When we need to process different products in the same line we want to work out the best job sequence to minimize lead time and maximize capacity utilization.

The ideal of "Lean Production" is lot size of 1 but this is not always possible when there is a change over time. This change over involves loading different components and changing jigs or molds. When change over or setup time is significantly higher than process time we are forced to work with larger lot sizes. 

 Scheduling Constraints

 In a sequential line products are processed through a number of workstations following a certain sequence but process parameters are typically different for each product. Each workstation, in order to do the work needs:

  • equipment available
  • operator ready
  • WIP (Work In Process) from the previous workstation available

And we want to do the job with:

  • minimum equipment time
  • minimum operator time
  • minimum WIP waiting 

The problem is that unless everything is perfect someone has to wait:

In the case of a space ship in order to minimize the astronaut time: a huge team of ground personnel is available just in case.

In an airport, in order to maximize the runway utilization (airport bottleneck): planes, pilots, personnel, customers are waiting for take off.

In Formula I races 7 second service time is achieved with a team of 10 people doing nothing most of the time during the race.

In our sequential line in a workstation either the equipment or the operator will be idle or there will be excess WIP.

 If process time for all the sequential operations are the same:

The process is perfect: nobody waits. While WS A is processing Order 2 WS B is processing Order 1 and the total lead time for each order is 4h.

If process time for operation A is shorter than B:

Order 2 will have to wait for operation B to finish with order 1 and therefore Order 2 will take 4h instead of 3 to complete and this will affect the total lead time seen by the customer waiting for this order. Also it will increase the amount of WIP in the line.

If time B is shorter:

Workstation B will be idle until order 2 arrives and this will decrease capacity utilization.

Excel Scheduler

You can download an Excel scheduler for 4 sequential operations:

SCHEDULE5eng.xlsx

 It is used to schedule an electronic circuit assembly line with 4 operations in this sequence:

  1. SMT: Surface Mount Technology automatic component placement and reflow sodering
  2. INS: Manual pin-thru-hole component insertion and wave soldering
  3. ICT: In-Circuit-Test
  4. FUN: Functional Test

Process Parameters

 In sheet Times we must input Equipment times, Operator times and Number of operators for each of the 4 operations and for each product. 

In the existing data we want to maximize equipment utilization by adding as many operators as required to do this. Therefore:

Number of operators = Operator time / Equipment time   (rounding up)

For instance number of operators for Prod A INS = 18:30 / 01:00  = 19 (rounded up)

Cycle time for each product and operation = maximum of Equipment time and (Operator time/ Number of operators)

The scheduler will use these calculated cycle times: Job operation time = Setup time + Cycle time x Quantity

Setup times for each operation are input in the Main sheet and are considered the same for all products. 

With the current number of operators you can notice that Cycle times are identical to equipment times: by adding enough operators we have insured that the line capacity is limited by equipment times and not operator times. 

Obviously the number of operators calculated may not be feasible, in which case we enter the available operators and processing will take longer as we will experience later.  

 Main Sheet

Column A has the order in which we want to run the jobs. It should have numbers 1 to 10 in the order we decide.

Column B has the products to be produced selected for the ones we defined in sheet Times.

Column C holds the number of operations already completed (0 to 4)

Column D has the quantities we need to produce of each product

Finally the starting time stamp is the day and time we will start producing

Gantt Chart

The Gantt chart shows the scheduling result:

By placing the cursor on the chart we can see the starting or ending time stamp for any operation and product.

WIP waiting times are in light colors and these are what we want to minimize to reduce lead times.

We can also notice when workstations are idle.

In this case, if we start on 6/2/2019 at 6:00 and all 10 jobs will be finished before 12/2/2019.

Additional Inputs and Results

The number of work cells in each operation is 1 by default but we may have up to 5. 

Setup times need to be defined for each operation. In this example it is the time it takes to unload all component reels and load the new ones for the next product. In the case of test it is the time it takes to change the test jigs and load the new program. We assume all products have the same setup times.

