A grocery store has a total of four checkout lanes: three regular checkout lanes

Question

A grocery store has a total of four checkout lanes: three regular checkout lanes (checkout 1, checkout 2, and checkout 3), and a Fast checkout lane, each with a single checker. Shoppers arrive at the checkout area with interarrival times having an exponential distribution with mean 2.4 minutes. The checkout service time for all shoppers follows an exponential distribution with a mean of 6.35 minutes. Shoppers with a service time of less than 5 minutes will always use the Fast checkout and those with service times that are 5 minutes or more will choose from the three regular checkout lanes. Regular 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). 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 determine the average and maximum time from when the shopper arrives at the checkout area until they complete their checkout. Also observe the average and maximum of each of the four queue lengths, and the utilization of each of the four checkers. Add a plot to track the length of each queue on the same set of axes, color-coded, and animate your queues and resources. Put a text box in your model containing a table of your results.

Explanation / Answer

All the shoppers with a service time of less than 5 minutes will always use the fast checkout lane. Those with a service time of 5 minutes or more will still choose from the three regular checkout lanes. The rest settings are same with first question.

Two part types arrive to a three-workstation system. Part type 1 arrives according to an exponential distribution with interarrival time mean of 5 minutes, and the first arrival is at time 0. This part type is first processed at workstation 2 and then workstation 3. Its processing time at workstation 2 follows a triangular distribution with minimum 2 min, mode 2.5 min, and max 4 min. Its processing time at workstation 3 follows a triangular distribution with minimum 3 min, mode 4.5 min, and max 7 min. Part type 2 arrives according to an exponential distribution with interarrival time mean of 7 minutes, and the first arrival is at time 0. This part type is processed at workstation 1 first, then workstation 3. Its processing time at workstation 1 is triangular (3, 6.8, 8) minutes, and its processing time at workstation 3 is triangular (3, 5, 7) minutes. Run your simulation for a single replication of 2000 minutes and observe the average and maximum time in system for each part type.

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