Design Rate Simulations can create simulations to answer common questions in Operations Research. The following example illustrates a common operations research problem which can be approached with a simulation model of the system to answer capacity planning questions.
Design Capacity: Maximum theoretical output of a system
in a given time frame (also called Design Rate)
Effective Capacity: Output expected given current operating constraints
Actual Output: Output as measured
Utilization: (Actual Output) / (Design Capacity)
Efficiency: (Actual Output) / (Effective Capacity)
Expected Production: (Effective Capacity) * (Efficiency)
Textbook Capacity Planning Example
A consumer product company examines the production capabilities of a manufacturing line which formulates and bottles shampoo. The system has a Design Capacity of 120,000 bottles per 8-hour shift. Because one of the three packaging machines is currently running 20% slower than designed (32,000 instead of 40,000), the Effective Capacity is 112,000 bottles. In practice, the production manager is seeing an average of 106,600 bottles per shift during the past month, which is the Actual Output. Utilization of the line is (Actual Output) / (Design Capacity) = 106,600 / 120,000 = 88.8%. Efficiency of the line is (Actual Output) / (Effective Capacity) = 106,600 / 112,000 = 95.2%.
The Operations Manager is striving for 100% Efficiency, by better training, personnel scheduling, and preventive maintenance. However, assuming the line Efficiency stays the same, and a fourth bottling machine is added along with additional infrastructure to support it, what is the Expected Production?
Since the problem as described is contingent on the bottling line, we compute the new Effective Capacity of the four bottling machines as (112,000 + 40,000) = 152,000 bottles/shift. The Efficiency is already computed as 95.2%. Therefore the Expected Production is (Effective Capacity) * (Efficiency) = 152,000 * 95.2% = 144,700 bottles.
Real World Capacity Planning Example
Now what does this example have to do with simulation? In the classroom, not very much, because hypothetical system capacities are well-defined and systems under study are generally small and well-behaved. On the physical production floor, on the other hand, production processes which are only moderately complex can quickly make it difficult or impossible to analytically determine the system Design Capacity and Effective Capacity. Further, relationships between the various parts of the system can produce operational dynamics that are impossible to calculate analytically, making simulation the only realistic, cost-effective approach to understanding and measuring the system capacities. In effect, while the above definitions of Effective Capacity and Efficiency are important concepts that we use as a benchmark for measuring our system, in practice the actual measurement or calculation of such values may be impossible.
Suppose your conglomerate is envisioning contracting with this consumer products company to subcontract production of your line of shampoo. The subcontractor's salesman assures you they have the production capacity to handle your product, and the terms being quoted you are attractive. But do they have the Effective Capacity to fulfill your order on a regular basis? Are they going to add capacity to handle your product, and if so, how did they calculate how much additional equipment is needed? Furthermore, did they provide a spreadsheet and show you what they expect to happen to accommodate your product, or did they prove to you the Effective Capacity with a simulation of their system?
Capacity Planning using Simulation
Design Capacity: Maximum theoretical
output (calculated from simulation)
Effective Capacity: Output expected given current operating constraints (calculated from simulation)
Actual Output: Output as measured (unchanged from theoretical)
Utilization: (Actual Output) / (Design Capacity) (calculated from simulation)
Efficiency: (Actual Output) / (Effective Capacity) (calculated from simulation)
Expected Production: calculated from simulation
Simulated Output: System output as calculated by the simulation model. Because the model will use variables to describe the operation of the system, we are going to be able to have our Simulated Output compute either the Design Capacity, Effective Capacity, or estimate the Actual Output. This will be explained in detail below.
To establish the Simulated Output equal to the Design Capacity, we set the simulation model parameters to the most optimistic values supported by the equipment. Such values typically will not account for down time, sub-optimum operation, or poor production due to shift schedules or staffing issues. In this example, the three original bottling machines are the bottleneck, and they are each rated at 5,000 bottles per hour. Running the simulation for an 8-hour day, our Simulated Output shows the system has a Design Capacity of 120,000 bottles per 8-hour shift. Of course this is exactly what we expected, because the system is simple and the bottleneck is easily identified. It would be hard to justify funding a simulation model to get this result, but we have shown how to set up and use the model to find the Design Capacity.
