Thursday, January 26, 2017

Waiting Line

How do waiting lines form?

 Waiting lines form because of a temporary imbalance between the demand for service and the capacity of the system to provide the service. The predominant issue in almost every waiting line situation is a trade-off decision between the system capacity and the waiting time.
          The added cost of providing more rapid service (by increasing capacity) must be weighed against the inherent cost of waiting. For instance, suppose some “x” quantity of product Y is waiting for a stamping machine “A”. The cost of installing one additional stamping machine could be compared with the value of increased throughput for the product Y. The decision could then be reduced to dollar terms and the choice easily made. However, the cost trade-off decision is not always straightforward. Consider a fast-food restaurant which experiences variable demand and variable service time since it does not know exactly what each customer will order (and how much will be ordered).  Therefore, it is necessary to design a service system with adequate but not excess capacity.
                Figure 1 illustrates the essential trade-off relationship between the capacity and the waiting line costs. The cost of waiting line is at a maximum when the service capacity is at its lowest. As service capacity increases, waiting line decreases and does the cost associated. The total cost curve indicates an optimal cost point where the service capacity and waiting line curves crossovers.

An Example

            For instance, consider the repair department of a large urban taxi company.The demand for cab repair can be met with minimal waiting time if number of service people and resources are increased which means a high cost of service capacity, especially during periods of low demand. On the other extreme, minimizing the service capacity would increase the waiting line (and the associated cost). As shown in Figure 1, the aggregate cost has a lowest cost at some optimal service capacity. For a taxi company, it is imperative to understand dynamics of the waiting line system which includes the arrival and service patterns, population source of taxi to be repaired, and the service system itself.           

What are the factors affecting a waiting line?


             Some of the major factors that need to be considered in analyzing waiting line situations are described below:
(1)   Customer population, their arrival rate and distribution – The customer population can be considered to be finite or infinite. If rate of arrival is not affected by the size of waiting line, the population is considered infinite, otherwise it is finite. For instance, if there are only 10 taxis in total, the arrival rate of the last taxi for repair would be the least since all other taxis are already in the waiting line or are being serviced. Other factor to be considered is distribution of arrivals, whether it is constant or variable. As mentioned, the demand for taxi repair has a random arrival distribution. Hence, periods between successive arrivals must be analyzed to see if these follow some statistical distribution.
(2)   Servicing system – The service system is characterized by the number of waiting lines, the number and arrangements the servers. A single line with multiple servers increases the customer’s perception of fairness in terms of equitable waits. The multiple waiting lines are useful for space considerations or during use of the specialized servers are used. Multi-server systems have parallel service providers offering the same service. However, not all taxis will have identical repair issues and hence multi-server may be useful only for general repair diagnostics.
(3)   Service rate, priority rules and exit system – The service rate is the capacity of the service system. A priority rule determines who is to be served next. Some frequently used priority rules are “first come-first served”, “best customer first”, “emergency first” and so on.  It is imperative to use a priority rule that best supports the organizational strategy or a given situation. A first-come, first serve model for the taxi repair may be biased against those taxis requiring short service times. Another factor to consider is an exit system. For instance, once a taxi is served at one station, does it need to come back to the same station? When it returns to the source population, it immediately becomes a competing candidate for the service again increasing the overall waiting line.
Although waiting line situation affects all providers of services, nature of those situations are seldom same. For instance, a waiting line in a hospital needs to have an “emergency first” priority model. This may not apply to a car repair center owned by a taxi company as an  example. In a repair center owned by a taxi company, its management would know (or should know) in advance which taxis need repairing and when. This is not the case in a fast-food restaurant where demand is rarely known in advance.  Therefore, a more efficient servicing is possible in the latter case.

How to minimize a waiting line? (using taxi repair center as a use case)


Let us consider an example of a repair center of a taxi company. Consider a scenario of excessive delays during repair.To address the problem of delay and unavailable resources that a company faces, there are several approaches its management can apply:
(a) Use of multiple service channels and single waiting line.
(b) Use of multiple service channels and waiting lines.
(c) Use of multiple phases for repair.
Since different taxis may have different repair needs, multiple channels coupled with multiple phases to address different repair tasks might be the optimal approach. A possible waiting line system to handle the issue is illustrated below:
As shown above, there would be more than one waiting line – classified according to whether repair is general or special. For special repair, there would be an inner queue (when needed) to handle more specialized repair.

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