The next 2 lines are outputs:

  • Total process times of each workstation (no waiting times included) 
  • Capacity utilization of each workstation. You can notice that SMT with 100% utilization is, in this case, the bottleneck for the whole line. 

Total lead time and average lead time are outputs that will affect the customers which we want to minimize.

 Schedule for Each Workstation

A detailed schedule is produced for each workstation with starting and ending timestamps and number of operators required.

The actual times can be added on the right columns to be used on the next reschedule.

Bottleneck Scheduling

Looking at the capacity utilization of the 4 workstations we notice that SMT has 100% utilization but all the rest are well below.

This indicates that the bottleneck of this line with these required quantities is SMT. In this case the bottleneck happens to be the first workstation so the following stations are starved of products so they can't process as much as they could. 

The order in which we have scheduled the 10 jobs has been from lowest use of SMT (bottleneck) time to highest use. 

Let's see what would happen if we reverse the order: Highest use of bottleneck first:

We notice that the total lead time has increased from 5 days 17h to 7 days: an increase of 1 day and 7 hours.

Average job lead time has also increased from 1d 10h 24m to 1d 13h 16m

It is obvious that it makes no sense to schedule products A and B at the end since they do no use the bottleneck so if we just put them first keeping the rest of the sequence as it is we would get a total lead time of 6 days 11h: still worse than the first option. 

The first conclusion is that we should schedule focusing on the bottleneck workstation and process from least to most bottleneck use

Bottleneck in the last operation

 In this case, with the same products but different quantities to be processed we notice that this sequence has a lot of waiting time before the INS and FUN operations. Capacity utilization is very good but average lead time is very high: all jobs except the first have a lot of waiting and these long lead times will be unacceptable to the customer. 

The bottleneck in this case is FUN: total time for all jobs is 114h 51m 40s much higher than the other workstations. 

We notice that with this sequence we are scheduling from highest bottleneck (FUN) use to lowest, so let's try the reverse order:

Total lead time has increased 1d 4h but average lead time has decreased from 3 days 16h to 1 day 10h (less than half).

This, therefore, reinforces our previous conclusion: schedule from less bottleneck use to more.

 Schedule with operators constraint

 In the examples so far we have assumed that there are enough operators in each workstation so that the equipment never stops but this assumption may not be feasible.

Looking at the schedule for the INSERT operation we are using 19 operators for product A and the number decreases down to 1 for product J. 

Let's assume that we only have 3 operators available to perform this operation for all products:

In the Times sheet we enter 3 in the number of operators for all products and the result is that now cycle times have increased above equipment times. This means that now the operators will be the constraint rather than the equipment in the INS workstation.

The resulting schedule is:

Now INS has become the bottleneck and there is an accumulation of products waiting to be processed in this workstation causing waiting time in all jobs. Average lead time has increased from 1 day 10h to 2 days 21h (it has doubled). Total lead time has only increased 10 hours. 

 Cell duplication

In a line we will always have a bottleneck which limits the capacity of the whole line. In some cases we might be able to duplicate the bottleneck workstation to increase the overall line capacity. 

Let's duplicate the SMT workstation which was the bottleneck in our first example to see the effect:

 Total lead time has been reduced from 5 days 17h to 3 days 15h (more than 2 day reduction)

Average lead time has increased 4 hours: we have waiting in INS and FUN.

We notice that SMT capacity utilization has decreased from 100% to 86% while utilization in the other 3 workstations has increased. 

Let's see if duplicate INS and FUN as well:

We notice that total lead time has not improved but average lead time has decreased 9 hours: practically no waiting time.

Since we have increased all capacities capacity utilizations have decreased.

 Reschedule

Going back to our first schedule starting on 6/2/2019 we normally have to update this schedule at least daily or when a major change has taken place. We need to remove what has already been done and add any new jobs. Let's see how do we reschedule on the next day 7/2/2019:

We change our starting timestamp to 07/02/19 06:00 and then input in the OK column: Products A and B completed (4 operations finished) C and D only FUN is missing (3 completed), etc.

If there are any new jobs we would add them at the end shifting all jobs up.

