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All previous contemplations were based on the idea that customers would be served in exactly the order in which they arrived. But is that an optimal procedure? The idea behind sequencing (which is also called triaging or prioritizing) is to determine, who should be served first, which is not always the customer who came in first (e.g. emergencies in a hospital). There are four basic models:
(1) First come-first-serve
This quite self-explanatory model (which is also known as FIFO = first in – first out) is easy to implement, seems fair and has the lowest variance of waiting time.
(2) Sequencing based on customer importance
Examples for this model are the prioritized treatment of emergency cases in hospitals as well as serving long-time or more profitable customers first.
(3) Shortest processing time rule
This model minimizes the average waiting time by putting the shortest job first and the longest job last. This does not impact the total working time but ensures, that those customers with the shortest working times get served more quickly. The problem with this model is, that it gives customers an incentive to claim false processing times (“I need only five minutes.”) in order to get served fist. For this reason, this rule is usually only used in manufacturing or in digital processing, where processing times can be accurately predicted (and no human customers are directly involved).
(4) Appointment rules
Some business are trying to solve the problem of customers not showing up in regular intervals by forcing them to show up in regular intervals through appointments. However, this model is quite impractical for many business (think about fast food restaurants or supermarkets) and downright impossible for others (think about emergency room treatment where individual demand is nearly impossible to predict).
The time in the queue is calculated as follows:
time in queue = activity time * (utilization / 1 – utilization) * ((Cv_a^2 + Cv_p^2) / 2)
activity time = service time factor (average processing time p)
(utilization / 1 – utilization) = utilization factor
((Cv_a^2 + Cv_p^2) / 2) = variability factor
Since the utilization factor is calculated as (u / 1-u), this means that as the waiting time gets higher, the utilization gets closer and closer to 1. The formula for the time in the queue always delivers an average value. This so-called waiting time formula can only be used if the demand is lower than the capacity. If the demand is higher than the capacity, the waiting time will ultimately not be driven by variability, but rather by insufficient capacity.
The total flow time of a flow object can be calculated as:
total flow time = time in the queue + processing time
If the batch size is so small, that the process step with the set-up time (assuming, that there is only one) becomes the bottleneck of the process, the process looses on overall efficiency. Thus, the batch size needs to be chosen in a way that assures, that it will not generate a new bottleneck.
If, however, the batch size is too big, any increase in capacity at the station with the set-up time (assuming, again, that there is only one) is ultimately of no use, because it will only lead to inventory piling up somewhere else in the process – wherever the bottleneck may be.
This goes to show, that the ideal batch size is one, in which the station with the set-up time has a processing time which is just identical to the process bottleneck. Only then will the batch size not lead to the creation of a new bottleneck or additional inventory pile-up. This is calculated as:
capacity determined by the batch size = capacity of the bottleneck
b / (s + b * p) = m / p
b = batch size
s = set-up time
p = processing time
m = number of resources