Slides

Low variability allows to increase the throughput, without increasing waitingtimes

Low variability allows to decrease waiting times, without lowering throughputs.

Batching of entities can be seen as something that creates artificial variability (created by management themselves). If for some items, very large batches are created, these batches may take a lot of processing time, while production orders consisting of a single entities hardy take process time.  Then batching causes the coefficient of variation of the process times to increase. Queueing formulas show us that this will cause waiting times to increase. However we can also realize the opposite! if one of the entities that we have to process requires the double process time of the other item, we can apply a smart batching approach by making the batch size for the second entity half the size of the other. That would me a smart way of batching that decreases process time variability instead.

We could consider the use of a smaller transport batch. If the entities that leave the process step are even transported one by one, there is no wait-in-batch time after the process. Moreover, this avoid an irregular arrival process at the next process step.

These graphs include a blue curve for what Hopp calls the Practical Worst Case (PWC). It is important to realize that in any line in practice the performance curve will have this kind of shape and will be between the best case and the worst case. In practice we will never realize the best case, as there will nearly always be a little bit of variability. At the same time the extreme variability assumed in the worst case is also non-existent in practice. The specific PWC levels in the blue curve have been calculated by assuming CVe =1 for each of the stations in the line. However, in practice the curve may still be closer to the worse case if the variability is more extreme then assumed by CVe=1. At the same time, the lower the variability in the line the closer the curves will move to the green curve, This is also reflected in the third graph on the next slide.

Results in higher TH at all WIP levels

Higher throughput reate at non-bottlenecks. Results in lower CWIP => higher TH in PWC

Results in moving from PWC curce in direction of best case

Variability reduction can also be relevant at stations before the bottleneck

Inventory, capacity, and time

At/before the BN or otherwise as close as possible

Stock that can be used to satisfy multiple types of demand

Inventory buffers imply that the flow entities are waiting, More precisely, the product/orders/people that move through the process are waiting for either demand from the next process step, or for capacity or for other flow entities (in case of batching or assembly). The flexibility is then a characteristic of the waiting entities. These waiting entities can be either used for multiple types of demands, or be processed by multiple types of capacities, or combined with multiple types of other entities. (This reduces the amount of waiting entities you need.)

Capacity that can be shifted from one process to another

Capacity buffering means that capacity is waiting for either demand/orders, or for entities to arrive. Flexible capacity is then capacity that can be used for multiple types of demands/orders or multiple types of entities. (This reduces the amount of overcapacity you need.)

Time that can be allocated to more than a single entity

Buffering by time relates to demands/orders that are waiting for entities to arrive or capacity to become available. Here you see the struggles of Hopp in defining ‘flexible time’.  Time in itself is not flexible. But the buffer time relates to the fact that the orders/demand wait. Flexible demand/orders is then demand or orders that can be fulfilled by multiple types of capacity or multiple types of flow entities.  (This reduces the amount of time buffer you need, either in terms of less orders have to wait, or order have shorter waiting times)

Hopp in his book:

Production of goods or service is lean if it is accomplished with minimal buffering costs

Suggested steps at Toyota:

1)     Elimininate direct waste

2)     Substitute capacity for inventory buffers

3)     Reduce variability

4)     Reduce capacity buffers

5)     Go back to (3)

According to Hopp these are typical workstation situation for Push and Pull control.  With push some schedule has caused material to available at a station and then it will be allowed to produce. With pull control this is only allowed if there is not too much WIP. In the depicted card-based (kanban) system WIP is controlled by only making a new authorisation card available for production, when a product leaves the outbound stock. The card was first connected to the product in the outbound stock but now become available for production. However take care that these are just typical examples. These situations do not DEFINE push and pull. The definition is given on the next slide.

Drum-Buffer-Rope, is a famous control method proposed by Goldratt in his seminal book ‘The Goal’ (1984). Goldratt wrote this book as a novel, but it introduces the ideas of bottleneck management.

DBR assumes that you can identify a bottleneck workstation that constrains the output of the system. T

-        This bottleneck determines the rhythm of the whole production system (the drum-function). So first a schedule is made for production based on this workstation.

-        Then a (time) buffer should prevent this bottleneck station from starving. Each order is planned such that it will arrive a certain time before it was scheduled at the bottleneck, if no interruptions would occur.

