America in three years, otherwise the automobile industry of Japan will not survive". At that time one American car worker produced approximately nine times as much as a Japanese car worker. Taiichi Ohno examined the American industry and found that American manufacturers made great use of economic order quantities - the traditional idea that it is best to make a "lot" or "batch" of an item (such as a particular model of car or a particular component) before switching to a new item. They also made use of economic order quantities in terms of ordering and stocking the many parts needed to assemble a car.

Ohno felt that such methods would not work in Japan - total domestic demand was low and the domestic marketplace demanded production of small quantities of many different models. Accordingly Ohno devised a new system of production based on the elimination of waste. In his system waste was eliminated by:

In this system inventory (stock) is regarded as an unnecessary waste as too is having to deal with defects.

Ohno regarded waste as a general term including time and resources as well as materials. He identified a number of sources of waste that he felt should be eliminated:

At the time car prices in the USA were typically set using selling price = cost plus profit mark-up. However in Japan low demand meant that manufacturers faced price resistance, so if the selling price is fixed how can one increase the profit mark-up? Obviously by reducing costs and hence a large focus of the system that Toyota implemented was to do with cost reduction.

To aid in cost reduction Toyota instituted production levelling - eliminating unevenness in the flow of items. So if a component which required assembly had an associated requirement of 100 during a 25 day working month then four were assembled per day, one every two hours in an eight hour working day. Levelling was also applied to the flow of finished goods out of the factory and to the flow of raw materials into the factory.

Toyota changed their factory layout. Previously all machines of the same type, e.g. presses, were together in the same area of the factory. This meant that items had to be transported back and forth as they needed processing on different machines. To eliminate this transportation different machines were clustered together so items could move smoothly from one machine to another as they were processed. This meant that workers had to become skilled on more than one machine - previously workers were skilled at operating just one type of machine. Although this initially met resistance from the workforce it was eventually overcome.

Whilst we may think today that Japan has harmonious industrial relations with management and workers working together for the common good the fact is that, in the past, this has not been true. In the immediate post Second World War period, for example, Japan had one of the worse strike records in the world. Toyota had a strike in 1950 for example. In 1953 the car maker Nissan suffered a four month strike - involving a lockout and barbed wire barricades to prevent workers returning to work. That dispute ended with the formation of a company backed union, formed initially by members of the Nissan accounting department. Striking workers who joined this new union received payment for the time spent on strike, a powerful financial inventive to leave their old union during such a long dispute. The slogan of this new union was "Those who truly love their union love their company".

In order to help the workforce to adapt to what was a very different production environment Ohno introduced the analogy of teamwork in a baton relay race. As you are probably aware typically in such races four runners pass a baton between themselves and the winning team is the one that crosses the finishing line first carrying the baton and having made valid baton exchanges between runners. Within the newly rearranged factory floor workers were encouraged to think of themselves as members of a team - passing the baton (processed items) between themselves with the goal of reaching the finishing line appropriately. If one worker flagged (e.g. had an off day) then the other workers could help him, perhaps setting up a machine for him so that the team output was unaffected.

In order to have a method of controlling production (the flow of items) in this new environment Toyota introduced the kanban. The kanban is essentially information as to what has to be done. Within Toyota the most common form of kanban was a rectangular piece of paper within a transparent vinyl envelope. The information listed on the paper basically tells a worker what to do - which items to collect or which items to produce. In Toyota two types of kanban are distinguished for controlling the flow of items:

All movement throughout the factory is controlled by these kanbans - in addition since the kanbans specify item quantities precisely no defects can be tolerated - e.g. if a defective component is found when processing a production ordering kanban then obviously the quantity specified on the kanban cannot be produced. Hence the importance of autonomation (as referred to above) - the system must detect and highlight defective items so that the problem that caused the defect to occur can be resolved.

Another aspect of the Toyota Production System is the reduction of setup time. Machines and processes must be re-engineered so as to reduce the setup time required before processing of a new item can start.

Ohno has written that Toyota was only able to institute kanbans on a company wide basis in 1962, ten years after they first embarked on the introduction of their new production system. Although, obviously, as the originators of the approach Toyota had much to learn and no doubt made mistakes, this illustrates the time that can be required to successfully implement a JIT system in a large company. Moreover you can reflect on the management time/effort/cost that was consumed in the development and implementation of their JIT system.

With respect to the Western world JIT only really began to impact on manufacturing in the late 1970's and early 1980's. Even then it went under a variety of names - e.g. Hewlett Packard called it "stockless production". Such adaptation by Western industry was based on informal analysis of the systems being used in Japanese companies. Books by Japanese authors (such as Ohno himself) detailing the development of JIT in Japan were not published in the West until the late 1980's.