 Job Splitting

Due to the setup times every time we change product we may think that the larger the lot size the better. Let's see this effect with a new example:

We need to produce these 5 products with quantities of 500 each. What would be the effect of splitting the jobs in two?

In spite of duplicating setup times we see average lead times have been halved and total lead time is also reduced.

Conclusions

  • In order to commit a delivery time to the customer we need to schedule taking into account existing jobs already in process
  • When a job is given priority we need to know the impact to all other current jobs
  • Job scheduling enables lead time reduction while increasing resource utilization
  • To minimize total lead time we should focus on the bottleneck
  • Schedule jobs from lowest to highest bottleneck utilization
  • After total lead time is minimized small changes in sequence will allow the reduction of waiting times and therefore the reduction of average lead time. 
  • By meeting the resulting schedule on each workstation we will insure on-time delivery to the customer.
  • Regular rescheduling is required to adapt to the real current situation

How many fully functional old smartphones are we still keeping?

Even though they normally have no phone line they still have multiple uses such as listening to music or watching videos. 

But can they still be useful in our work?

In an area with WIFI there are still multiple work applications for these old phones which might save on expensive IT applications.

One major advantage of using these phones is that the skill is already there: a new IT application would require training. 

Some Possible Business Uses for an Old Smartphone with no Phone Line

  1. Workplace data collection in real time
  2. Incident reporting anywhere any time
  3. Maintenance repair action reporting from anywhere when it is complete
  4. Value Stream Map building and validation in Gemba (where the action is)
  5. Real-time Statistical Process Control
  6. Real time manufacturing status display for all those concerned

 Workplace data collection

Pencil and paper data collection is still very common even in high-tech manufacturing industries:

 https://polyhedrika.com/2-uncategorised/19-pencil-paper-data-collection

This approach, apart from being time consuming, makes it impossible to control the process in real time.

An alternative is to collect the data in a spread sheet in the cloud (Google Drive, One Drive, Intranet, etc.) using our old smartphone connected via WIFI.

Defects can be detected anywhere along the process and it may be inconvenient to go to the nearest terminal to report. With our old smartphone we can report the defect in our spreadsheet in the cloud but also make a photo and attach it to the file so you don't need any additional explanations.

This approach enables data entry validation avoiding data entry errors.

Data entry could be done with pull-down menus to avoid typing.

Timestamps can automatically be added to register the reporting time. 

http://polyhedrika.com/2-uncategorised/13-time-stamp-a-key-process-metric-you-can-collect-for-free

In case of having to enter a written clarification text can be entered with voice from the smartphone.

 Incident and Repair Action Reporting

Incidents affecting the process may take place anywhere any time. If reporting is done at a later stage time information is lost: when exactly happened. This information is critical when it comes to failure analysis: correlation with process parameters or other incidents, etc.

By using our smartphone we are able to report it when it happened and the timestamp can be automatically added. 

The maintenance spreadsheet in the cloud can keep track both of incidents and repair actions by the maintenance department. 

Pull down menus can be used to report the equipment, component, failure, etc. and this will enable the maintenance department to track failure frequencies and get to the root cause of problems. 

Incidents can be classified by urgency to enable maintenance assign priorities. Pending actions already late are marked in red and due actions in orange. 

Using a smartphone simplifies reporting of both incidents and repair actions.

Association of defect type and repair action is also possible with this integrated worksheet helping Maintenance in their diagnostic.

Value Stream Map building and validation

A Value Stream Map of the process we want to improve is built after visiting the line where the process takes place. 

This VSM can be built in a spreadsheet in the cloud by using a smartphone from the line itself:

 https://polyhedrika.com/2-uncategorised/14-value-stream-map-with-excel

  • The VSM is built directly in the cloud (Google Drive) and all participants visiting the line have write access with their smartphone.
  • As they move along the line they all agree on who is doing what and when.
  • Typing of the process steps in the Excel sheet can be done by voice. 
  • The VSM, as it is being built, can be shown to the line operators in order to validate it.
  • After the VSM is complete the same method can be used to collect process parameters (process time, WIP, etc.) in the VSM Excel visiting the line.
  • An Excel file can be used to measure and collect process times with the smartphone:

Real Time Statistical Process Control

 Statistical Process Control (SPC) requires real-time data collection in the different control points. It may be difficult to provide terminals in all these points to report so our old smartphone may be a valid alternative by building our SPC chart in a spreadsheet in the cloud (Google Drive, etc.)

https://polyhedrika.com/2-uncategorised/20-real-time-spc

This Individuals-Moving Range SPC chart applies the Western Electric rules to detect out-of-control situations in real time as the data is being entered. 

