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Contact: Alec Jezewski CDT (C-Desk Technology) www.visualrota.co.uk

The Old Vicarage, Station Road, Rolleston, Newark, Nottinghamshire, Great Britain, NG23 5SE

The Software "Call Centres Simulator" is aimed at solving some of the problems faced by call centres when trying to discern how many operators are needed at any given time.

The Call Centre Simulator is software, which simulates staffing problems and enables you to try out solutions. The main purpose of this software is to enable you to find out exactly when a problem occurs, why it occurred and the best solution to use in the future.

It is to questions like these that the answers must be known in order to staff correctly. After all it’s no good knowing how many staff are needed if there has been no allowances made for operators having breaks.

The tricky situation is when the call rates increase from one level to another and a decision has to be made when to start another operator and for how long. Similar situations occur when operators take breaks, e.g. how long can they be away from their station before calls are delayed for too long, and how long must the interval be between one operator returning and the next one going off for their break. No other program solves this.

The program allows you to run the simulation of increasing call volumes, calculate the call delay and show how many calls are unanswered. When another operator(s) is brought in, they can be seen to reduce the call delay. When the call delay reaches zero, all the calls are answered.

This model can be of a lot of help to call centre managers when trying to determine how many operators have to be on duty because unlike equations to calculate average waiting times of customers the program will calculate individual waiting times quickly. When other Simulators or Formulas calculate "Average Call Delay" the Call Centre Simulator Calculates each callers Delay. This is of a lot more use because in practise to calculate "Average Call Delay" is illogical. If the "Average Call Delay" is above zero then the operators can not handle the rate at which calls come in. Therefore you have two results, either the callers hang up and you loose their business, or the call delay tends to increase to infinity. However using the Call Centre Simulator you can test different solutions to find the exact point when and for how long an extra operator is needed.

Since the program is a stochastic model the program can be run many times with the same parameters and it will produce different results each time to give you a range of results just as each day is different in ‘real life’. Thereby achieving a better idea of the situation. The program can also be used to test what would happen in different situations, for instance, if an operator went on a break when everything was going smoothly. Would everything be going smoothly ten minutes later?

By using the data available from call centres, a stochastic simulation model of the operations of a call centre is created.

This model is based on queuing theory, mainly a queue of exponential interarrival time distribution, deterministic (constant) service time distribution, with c parallel servers. This is a queue where the arrival rate of customers is memoryless and random.

A Call Centre is most profitable when staffing numbers are correct for the volume of calls and the level of service required by the client. Some Call Centres attempt to overstaff, e.g. if each incoming call generates a large profit, or when lives are in danger. This is because every missed call is expensive or peoples’ lives are put at risk. A Call Centre can also understaff so that all operators are working at 100% however, a certain number of calls will be abandoned. This can be simulated as well. However, a simple calculation will show this. E.g. if the operators can handle only 100 calls/hour then when the call rate is 200 calls/hour, obviously 100 calls are abandoned.

The best way for a call centre to operate is to work out the cost of one extra member of staff and calculate the amount of profit that will be created by employing them. E.g. if one extra operator means that 10 more calls per hour will be answered, and each call generates a profit of £5 and if the operator only costs £7 per hour then it is worth employing that extra operator.

For a certain number of calls or a call rate, and for an average time for each call, the program can work out the best number of operators to answer the calls. If too many operators are on duty, then the call delay is zero and you can see this immediately. As the operator numbers are reduced, there comes a point when the Call Delay is noticeable. It is unrealistic to expect the result to be always an exact number of operators for any combination of parameters. You will always have to decide whether you go for just being over-staffed or just being under-staffed in any situation.. Hence you never have exactly the correct number of operators on duty because it is impossible. There are other ways to determine staffing levels such as using the Erlang formulas, however that does not tell you what is happening as the calls are coming in, which makes decision making very difficult. When there is a problem with the number of staff at a certain point, Erlang formulas will not tell you what is happening or how to rectify the situation.

Call operators are Humans, not machines and as such, they do not act and react like machines. In a Call Centre operation, due consideration must be given to ‘breaks’ in the day for drinks, food, etc. also for human nature e.g. a propensity to delay the start of work and to finish early. This behaviour is difficult to model and is not modelled in this program. What can be modelled is the average response from responsible people prepared to share work equally. For instance, it is possible to model a ‘slow’ operator that takes longer to deal with a call than the average. This would show up as a longer call delay average for all staff and could be plotted separately if required.

Your program will arrive as an email attachment, do not try to run it, you need to save it first. The Call Centre Simulator is a Excel/Lotus 123 template file, which is identical to all other Excel/Lotus 123 files.

Instructions

1. Open email and Save attachment to a new folder called "Call Centre Simulator".
2. Make a backup copy in another folder called "CCSbackup" so, if you accidentally delete the original file, you can retrieve it from here.
3. Open Excel/Lotus 123
4. Use File/Open to open the call centre simulator file just as you would for any other Excel/Lotus 123 work file.
5. Save different sets of results under different names so you can retrieve past simulations.

Figure 1

Figure 1 shows the input and results table.

