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!
Inter-arrival times
Inter-arrival times
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- Case Studie Strategie 2.mod
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Re: Inter-arrival times
Hi Ikoomen,
please correct me if I'm wrong, but I understand your situation as follows:
Tobias
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.
- 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).
Tobias