This chart is visible to the operator entering the data with his smartphone and also to the operators responsible for that process step with a tablet or PC connected via WIFI to the Google Drive spreadsheet.

In this example there is a significant drop in yield between 10:00 and 16:00 (4 out of 5 consecutive values more than 1 sigma below the average)

 Real Time Manufacturing Status

In order to keep everyone involved in the process informed on how are we doing we need this information to be available and up to date at all times.

 A Gantt chart can show the plan and it could be updated by the production system or by the person responsible with a smartphone. 

An Andon can be displayed in the line to show the status but also accessed from the smartphones to see how are we doing. In this example:

  • Component manual insertion DPMO (Defects per million insertions) is 4124: above the target of 1500 (RED)
  • Pin-Thru-Hole wave solder DPMO (Defective solder joints per million joints) is 32: below the target of 190 (GREEN)
  • Current throughput: 13 cards/ hour at 13:55 on 15/11/2005 at the PTHHW station

With this real-time information the operators involved can react before it is too late and correct the situation. 

 Conclusions

An old smartphone, even if not the latest generation, may still have a useful life in your business by using your existing WIFI to connect to the cloud.

Data collection in real time is one of the most useful applications even if the smartphone has no phone line connection.

Since everyone already has the skills you can easily implement these proposed solutions to control your process in real time and keep everyone informed at all times.

 

Understanding variation is key to interpret process behavior. 

This simple exercise can help to experience process variation and understand the difference between process change and inherent process variation. 

This understanding is key on management decisions to avoid both overreaction and lack of reaction.

Manual dice throwing

To run the exercise with actual dice download and print the form:    Manual.JPG

Exercise:

  1. You will need a printed form and 4 dice for each team
  2. Throw 4 dice and add the outcomes
  3. Record the result in the Run Chart
  4. Repeat 50 times
  5. Join the dots in the Run Chart with a line
  6. Build the Histogram by counting the total number of dots on each group of 3 values 

Run the exercise with the simulator

Download this Excel Simulator:   Variation.xls

Close all Excel sheets before you open this one and enable MACROS.

Press RESET in the DICE sheet and keep on pressing F9 to throw the dice. 

Results Interpretation:

Try to answer these questions on each team and then discuss all teams together:

  1. Does each outcome depend on the previous one?
  2. Are there any special trends or indication of process change in the run chart? Is this a stable process?
  3. Is there a special cause that explains the maximum and the minimum values? Did you do anything different to obtain them?
  4. Is the frequency distribution close to normal: maximum at the center, declining frequency on both sides, symmetrical?
  5. What distribution would result throwing one single die? Why?
  6. Is it possible to predict the outcome of one specific throw?
  7. Is it possible to predict the frequency  of one specific outcome for a large number of throws?
  8. Can two different run charts produce the same histogram?

 Is there a downward trend?              Is this an upward trend?

Neither are statistically significant trends. The conclusion is that this is a stable process: there are no significant trends.

This is what we would expect since we have not changed the way we throw the dice so the process will continue to behave this way until we do so.

Stability doesn't necessarily mean that the process is OK: it just means that the process is neither improving nor getting worse. 

This is a stable process following a normal distribution with average 14 and standard deviation around 3.

If we throw one single dice the distribution would not be normal: it would be a uniform distribution (flat) because all values have the same probability. Throwing 4 dice there is only one combination that gives a sum of 4 (all 1's) but there are many combinations that give a sum of 14. The distribution of sums of 4 throws follows a normal distribution in spite of the distribution of single values following a uniform distribution (Central limit theorem).

