Inter-arrival times

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lkoomen
Posts: 1
Joined: Friday 19 January, 2018 - 12:36

Inter-arrival times

Post by lkoomen »

Hello there!

First of all I want to say that I am a noob and do not have much experience with ED, so my apologize if the story is bit fuzy.
So now here is the story. I have received a case study about a supermarket that is having trouble with waiting lines especially on Saturdays. There are 8 check outs. The service time is based on the number of products customers buy, and this is put into an emperical distribution (max of 50 products).
I have two strategies first one is:
1. 1 server for people with 10 or less articles and the other 7 servers are open for the other customers.
2. I categorize the products and direct customers to a specific check out so: 1 server for 1-10 products; 3 servers for 11-25 products, 2 servers for 26-37 and 2 servers for 38-50 (I refer to them as categories).

So now my starting point was a simple strategy were all 8 servers are open and available for everyone. I used an inter-arrival time of NegExp(20.9), based on some data I received for this study. But for the upper-described strategies they are different: 1. for server 1 inter-arrival time is NegExp(83.9) and server 2-8 its NegExp(28). For strategy 2 the inter-arrival times are also different per categorie negexp(74,9); negexp(49,9); negexp(123,4); negexp(161,4).

So now my problem is that I do not know how to model these strategies with the different inter-arrival times since they depend on the number of products. What I modelled now is just with the inter-arrival time of NegExp(20.9), but I know this cannot be correct since customers with 1-10 products arrive in a different pattern. What I do not understand is how to connect the emperical distribution and the inter-arrival times.

Hopefully I explained this problem in a way you can understand! I put my model of the first strategy in the attachement so hopefully it will becomes more clear.

Thanks!
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Case Studie Strategie 2.mod
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tobias.reithmann
Posts: 7
Joined: Monday 02 March, 2015 - 16:34

Re: Inter-arrival times

Post by tobias.reithmann »

Hi Ikoomen,

please correct me if I'm wrong, but I understand your situation as follows:
  • At first you had two independent distributions: one for the number of products and the other for the inter-arrival times of the customers.
  • Then you changed to two different strategies: one with only a single fast check-out and the other with multiple categorized check-outs. What both strategies have in common is that you loose the independency of your distributions.
I don't know how you calculated the new inter-arrival times of your second approach, but it seems that they are a fixed parameter of the simulation. The important fact is that you already know in advance how many products the next customer of server 2 will have, namely between 11 and 25. So you create customers depending on categories instead of the number of products. So each category should get its own source with its own inter-arrival time. The only thing you must adapt is the empirical distribution of products which now has to be divided between the categories. There are two ways to do that:
  • Stick to one distribution and draw until you get a number that belongs to your category.
  • Calculate an separate distribution for each category (1..10, 11..25, 26..37, 38..50) based on the single one (1..50).
Best regards,
Tobias
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