A Grocery Store Has Three Checkout Lanes Assignment

Assignment Task

A grocery store has three checkout lanes (checkout 1, checkout 2, and checkout 3), each with a single checker. Shoppers arrive at the checkout area with interarrival times having an exponential distribution with a mean.

The shoppers enter the lane that has the fewest number of other shoppers already in the queue (not counting any shopper already in service at the checkouts). If there are ties for the shortest queue, the shopper will join the lowest-numbered checkout (that is, 1, 2, or 3). The checkout service time for all shoppers follows an exponential distribution with a mean of 6.35 minutes regardless of which checkout they choose.

Create a simulation of this system and run it for a single replication of 48 hours (starting empty and idle, and with the first shopper's arriving at time zero) to (1) determine the average and maximum time from when the shopper arrives at the checkout area until they complete their checkout. (2) Add a plot to track the length of each queue on the same set of axes, color-coded. (3) Add some text/drawings to your simulation

Two part types arrive to a three-workstation system.

Part

1. Arrives according to an exponential distribution with an interarrival-time mean 5 (all times are in minutes); the first arrival is at time 0. This part type is first processed at the workstation and then the workstation.Its processing time at workstation 1 follows a triangular distribution with minimum 2, mode 2.5, and maximum.

2. Arrives according to an exponential distribution with interarrival time mean the first arrival is at time. This part type is first processed at workstation and then the workstation. Its processing time at the workstation follows the same distribution as does part type 1 at the workstation. Its processing time at workstation 3 follows a triangular distribution with minimum mode and maximum. Run your simulation for a single replication of 2,000 minutes and observe the average and maximum time in system for each part type separately; put a text box in your model with your results. 

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