Alternative process

 Let's now analyse another process: Open Variation.xls sheet ALT, press RESET and keep pressing F9 to run the process.

Now try to answer these questions on each team and then discuss all teams together:

  1. Is it likely that this data comes from the previous process of throwing 4 dice? Why?
  2. Is this a stable process?  Why?
  3. What is the meaning of the frequency distribution histogram in this case?
  4. Can we use it to predict the process behavior?
  5. What is the probability that values 7 - 13 happen again? Can you conclude that by looking at the histogram?

Alternative Process Conclusions

We can clearly notice that this process has an upward trend, therefore it isn't a stable process: its average is shifting up. 

Therefore it is very unlikely that it comes from throwing dice (apart from the values above 24 impossible with 4 dice).

In this case of an unstable process, as shown by the Run Chart, the Histogram is completely misleading if we want to predict the process behavior. Indeed, the histogram predicts that values below 15 have a certain probability of occurring but from the Run Chart we see that this is very unlikely. 

We can conclude that the Run Chart and the Histogram are both necessary and they complement each other. 

First we must check that the process is stable with the Run Chart and only if it is we can use the Histogram to characterize the process behavior.

 The question is how do we know if the process is stable (apart from just our impression)? The answer is to use a statistical analysis program such as Minitab:

Both significant Clustering and Trends confirm that the process is not stable.

Defect Rate Comparisons

Open Variation.xls sheet Defects

This are the defect rates produced by the 6 operators during one week. 

The department manager should decide, based on this data, whether he/ she should take some action such as:

  1. Talk to Amparo to remind her of our zero defects commitment with the customer
  2. Congratulate Fernando for his results and, maybe, give him a prize
  3. Ask the process engineer to explain why Mondays produce more defects than Fridays
  4. Tell operators that anyone producing above 8% average weekly defects will be penalized

If you have decided on any of these actions you are wrong. If fact, they may be counter productive.

This is an example of overreaction on the part of management due to a lack of understanding of process variation.

To see this just press F9 to simulate another week with this same process. 

If we analyse the results of 4 weeks we notice that the differences among operators aren't that large 

How do we know if there is a statistically significant difference among the different operators or days of the week?

This analysis can be done with the Analysis Tools in Excel: 2 Way ANOVA

The conclusion is that neither the differences among operators or days of the week are statistically significant.

Management improvement actions, in this case, should be directed to improve the overall process to reduce the defect rate. The process owner may run a Design Of Experiments (DOE) to optimize the critical process parameters. 

 Process Control

Open Variation.xls sheet Control press Reset

  1. You are responsible to control a machine to insure the deviation from target is zero in every run
  2. You can set the adjustment value (+ or -) to be applied to the next run 
  3. Set the adjustment and press F9 for the next run
  4. Repeat for 25 runs

  1. Did you achieve your objectives of controlling the process to obtain zero deviation in every run?
  2. Why?
  3. What strategy did you follow?
  4. What could you have done differently?
  5. Can you be held responsible for these results?
  6. Why?

 These are the results of overreaction:

If we made no adjustments:

Before we start making adjustments we should have seen how the process behaves with no adjustments. We see that the process has random variation and it is well centered in zero: this means we can't improve it with our adjustments, in fact, we will increase the variation and make it worse. 

In this case the operator has been given an impossible task.

 Conclusions

  1. An understanding of process variation is essential in order to take the right improvement decisions
  2. Decisions based on one single outcome can lead to overreaction and making the process worse
  3. Statistical analysis is required to distinguish between a change in the process and intrinsic process variation
  4. Statistical applications such as Excel Data Analysis Tools or an application such as Minitab can help in this analysis
  5. Six Sigma education for professionals and management can be useful to adopt this new way of thinking

 The Obeya room is a "war room" used by process improvement teams to meet and solve critical multi functional problems.  The room walls are lined up with boards, highly visual charts and graphs showing program timing, milestones and progress to date and countermeasures to existing timing or technical problems. The team meets in this room regularly but team members can also visit the room, which is fully dedicated to the project, throughout the day.

