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
Check out 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.

c) If it is up to you to sequence the customers in any order you wish, how would you sequence them including yourself to find the minimum time in system for all of them (mention which method would you use. Do not enumerate all possibilities to find the best one, and don’t give yourself extra priority). Draw a Gantt chart that shows completion time values.

d) How would you sequence the customers including yourself to process all of them as soon as possible? What would the objective function be in this case and what is its value? Show your calculations and draw a Gantt chart that show completion time values

e) Suppose another cash register opens up before any of the 8 customers starts checking out and suppose you can schedule all 8 customers in any way you want over these two cash registers, which method would you use to obtain an optimal solution with minimum total completion time? Show your calculations of the objective function and draw a Gantt chart that shows completion time values.

f) For the scenario in part (e), create an optimal solution to minimize the makespan. Draw a Gantt chart that show completion time values (Hint: Since this is a small problem you can find the optimal by inspection or trial and error)

g) For the scenario in part (e), create a schedule using a heuristic or a rule that would typically produce a schedule with a good makespan. How would you measure how good the solution is? Be specific and show your calculations. Draw a Gantt chart that shows completion time values.