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Investigate whether or not my local petrol station would benefit, in the way of cutting waiting times, from having more fuel pumps open.

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Introduction

Decision and Discreet Coursework Aim: To investigate whether or not my local petrol station would benefit, in the way of cutting waiting times, from having more fuel pumps open. By doing this I hope to be able to simulate opening enough pumps in order to create waiting times less than 1 minute, what I would be willing to wait at a petrol station for petrol. The way in which I will do this is by collecting sufficient data from my local garage that would enable me to simulate 20 cars using the petrol station. The data of which I will need to collect to complete a simple simulation is: Arrival Time of Each Car: This will allow me to calculate an inter arrival time of which is needed to simulate the time in between cars arriving at my garage. Arrival Time of Car n+1 - Arrival Time of Car n = Inter Arrival Time n = number of car in order of arrival This will be done for all of the cars of which I have collected data for. I will then group these figures in sensible ranges, of which I can refine later, to calculate the probability of each inter arrival event range occurring. Length of Service of Each Car: I have decided that the most accurate way of calculating length of service will be to record the time in between the customer exiting his/her vehicle and re-entering it. Time Customer Re-enters Car - Time Customer Exits Car = Length of Service This length of time will be the length of service. ...read more.

Middle

(N.B If the car has a petrol cap on the left side, it would go to the right side of the fuel station to fill, for convenience). I calculated probabilities of petrol cap side by collecting data showing during the passing of 40 consecutive cars 26 had caps on the left side and 14 had caps on the right. I then calculated the probabilities of each event, left/right, occurring using the formula: Number of Cars With m Side cap / Number of Cars * 100 m= side of car (left/right) In the same way as was done with inter arrival times and service lengths I created a lookup table that was to be used in my simulations. No ranges needed to be created, as there were only two outcomes possible, left or right. See data sheets for all lookups. Simulation 4 now takes into account what side of the car the pump is on and then assigns it to the pump that is earliest free out of the necessary side. As it can be seen from simulation 4, although there are more pumps than that of simulation 3, the average mean waiting time has increased. The mean waiting times range from 1.75 seconds to 102.73 seconds. The increase is due to the fact that I have failed to include an unless statement to shape the way in which 'although naturally the customer would go to its necessary pump side, coinciding with the side of which the petrol cap is on, if both these pumps are being used, to go to the next pump available or is without a customer, even if it is on the opposing side'. ...read more.

Conclusion

However, as money plays a major role in development, a 3 pump station would do the optimal job and therefore I can conclude, in order to decrease customer waiting times to less than 1 minute, my local petrol station would have o have 3 petrol pumps. Evaluation: My simulations worked very well in the fact that they 1,2, 3 and 4 produce results, which with little assumption would benefit customer satisfaction. Although I was unable to collect sufficient data to properly design simulation 4, the idea works. If I was able to generate a calculation that would outline its defaults then I am sure it would decrease waiting times from that of simulation 4's. If I had enough time, I would also refine each simulation as it could possibly bring the simulation of a 2 pumps stations mean waiting times under 1 minute. Each simulation is not bias as I have used random numbers using spreadsheet software which means to human tinkering could have changed these random numbers, this can be seen as each random number cell has the formula 'RAND()', showing the computer has done it itself. To make it more sensitive, I would have to measure times to decimal seconds in order to produce even further accurate results. The way in which I have kept all random numbers to 6 decimal places has also kept it fair. So from this evaluation I can say I have successfully created a simulation able to predict the optimal number of pumps needed to satisfy customers and staff at my local garage. Data Sheets: Raw Data Lookups Simulations 1,2,3,4 and 5 Simulations 1,2,3,4 and 5 Average Mean Wait Times Simulations 1,2,3/5 and 4 Annotated Formula ...read more.

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