Obeya Room Benefts

  1. Remove organizational barriers
  2. Visual management by displaying all relevant data required in the improvement project
  3. Encourage a collaborative environment through regular meetings
  4. Implement quicker, more effective solutions
  5. The whole team knows what is going on in real time

Some Practical Constraints in the Implementation

  1. Some companies can't afford the luxury of a fully dedicated room
  2. Some of the team members may be located far away so they will only attend the meetings
  3. The data displayed on the walls may, very quickly, become obsolete: some team members may be too busy to physically go to the room to update their charts
  4. Some team members may attend the meetings unprepared because they didn't have the time to analyse the data in the walls before the meeting

 Alternative: Virtual Obeya Room

The improvement team shares a folder in the cloud: Company intranet, Google Drive, Microsoft One Drive, etc.

This folder has the same charts and documents which were displayed in the physical Obeya room.

In this case each chart can be hyperlinked to other documents with more detailed information. 

Each chart has an owner who has WRITE access and the rest of the team READ ONLY access.

Obeya meetings are still held the same way but they can take place in any room with a large display. The room is only used during the meeting and then it can be used for other meetings along the day.

Some people have their meetings standing in front of the screen to keep them short. You may want to use a standing table to hold the portables.

The owner of each document is able to update it from a portable in the office or anywhere with a smartphone. Even during the Obeya meeting. 

The Obeya virtual room can be visited from anywhere at any time: for instance while visiting the line or a customer.

Some team members may be located in remote locations, in which case they can take part in the meetings with video-conference and have the same access to the virtual Obeya room as everyone else.  

This alternative may be put in place for free in a very short period of time: no IS application is required.

Process Value Stream Map

One of the charts in the Obeya room for a process improvement project is the Value Stream Map.

It is typically constructed by the project team after a detailed visit to the line and it may require more than one visit to clarify some specific points. 

With the physical Obeya room this may require travelling to and from the line and may be time consuming. 

An alternative is to build the VSM in the line itself while visiting with the smartphones or tablets of the participants:

  • The VSM is built directly in the cloud (Google Drive) and all participants visiting the line have write access.
  • As they move along the line they all agree on who is doing what and when.
  • Typing of the process steps in the Excel sheet can be done by voice. 
  • The VSM, as it is being built, can be shown to the line operators in order to validate it.
  • After the VSM is complete the same method can be used to collect process parameters (process time, WIP, etc.) in the VSM Excel visiting the line.

Actions Tracking Spreadsheet

A key document in the Obeya room is a sheet to keep track of all the actions committed during the meetings: who is doing what and when. 

In the virtual Obeya this can be done with a spreadsheet where all participants have WRITE access. 

Google Drive keeps track of all changes made to the document: who did it and when.

Instead of committing actions "before the next meeting" you can commit  date and time. The moment the action has taken place the person responsible can enter the timestamp it was done from a smartphone with a single click. 

With this approach all team members have real time information on the project status on their finger tips no matter where they are.

 System constraints are key when it comes to optimizing our process. The process bottleneck limits the overall throughput and it determines such things as manufacturing lot sizes. 

With this simple manufacturing line simulation you can experience the effects of alternative solutions in order to maximize profit. 

Download Excel file:  TOCeng4.xlsm

Close other Excel files before you open this one and enable Macros.

Process Objective

Run the simulator to obtain the maximum profit after one simulated week. 

You have an initial capital of 1000 € which you can use to buy materials to feed the blue, green and orange machines. 

The green machine performs 3 operations: b, c and d. All parts should be processed through all 3 so you should decide what manufacturing lot size you want and process the lot through each of these operations. Before each operation there is a setup time. In the same way the orange machine has 2 operations: e and f. 

The market will accept any amount of product P with a price of 70 €. Spares P1 and P2 can also be sold but their quantities can never be above the number of products P already sold (if you have already sold 5 P's you can sell, if you want, 5 P1's and 5 P2,s).

Fixed expenses amount to 2000 €/ week and they will be subtracted from the cash balance at the end of each week. 

