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Schedule Model

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Suppose you are waiting in line to check out at a grocery store and there are 7 other customers in front of you (so you are customer 8). By inspecting the amount of items in their baskets, you estimate the following check-out time in minutes:

Customer 1 2 3 4 5 6 7 8
Checkout time 10 5 3 7 5 10 2 5

a) What would be the scheduling model for this situation (environment, restriction, constraints) if you wish to minimize the total time in system? Use the appropriate scheduling notation.

b) Calculate the objective function value for the sequence of customers of 1 to 8 to minimize the total time in system. Draw a Gantt chart that shows completion time values.

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Solution Preview

a) In this problem, we have:

- a single machine (the lone cash register)
- eight jobs to be completed (j = 1 to 8 for cutomers 1 to 8)
- processing times t_j for each j (checkout times)
- completion times C_j for each j (waiting time plus checkout ...

Solution Summary

The solution discusses what a schedule model would be like for the situation.