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Queuing – Production and Operations Management
Queueing theory tries to analyse why such waiting lines occur and what solutions can be offered to improve the desired performance. Should there be one clerk, or two, or three clerks at a counter? How should jobs waiting at a work centre be taken up for processing—in the order they arrive, or in accordance with their increasing processing times, or in accordance with their due dates? Such are the questions which queueing theory attempts to answer.
Thus, from the above, it is obvious that the delays or stoppages in a flow system are called ‘Queues’ or ‘Waiting Lines’.
FEATURES
Queueing Systems have the following three features:
Arrival
(a) Commuters arriving to buy railway tickets.
(b) Parts received to be used for assembly in production department.
(c) Invoices arriving at an order desk.
Arrivals can either be single item or grouped with items; controlled or uncontrolled. Occasions, where the arrival process is almost Under control may be called ‘deterministic’; while occasions where there is no absolute control may be called ‘probabilistic’.
Service
Examples of service are as follows:
(a) The number of commuters that a railway ticket counter clerk attends to.
(b) Count of parts being assembled in Production.
(c) Count of breakdowns being resolved in the Maintenance department.
(d) The number of orders or invoices processed by the order clerk.
The waiting line characteristic is influenced by the service feature being offered. It may be important to analyse:
(i) Whether the service-time or service-rates as mentioned above, are constant or are probabilistic?
(i) Whether service-rates are dependent upon the queue-system itself? For instance, does a barber consciously or subconsciously increase his speed looking at the number of people waiting for his services on a Sunday morning?
Queueing Discipline
It refers to a single rule or a group of rules which describes the order in which the arrivals will be serviced, for example:
(i) First come first served.
(ii) Serve the shortest duration next; this means that you service the operation taking the shortest time first, next shortest second, and so on. (For instance, a barber trims the moustache first, shaves next, and does the hair-cut job thereafter.)
(iii) When there are more than ten commuters waiting in a queue at the booking office, open another counter for issuing tickets.
(iv) Serve the last arrival first.
(v) Serve the job taking the longest amount of time first, and proceed to the next longest job.
(vi) Serve each unit in the queue system partially. (for excam ple a barber attends partially to one customer and then move to next customer, thus attending all customers though also keeping them waiting. Many manufacturing systems behave on similar lines.)
(vii) Serve the jobs that are intrinsically high-priority jobs by stopping work on lower-priority jobs. If an order from a prestigious firm arrives, give it preference over all others, even those in process, and take it up immediately for manufacture.
Hence, queue discipline simple refers to development of priorities scheme operating in the servicing of various units in a system.
DESIGN
The design of the queue system, i.e. the service process, the prioritisation of the units for service, and perhaps the arrival process as welt, depends upon what the queue system wants to achieve ultimately, i.e. the desired objectives or the set of criteria with which the system will be measured for performance. One cannot expect the criteria to be the same for a consumer-product industry and a defence industry or ordnance factory, an outpatient check-up ward and a casualty section in a hospital.
ANALYSIS
The questions to be asked in queueing theory analysis are, for example:
(a) What is the average number of units (i.e. customers, jobs) waiting in the queue?
(b) What is the average waiting time for the units in the queue system?
(c) What are the criteria of performance for the queue system?
(d) How might one design/change the service and/or arrival characteristics of the system?
(e) How might one, suitably, design the Queueing Discipline to achieve the desired objective/s?
(f) In the achievement of one objective, how can the other objective/s possibly be compromised?
The analysis of the Queueing systems should provide us with a number of scenarios for policy alternatives with the corresponding expected results. Queueing theory is a decision-making tool for the manager’s benefit, just as the other Operations Research techniques.
CHARACTERISTICS OF SINGLR CHANNEL SINGLE SERVICE QUEEING SYSTEM
This is one of the basic analytical queueing models. The assumptions are:
(i) Single channel single service.
(ii) The distribution of arrival rates is modelled by Poisson distribution.
(iii) The distribution of service rates is also modelled by Poisson distribution.
(iv) The Queue Discipline is first come first served (FCFS).
(v) It is possible for the waiting line to grow infinitely long.
(vi) The queue system does not influence either the arrival or service rates.
(vii) Each arrival (customer) needs the same unit of service.
USE OF SIMULATION
Analytical solutions are available for two/three work centres cases, and that too for a limited number of situations. In such contexts digital simulation being done by computers, is helpful. Job-shop problems have been handled by ‘simulating’ the arrival, processing, and queue discipline and then evaluating the simulated system’s performance on the desired criteria.
Monte Carlo Simulation
Monte Carlo is an approach for simulating the probability distribution by associating and then selecting random numbers. Monte Carlo offers inclusion of many real-life constraints as an example, customer visiting a shop mostly in evening or on holidays, such constraints can easily be applied for digital simulation model.
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