As an indication of the growth of interest in JIT over time the graph below shows the number of documents (such as books and conference proceedings) referring to just-in-time in the British Library, which has a very extensive collection of such documents relating to the UK. The earliest material I could find was from 1984, when there was one book published and one set of conference proceedings. The graph shows the number of documents published each year as well as the cumulative number published.

One often reads nowadays that JIT involves employee participation, involving workers so as to gain from their knowledge and experience. Such participation is meant to ensure that workers feel involved with the system and make suggestions for improvements, cooperate in changes, etc. Personally I am not convinced that this aspect of JIT, as it is interpreted nowadays, played any part in its initial development. Certainly Ohno, writing in 1978 long before the appearance in the West of material related to JIT, in 8 pages of single spaced A4 paper outlining the Toyota Production System makes little mention of this aspect. My best guess, from my reading of the subject, is that JIT started out as a top-down, centrally organised and imposed production system. Whilst it may later have come to take on a "human-face" with connotations of worker involvement and participation I personally doubt it started out that way.

Toyota still describes itself as using the Toyota Production System for car manufacture, e.g. here in relationship to a manufacturing plant in the USA.

Japanese terms

There are a number of Japanese terms (words) associated with JIT that you may encounter. I have listed some below for you:

In the Toyota system the Andon, indicating a stoppage of the line, is hung from the factory ceiling so that it can be clearly seen by everyone. This coupled with line stoppage clearly raises the profile of the problem and encourages attention/effort to its solution so that it does not reoccur.

As an indication though of the difficulty of implementing JIT in a Western environment when General Motors instituted an Andon for line stoppage workers were simply not prepared to take responsibility for stopping the line. Hence defective items were passed though the system, rather than the Andon functioning as planned and highlighting problems and hence leading to their resolution. General Motors resolved the problem by allowing workers to indicate that they had a problem whilst the line continued to operate.

Reconciling JIT and EOQ

It is a common misconception that JIT, a Japanese originated concept, is somehow radically different from the classical Western concept of the Economic Order Quantity (EOQ), based as it is on the most economic level of stock. I hope below to convince you that this is not so.

Recall from the notes about inventory theory the problem of deciding the appropriate amount of stock to order.


Then we need to decide Q, the amount to order each time, often called the batch (or lot) size.

With these assumptions the graph of stock level over time takes the form shown below.

Hence we have that:

where Q/2 is the average inventory level

where (R/Q) is the number of orders per year (R used, Q each order)

So total annual cost = ch(Q/2) + co(R/Q)

Total annual cost is the function that we want to minimise by choosing an appropriate value of Q.

Note here that, obviously, there is a purchase cost associated with the R units per year. However as this is just constant as R is fixed we can ignore it here.

The diagram below illustrates how these two components (annual holding cost and annual order cost) change as Q, the quantity ordered, changes. As Q increases holding cost increases but order cost decreases. Hence the total annual cost curve is as shown below - somewhere on that curve lies a value of Q that corresponds to the minimum total cost.

We can calculate exactly which value of Q corresponds to the minimum total cost by differentiating total cost with respect to Q and equating to zero.

d(total cost)/dQ = ch/2 - coR/Q² = 0 for minimisation

which gives Q² = 2coR/ch

Hence the best value of Q (the amount to order = amount stocked) is given by

and this is known as the Economic Order Quantity (EOQ)

To get the total annual cost associated with the EOQ we have from before that total annual cost = ch(Q/2) + co(R/Q) so putting Q =(2Rco/ch)0.5 into this we get that the total annual cost is given by

ch((2Rco/ch)0.5/2) + co(R/(2Rco/ch)0.5) = (Rcoch/2)0.5 + (Rcoch/2)0.5 = (2Rcoch)0.5

Hence total annual cost is (2Rcoch)0.5 which means that when ordering the optimal (EOQ) quantity we have that total cost is proportional to the square root of any of the factors (R, co and ch) involved.

The Economic Order Quantity is (by definition) the order quantity that minimises total annual cost and hence (on cost grounds) should always be the quantity that we order.

What then of JIT with its philosophy of (essentially) very small orders/levels of stock (i.e. Q=1). Is there not a contradiction?

If fact there need not be. This is because in JIT we notice that we need not take co and/or ch as fixed. In particular if we can reduce the cost of ordering co then the EOQ reduces. For example, if we were to reduce co by a factor of 4 we would reduce total cost by a factor of 2 (note the EOQ would change as well, being halved). This, in fact, is one of the ideas behind JIT to reduce (continuously) co and ch so as to drive down total cost.