-        The rope should prevent that orders are released too early. The situation at the bottleneck determines when new work is pulled (the rope idea) into the system at the first workstation.

This is a clear example of a pull system focused on releasing work based on the system status at the bottleneck.

Basic CONWIP:

When work leaves (the outbound stock of) the last station, this authorizes the release of a new order at the first station. For example, a card can be attached to each order. As soon as a card is disconnected at the last station it goes back to the planner who can release a new order. Then the amount of cards will determine the WIP level in this system and thus WIP in this sytem will be constant, which explains the name CONWIP system.

Multiloop:

But we can also have multiple card loops. In the second figure an order leaving the buffer after the last station will allow the second but last station to start working on a new order. This will withdraw material from the preceding buffer. To this material a card from the previous loop was attached and the preceding stations are now triggered. Etc.

Kanban:

In a traditional Kanban system each station has its own loop, so starting to work on the next product at a station (thus withdrawing material from the preceding buffer) will authorize the previous station, etc.

the loop that ends at a bottleneck station will not include the buffer after the bottleck. This is and uncoupled loop.

If work would build up after the bottleck and it would be coupled, then the bottleneck migh not be authorized to start a new order. This may happen if there is a short breakdown after the bottleneck. However, the bottleneck should not starve, while, if the stations after the bottleneck are non-bottlenecks, they will probably catch up after the breakdown and clear the buffer after the bottleneck again.  Uncoupled: Since what happens after the Bottleneck should not affect the Bottleneck.

A traditional method to determine the order quantity for stock replenishment is to consider the trade-off between inventory holding (also called carrying) costs and  the order cost (fixed cost related to placing and/or receiving each order). The quantity that minimized the sum of these two logistic cost components is called the Economic Order Quantity. Though it is often difficult to make a reasonable estimate of each of the cost parameters, the advantage of the EOQ is that even if the order quantity deviates slightly from what should be the EOQ, it hardly leads to an increase of total costs. See slide. This is because holding cost slightly increase for a larger order quantity, but then order cost will decrease, and the other way around for an order size that is chosen slightly smaller than the EOQ.

The Safety Stock (SS) acts as a buffer against a higher than avg demand ( up to +50) within the lead time (or a longer lead time)

> Re-order point (ROP): average demand during lead time (µ) + Safety Stock (SS)

The Safety Stock should be based on demand variability during the lead time

Then we can choose z as a certain percentile of the standard normal distribution if we choose z=1.645, the 95% percentile of the standard normal distribution, then we make sure that in 95% of the cases we still have sufficient stock at the time that the replenishment order arrives.  If we choose a slightly higher z=2 to determine the safety stock, we already cover 97,7% of the probably, so the risk is only 2.3% that we are out of stock before delivery of the replenishment order.

Notice that these 95% and 97.7% are the so called cycle service level, which do not look at the size of the shortage (like the so called fill-rate does), but only at the probability that we run out of stock before delivery delivery during a delivery cycle. Which percentile is desirable depends on b (the annual cost of being one unit out of stock) and h (the cost of holidng one unit of inventory for one year). The percentile α to determines the appropriate z (z can better be written as zα)  can be calculated as b/(b+h).

In periodic review systems we define an order-up-to level (OUTL) instead of a reorder level.

At the beginning of each order period (e.g. week) the stock level is brought up to OUTL.

OUTL = µ + zσ

with z: the b/(b+h) percentile of…

But now, µ and σ are the average and stand.dev. of demand during the order period!

In a base stock system we replenish up to the base stock level (BSL) as soon as the inventory falls below it.

Note: inventory position stays constant at BSL in base stock system.

net inventory = on-hand inventory – backorders (i.e. negative at outage)

Inventory position = net inventory + replenishment orders

The criterion Demand Value is NOT appropriate for differentiating the service levels of A,B and C items.

Often you do not need full flexibility (everyone can do everything or serve every demand) to already realize a large part of the pooling advantages. Chaining (e.g. each demand can be served by two different plants) may already help a lot to deal with flexibility.

Suppose we have to buffer against variation for demand a and demand b. Both will have seperate buffer stocks, based on each own standard deviation. However the standard deviation of the sum of demands is not equal to the sum of the standard deviations. σa+b = √(σa2 + σb2) can be used instead of σ2a+b = σa2 + σb2. If σ=1, then σa+b = 1.4 instead of 2.

A bakery