Incoming Call Rate is the number of calls a call centre receives per half-hour. These include all calls abandoned and duplicate calls when abandoned calls are redialed into the call centre. Half an hour is defined to be from the start of the hour (or half hour) e.g. 12.00 to one second before the next half-hour e.g. 12.29.59. Call centres will always have some variation of these figures available.

Incoming calls Rate of change. Call centres never receive a flat rate of calls. The number of calls fluctuate depending on the time of day, e.g. people discover electricity faults which have occurred at home during the day when they get home from work, so an electricity company will have more calls after 5.00pm than at 2.00pm. This is entered as a percentage increase e.g. if the call rate increases from 50 to 100 calls per half hour you would enter x%, where x is the percentage increase in the two hundred calls covered by the program, e.g. 100. However this parameter has not been solved fully therefore a degree of inspection is needed.

Average length of call is the time it takes to deal with the call from initiation to wrap up. i.e. time required on the phone and the time to deal with any paper work etc. produced by the call. Call Centres will have this information available. The program does not take this to be a random variable because it is not random but dependent on human nature.

Number of Operators is the number of operators actually on duty to answer calls during the half-hour. The current maximum number of operators is set at 25, however this could easily be expanded indefinitely for special cases.

Initial Call Delay is the average number of seconds that a call is delayed for, at the start of a cycle. This is to model any situation where you are already in trouble and need to find a solution. When running a simulation, you will cause the problem on the first run and try out solutions on subsequent runs. You might already have data or the program will find this data on a previous run. In the first run this parameter is set to zero, in order to find the delay on the last call. When you have found the delay on the last call enter it on consecutive runs as the Initial Call Delay.

Calls Prematurely Terminated is a percentage of the total number of calls entering the system. Callers do not hang on forever and if they have been waiting too long will hang up. The call centre will have this information available to them, however there is a problem when a call is started in one half hour and then abandoned in the second so this is not a hundred percent accurate. Call Centres will always have abandoned calls therefore they must be included in the calculations.

Calls waiting initially is the number of calls waiting to be answered at the start of the cycle. Call Centres will know this parameter.

Average Call Delay is the average delay experienced by the 200 calls. This is to be used in collaboration with the graph "Call Delay".

This is to be used with "Initial Call Delay".⁵ This shows the time that the last call was answered.

This shows the time that the last call arrived. In this example the 200^th caller would have arrived at 40.4 minutes into the cycle.

Last Call Delay is the time it took to answer the last call. In this example the last call was delayed for nearly 11 minutes. This is an unacceptable level of quality. Therefore more operators would be required.

Figure 2

Figure 2 shows the Call Delay over the 200 calls.

This graph can be found by clicking on the tab marked "Call Delay" which is highlighted in the figure.

In this example the call delay is increasing with each call, therefore it is clear that more operators are required to combat this problem.

Figure 3

Figure 3 shows the Average Call Rate/per half-hour over the 200 calls.

This graph can be found by clicking on the tab marked "Call Rate" which is highlighted in the figure.

The above graph shows that whilst the average number of calls per half-hour is 150, the variation in time between incoming calls can vary between 125 and 170. This average is the rate at which any 5 adjacent calls come in. This shows the randomness of the incoming calls using the random factor and an appropriate Poisson Distribution.

Every time the F9 key is executed, a different set of results will be calculated. In an operation such as this, there is not just one result, each ‘day’ is different and will produce different data. The program needs to reflect this randomness by producing a range of results and then staff accordingly.

Below are 4 results, all based on the same parameters.

The same data obviously produces different results due to the randomness of the incoming calls. As a Call Centre Manager you will have to gauge your response to this variation when staffing a call centre. In this example, clearly all the call delays are less than 30 seconds and are acceptable.

It is important never to rely on one set of results from the program, all results are unique solutions. A range of results needs to be found to staff accordingly

Because the Call Centre Simulator generates many sets of results to each set of parameters, you will need to save those results that are important. Each time you press the F9 key a new set of results is produced.

To store any set of results and graphs, there are a number of ways to chose from.

Each set of results is saved as a picture in a Paint program. To do this, use the Print Screen button on the keyboard. This method stores the results as a picture snapshot on the Windows Clipboard and these pictures can be pasted directly into a report, or as gif or bitmap images for later use.

This method stores the results in the program on separate sheets. The method is:

1. In Excel/Lotus 123, open the Call Centre Simulator.
2. Use Create/Sheet to set up a new sheet. Name this sheet ‘results’ or similar.
3. Use the Simulator until you obtain a set of results you want to keep.
4. Use the mouse to highlight the input and results cells A4:B15 and use edit/copy or Ctrl+C to copy the results onto the Windows Clipboard.
5. Go to the result page and click on an empty cell in an area of the sheet large enough to paste your results.
6. Use Edit/Paste Special and a window opens asking what you would like to do. Tick the box labelled ‘Formulas as values’



7. This will paste the values onto the sheet.
8. Repeat for all the set of results that you would like to keep.
9. You can save the graphs in the same way alongside the table of results.
10. Click on the graph you want to save and use Edit/Copy or Ctrl+C. and Edit/Paste Special to paste it into the results sheet. However, this time you can save it as a picture, rather than a graph.

We have the following parameters.

Call Rate is 100-calls/half hour, there are 10 operators, average call length is 180 sec’s, no calls waiting, no initial delay. See figure 4.

Figure 4