Week 1 will start with an empty line so you can simulate one single week leaving an empty line at the end.

You can also simulate several weeks, in which case you don't empty the line at the end. 

 Simulator Operation

You operate the simulator with control buttons:

You can either press the start button or use Ctrl + s. The same with the others. The reset button will empty the line and start simulation from zero.

The counter will tell you where you are:

One week is 5 working days of 8 hours. The simulator will stop at the end of each day: just press start to continue.

You start by buying materials based on the lot sizes you have decided and you must select the operation you want to run in the green machine from the pull-down menu: b, c or d.

The same with the orange machine: select e or f.

You can see the details in the Help sheet.

To transfer to the next machine type the amount to be transferred on the yellow boxes. 

Financial control

You can control your financial situation in real time:

You can buy materials as long as you have a positive balance. 

System Constraints

You may want to try your manufacturing strategy with this simulator before you go into a deeper analysis.

These are the constraints of the different machines:

The bottleneck of the whole line is therefore the blue machine (operation a): each product P will need 60 minutes of this machine. 

You will notice that we are only considering the process times (not the setup times). The reason is that the influence of setup times can be eliminated by using large enough lot sizes as we will see later.

Another constraint is the fact that all products P and spares P1 need machine a (the bottleneck). Spares P2, although they don't need machine a to be produced they can't be sold unless products P (which need machine a) have been sold. 

The bottleneck dictates how much we can produce and therefore the profit. We must focus on optimizing the bottleneck time to maximize profit:

To produce a spare P1 we need 60 minutes of bottleneck time and obtain a profit of 30€. If we use that time to produce a product P this allows us to sell also a spare P2 (which doesn't use the bottleneck) and the profit will be 70€.

The conclusion is that we should not produce any spares P1.

Theoretically we should be able to produce and sell 40 P's and 40 P2's per week.

 Lot size

If we decide to produce only P and P2 it will take 60 minutes of bottleneck a to produce one of each. In the green machine we will need to process 2 units: one for P and one for P2; this will take 18 x 2 = 36 minutes of process time.

To process a lot in the green machine we will need 3 setups of 40 min (total 120 min) and 18 x lot size processing time.

During this time bottleneck a must process lot size/ 2 units (only for P). If we dedicate all spare time in the green machine to do setups we conclude that the lot size is 10. 

Indeed, to process these 10 parts we will need 300 minutes which is the time it takes to process 5 parts in the blue machine a.

This means that if we reduce the lot size below 10 the green machine will be more restrictive than blue a so it will become the new bottleneck.

In practice to avoid the green machine from becoming the bottleneck we must leave a margin choosing a lot size greater than 10.

If we apply the same reasoning to the orange machine:

In this case the minimum lot size is 8. It may not be practical to have different lot sizes in both machines so we may decide on a value above both such as 12 to compensate for any inefficiencies.

Possible Results

Theoretically starting with a full line we should be able to produce and sell 40 P,s and 40 P2,s which gives us a weekly margin of 40 x 70 = 2800 €. If we subtract the weekly fixed cost of 2000 € that leaves us a profit of 800 €

Starting with an empty line and leaving it almost empty at the end of one week we obtained the results:

Capacity Utilization

On the top right corner of the simulator we can keep track of the capacity utilization on each of the machines.

At the end of the week we obtained the following results:

The first thing we notice is that the bottleneck a has been producing 100% of the time: one minute lost in the bottleneck would be a loss for the whole line.

The green and the orange machines have been stopped at the end of the week in order to empty the line and also due to inefficiencies on each setup. 

Machines g and h were stopped at the beginning of the  week due to the empty line and also along the week due to their excess capacity. 

 Conclusion

System constraints need to be considered when it comes to optimizing a process.

The bottleneck defines the maximum possible throughput for the total process.

The bottleneck defines the rate at which product should be started in the line: starting above the bottleneck capacity will only build up Work In Process and it will not increase throughput

In machines with several operations we want the minimum manufacturing lot size but not so small that it becomes the bottleneck of the total process.

Capacity utilization should be 100% in the bottleneck but not in the rest of the operations.