Chapter 18 Objectives

 

 

  1. Planning and analysis of service capacity frequently lends itself to queuing theory, which is a mathematical approach to analysis of waiting lines.

 

 

·        The foundation of modern queuing theory is based on studies about automatic dialing equipment made in the early part of twentieth century by Danish telephone engineer A.K. Erlang

 

·        One reason that queuing analysis is important is that customers regard waiting as non-value added activity

 

·        Managers have a number of very good reasons to be concerned with waiting lines. Chief among those reasons are the following:-

 

    1. The cost to provide waiting space.
    2. A possible loss of business should customers leave the line before being served or refuse to wait at all.
    3. A possible loss of good will.
    4. A possible reduction in customer satisfaction.
    5. The resulting congestion may disturb other business operations and/ or customers.
    6.  
  1. The goal of queuing is essentially to minimize total costs

 

·        The two basic categories of cost in a queuing situation are: -

 

1.      Those associate with customers waiting for service and

2.      Those associate with capacity.

·        Capacity costs are the costs of maintaining the ability to provide services. Examples include the number of bays at a carwash, the number of checkouts at a supermarket and the number of line on the highway.

·        The cost of customer waiting includes the salaries paid to employees while the wait for service (mechanic waiting for tools, the drivers of trucks waiting to unload).

  1. The traditional goal of queuing analysis is to balance the cost of providing a level of service capacity with the cost of customers waiting for services.
  2. There are numerous queuing models from which an analyst can choose. Model choice is affected by the characteristics of the system under investigation. The main characteristics are: -
    1. Population source.
    2. Number of servers (channels)
    3. Arrival and service patterns.
    4. Queue discipline (order of service)

1.      Population source:- the approach to use the analyzing a queuing problem depends on whether the potential number of customers is limited. There are two possibilities: infinite source and finite source

·        Infinite source:- customer arrivals are unrestricted.

·        Finite source:- the number of potential customers is limited.

2.      Number of servers (channels): - the capacity of queuing systems is a function of the capacity of each server and number of servers being used. System can be either single or multiple-channel. (a group of servers working together as a team, such as a surgical team, is treated as a single channel system.)

Examples of single-channel systems are small grocery, stores with one checkout customer, some theaters, single bay carwashes and drive-in banks with one teller. Multiple-channel systems (those with more than one server) are commonly found in banks, at airline ticket counters, and auto service center, and gas stations.

3.      Arrival and service patterns: - waiting lines are a direct result of arrival and service variability.

4.      Queue discipline:- refers to the order in which customers are processed.

5. The operations manager typically looks at five measures when evaluating existing or proposed service systems. These measures are: -

1.      The average number of customers waiting, either in line or in the system

2.      The average time customers wait, either in line or in the system.

3.      System utilization, which refers to the percentage of capacity utilized.

4.      The implied cost of a given level of capacity and related waiting line.

5.      The probability that an arrival will have to wait for service.

6.       

6. Many queuing models are available for a manager or analyst to choose from. The most basic and most widely used models are: -

·        Single channel, exponential service time.

·        Single channel, constant service time.

·        Multiple channel, exponential service time.

·        Multiple priority service, exponential service time.

  1. Single channel, exponential service time: - the simplest model involves a system that has one server (or a single crew). The queue discipline is first-come, first served, and it is assumed that the customer arrival rate can be approximated by a Poisson distribution and service time by a negative exponential distribution
  2. Single channel, constant service time. The effect of a constant service time is to cut in half the average number of customers waiting line.
  3. Multiple channel: - A multiple channel system exists whenever there are two or more servers working independently to provide service to customer arrivals. Use the model involves the following assumptions:

1.      A Poisson arrival rate and exponential service time.

2.      Servers all work at the same average rate.

3.      Customers form a single waiting line(in order to maintain first-come, first-served processing).

4. Multiple priorities: - customers are processed according to some measure of importance. (e.g. hospital emergency waiting room).