Hence if, for example, we were to build close links with our suppliers so as to reduce ordering cost dramatically it becomes, just by a straightforward application of the EOQ formula, much more attractive to have small order quantities. In the limit if co is zero, i.e. ordering is free, then we order each and every unit as we need it (remember here our simple EOQ model assumes a zero lead time, i.e. orders received as soon as they are placed).

Note too from the formula (2Rcoch)0.5 for the total annual cost associated with the EOQ reducing co also reduces cost.

In summary then in order to reconcile JIT and EOQ we do not take co and/or ch as fixed but seek (continuously) to reduce them, thereby reducing the EOQ thereby simultaneously reducing the total annual cost.

Obviously seeking ways of reducing co and/or ch takes management time (thereby incurring cost) and we may reach a point of diminishing returns, i.e. it may not be worth the management effort (cost) required to reduce total annual cost further.

General Motors

An example of the use of JIT in General Motors is given below.

General Motors (GM) in the USA has (approximately) 1700 suppliers who ship to 31 assembly plants scattered throughout the continental USA. These shipments total about 30 million metric tons per day and GM spends about 1,000 million dollars a year in transport costs on these shipments (1990 figures).

JIT implies frequent, small, shipments. When GM moved to JIT there were simply too many (lightly loaded) trucks attempting to deliver to each assembly plant. GM's solution to this problem was to introduce consolidation centres at which full truckloads were consolidated from supplier deliveries.

This obviously involved deciding how many consolidation centres to have, where they should be, their size (capacity) and which suppliers should ship to which consolidation centres (suppliers can also still ship direct to assembly plants).

As of 1990 some 20% by weight of shipments go through consolidation centres and about 98% of suppliers ship at least one item through a consolidation centre.

All this has been achieved without sacrificing the benefits of JIT.

JIT outline points

Originated in Japan

Often said Japanese industry works - just-in-time, Western industry works - just-in-case

JIT is also known as stockless production or lean production

JIT is a suitable production system when:


It is often said that:

I believe that this is an incorrect analysis - MRP is a system based on fulfilling predicted usage in a set time period.

JIT is a system based on actual usage - parts of the production system are "linked" together via kanbans as the system runs

It is this linkage that is the distinguishing difference between MRP and JIT - JIT is a dynamic linked system, MRP is not

JIT philosophy

Elements of JIT

JIT need not be applied to all stages of the process. For example we could keep large stocks of raw material but operate our production process internally in a JIT fashion (hence eliminating work-in-progress stocks).

Classic JIT diagram

The classic JIT diagram is as below. There the company (the boat) floats on a sea of inventory, lurking beneath the sea are the rocks, the problems that are hidden by the sea of inventory.

       \             /     
========\ Company   /============ Sea of inventory
                       xxx     xxxx
                      xxxxx   xxxxxx    Rocks - the problems hidden
                     xxxxxxxxxxxxxxxx           by the sea of inventory

If we reduce the inventory level then the rocks become exposed, as below.

       ---------------     x 
       \             /    xxx     xxxx    
========\ Company   /====xxxxx===xxxxxx========
         \---------/   xxxxxxxxxxxxxxxx 

Now the company can see the rocks (problems) and hopefully solve them before it runs aground!

One plan to expose the problems is simply to:


The benefits of JIT are:

However you should be absolutely clear that implementing a JIT system is a task that cannot be undertaken lightly. It will be expensive in terms of management time and effort, both in terms of the initial implementation and in terms of the continuing effort required to run the system over time.


Suppliers can be crucial to JIT success

Supplier gets:

In return the supplier agrees to

Supplier selection criteria:

With suppliers satisfying these criteria you can reduce the total number of suppliers, indeed it seems logical so to do. If you had five suppliers meeting all these criteria why do you need five? Obviously you might decide to have more than one supplier for safety reasons. Even the best run supplier can suffer a factory fire or an earthquake, but probably no more than two or three suppliers.

As an illustration of this in 1997 Toyota was affected by a fire at a supplier of brake parts that cost the company an estimated $195 million and 70,000 units of production. The fire was at a plant that was the sole supplier of brake parts for all but two Toyota models and forced the company to shut its 18 assembly plants in Japan for a number of days. As a result Toyota embarked on a review of components that were sourced from a single supplier.

Having a single supplier may be attractive in cost terms, but one does need to balance the risk (albeit a low probability risk - perhaps a fire every 100-250 years say) against the cost savings.