Warm-up period in simulation

[4tun8]

Why do we need to have a warm-up period in a simulation model?

[rlote]

Without warm-up period, the simulation model would start empty (no products at any of the machines), but real factories almost always start with work-in-process inventory. A situation where you would not need a warm-up time in a simulation might be when you are simulating a situation which starts empty each day: like a shop, or a parking lot. However, even in these circumstances you would probably want to separate off the results you get during the early part of the day from the results under peak conditions because knowing the 'average' performance of an operation which never works under 'average' conditions is probably not worthwhile. Most simulation packages contain facilities to set a 'warm-up' time during which results are either not collected, or which can be separated off from the main results collection period.

[ewilliams]

Excellent comments. A bank (opens empty and idle each day) model does not require warm-up (and indeed should not have warm-up). Common examples of situations requiring warm-up are manufacturing in general, hospital emergency rooms, 24-hour telephone exchanges, etc. Sometimes it is possible to shorten the amount of warm-up required by initializing storages (buffers) in the simulation model to half-full (versus default of empty), thus starting the model closer to average conditions. Let us say model results are collected and analyzed in 5-day week units, and 4.3 days of warm-up are required. It is better and more convenient to warm up the model for 5 days (one weekly unit) to make its results easier to interpret.

[Nirmala]

How could we determine the warm-up period for a simulation model?

[rlote]

Here is the procedure to determine warm up time:
1) Decide what performance measures are of interest to you. For example you might be interested in the number of products leaving the factory, or the utilization of a machine or the length of a queue. If there is more than one then you might want to carry out this procedure for some, or all, of the measures which interest you and use the longest warm-up time indicated. Let’s just assume you are interested in the number of products leaving the factory.
2) Run the simulation for a short period of time. The amount of time you run the simulation for is dependent on what you are simulating but if the total time you wanted to run the simulation for was, say, a week (see below for how to decide this) then you might make this "short period of time" an hour. It needs to be an amount of time in which you might expect to get a few products out of the factory. Having run the simulation for, say, 60 minutes, record the number of products which have emerged from the factory. This will almost certainly be zero for the first 60 minutes! This is because of the nature of the need for a warm-up time. No products will have reached the end of the factory yet!
3) Run the simulation for another 60 minutes (or whatever time you have chosen) and record how many products left the factory in the second 60 minute period. i.e. the number which emerged between 60 and 120 minutes - not the total at the end of 120. Keep doing this and plot all the values.
4) The time at which the graph hits the steady state is the warm-up time of the model.

[rwilcox]

Does it help much (or at all) to "initialize" the model with some work items (e.g., put some in various buffers)?

[ewilliams]

Yes, this technique can shorten warm-up time (e.g., if the average content of a buffer is about 10 parts [the buffer may have a capacity of 15]), initialize the model with 10 parts there. In a typical situation, this initialization will need to be done for several or many buffers. However, I caution against embracing this technique enthusiastically to the extent of reducing needed warm-up time to zero.

[kvasudevan]

I will post a formalized methodology for finding warm-up titme of a simulation model. However, first a simple method. Plot a graph of throughput versus time. You should see a graph that increases initially and eventually stabilizes or falls into a cyclic pattern. The time of stabilization or repeating pattern is where your warmup period ends and results collection period begins.

[kvasudevan]

As promised, now for formalized methods to estimate warmup methods.
An easy to use method is the Welch's Moving average method, which involves conductiong multiple replications of the model to constructed a variable window moving average graph of throughput versus simulation time.

This paper (see link below) provides a quick yet comprehensive analysis of methods available for warmup determination including Welch's moving average method. Note that these methods are very useful in cases where the system response is variable and it is difficult to vissualy see the warm-up period.

http://www.informs-sim.org/wsc04papers/080.pdf

[ewilliams]

The paper by Professor Christos Alexopoulos at http://www.informs-sim.org/wsc06papers/017.pdf, "A Comprehensive Review of Methods for Simulation Output Analysis," is also useful, although less explicitly devoted entirely to warm-up period lengths than the previous suggestion.