To establish the Simulated Output equal to the Effective Capacity, we set the simulation model parameters to the most optimistic values supported by the actual line operation. Such values typically will account for down time, sub-optimum operation, or poor production due to shift schedules or staffing issues. In our example, one of the three packaging machines is currently running 20% slower than designed (32,000 instead of 40,000). We simply change that parameter in the model, our Simulated Output finds again the Effective Capacity is 112,000 bottles. Again this is as expected, and we have shown how to set up and use the model to find the Effective Capacity. Note we have used the same model, just varying one of its parameters.
In practice, the production manager is seeing an average of 106,600 bottles per shift during the past month, which is the Actual Output. This is physical production data, and as such is an important, if not the most important, value in our calculations. There is no substitute for this value, as both the theoretical and simulation approaches have no way of establishing how much actually got produced. However, these values are generally readily accessible in a manufacturing environment.
Now here is where the big twist comes in for the simulation approach. We want to find the causes of why our Actual Output is 5,400 bottles less than our Effective Capacity. And when we identify these losses, we are going to incorporate them into our simulation model, so that the resulting Simulated Output equals our Actual Output.
How do we understand the causes of our Actual Output being 5,400 bottles less than our Effective Capacity. There are a couple ways, the first being hard data collected on the floor which pinpoints each of the causes and provides a numerical value (for example, a conveyor feeding one of the bottlers is now starting to fail an average of 12 minutes an hour, and the bottler is starving at the rate of 50 bottles an hour or 400 bottles per shift). If the raw data is not available, informal talks with the production personnel will help estimate the scale of each production loss. The numbers can be estimates, but they need to be intelligent estimates. Obviously the better data one has describing the internals of the production system, the more accurate the resulting simulation can be.
We continue this process until we account for all 5,400 bottles of production loss. All the loss must be accounted for as an element of the simulation, because the goal is to have the Simulated Output match the Effective Capacity. The worst thing that can happen is that the production loss is mistakenly allocated to the wrong system elements, and you simply have to strive for an intelligent allocation. However, even if there is some confusion as to where the cause of the loss, all is not lost. Two or three (or more) scenarios of allocations can be theorized, and then the following exercises can be repeated for each scenario. With a decent simulation model and a methodical approach to problem solving, a few runs with varying scenarios will still help enormously is bringing the problem into
To establish the Simulated Output equal to the Actual Output, we set the simulation model parameters to the actual values supported by the physical line operation. Such values will account for all loss measured or estimated. We simply change the necessary parameters in the model, our Simulated Output finds the Actual Output is 106,600 bottles. Again this is as expected, and we have shown how to set up and use the model to find the Actual Output. Have we have used the same model, just varying some of its parameters? Possibly. However, more likely is that some elements of system operation have been shown to cause production loss, and those elements were not modeled originally. These elements must be added to the model so they can be varied to account for the losses. An experienced simulation engineer will know how to simplify these elements so they are as easy as possible to include.
At this point we are in pretty good shape, because we have a model which describes the key elements of the system to the degree needed to accurately predict the Actual Output. Now the sky is the limit with what you can do with this thing, and as soon as management sees what you've created, be ready for an onslaught of questions about what you could do with the production line. This is a good thing, because with an accurate engineering model of your production system you don't have to guess or estimate what the effect is going to be of many possible changes to the system. Change some model variables and review and understand the results. Print graphs for reports, display animations in meetings, and let the model answer the questions.
To finish this example, assuming the line Efficiency stays the same, and a fourth bottling machine is added along with additional infrastructure to support it, what is the Expected Production?
To establish the Simulated Output equal to the Expected Production, we set the simulation model parameters to the actual values supported by the physical line operation. We also change the model to include the proposed system changes, in this case the fourth bottling machine. We then simply run the model, and the resulting Simulated Output is equal to our Expected Production. That's it, done.
Wasn't this a lot of preliminary effort to get to the payoff? Yes, there is upfront work in building and validating the model. For a simple production line it might not be cost-effective, and a spreadsheet approach completely sufficient. However, once the production processes become complex, actual calculation of system operational values may be impossible. The trick is to know when the system is too big for a spreadsheet, and the questions are too important for an estimated answer.
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