A new Y-Mart grocery store opened in a town near you early in 2012 complete with a Subway restaurant, wide aisles, well-stocked shelves, a level parking lot and long lines at the checkout stations.

An MBA student fluent in time/motion studies was hired temporarily to observe hourly store customer checkout patterns. This same student also observed waiting times, line lengths, etc.

From the collected data and some simple simulations, the student identified the following ‘optimal’ number of checkout stations to be open (including express lanes) during each of the hourly time frames.

Checkout specialists at this Y-Mart start at five different times – 8am, 10am, noon, 4pm and 5pm. At 8am, they work 3 hours, take and hour off, then work 2 more hours. For the other four starting times, they either work 3 hours on, 1 hour off, and then 2 hours on again, or 2 hours on, 1 hour off, and 3 hours on.

Checkout specialists who work the 8am shift are paid $60 (12/hours), those who work the 10am and noon shift are paid $50, those who work the 4pm shift are paid $54 and those who work the 5pm shift are paid $56 (daily).

Determine how many people should be assigned to each of the shifts (which you need to identify) in order to best meet the needed hourly number of checkout specialists. Minimize costs as your criteria. Make sure there are integer solution values, but it is okay to wait until after a trial ‘run’.

5 ......................................................... 8-9am

7 ........................................................ 9-10am

9 ...................................................... 10-11am

10 .................................................... 11-noon

15 ................................................ noon-1pm

14 ...................................................... 1-2pm

12 ...................................................... 2-3pm

14 ...................................................... 3-4pm

20 ...................................................... 4-5pm

25 ...................................................... 5-6pm

20 ...................................................... 6-7pm

15 ...................................................... 7-8pm

12 ...................................................... 8-9pm

10 .................................................... 9-10pm

8 .................................................... 10-11pm