To the extent permitted by local law, each Acme Home Improvements store, including AMC, is open from 7 am - 11 pm every day. Acme Mexico City advance planners in North Carolina have provided the following table, which identifies the minimum number of customer service employees estimated to be needed on the floor of the store each hour of a typical work day:
Customer Service Employees
Time Period Minimum number needed on the floor
7 am - 8 am 10
8 am - 9 am 12
9 am - 10 am 18
10 am - 11 am 22
11 am - 12 pm 22
12 pm - 1 pm 26
1 pm - 2 pm 26
2 pm - 3 pm 26
3 pm - 4 pm 26
4 pm - 5 pm 26
5 pm - 6 pm 28
6 pm - 7 pm 28
7 pm - 8 pm 24
8 pm - 9 pm 22
9 pm - 10 pm 14
10 pm - 11 pm 12
In the interest of cost control, the planners have also imposed a not-to-exceed maximum of 30 customer service employees on the floor at any time.
Full-time customer service employees at AMC work a 9 hour shift (8 hours of work plus a 1 hour meal break) either from 7 am to 4 pm or from 2 pm to 11 pm. Workers on the 7-4 shift are assigned an hour-long lunch break at either 11 am or 12 noon. Workers on the 2-11 shift are assigned an hour-long dinner break at either 5 pm or 6 pm.
Part-time customer service employees work four consecutive hours per day and their shifts can start any hour between 7 am and 7 pm.
By corporate policy, which is consistent with Mexican labor law, the company limits the hours worked by part-time customer service employees to 50% of the day's total scheduled hours.
Part-time customer service employees earn $500 per day, and full-time customer service employees earn $1100 per day in salary and benefits (here, $ = Moneda Nacional, ie, the Mexican peso).
Acme operations analysts working in North Carolina, working with the AMC advance planners, have used integer linear programming, an important tool employed by operations managers, to propose in accordance with the foregoing factors, an employee assignment schedule for a typical day. Their proposed schedule is the following item in Course Content.
Each student recommends to the AMC store manager, who is unfamiliar with integer linear programming, a customer service employee daily assignment schedule for Acme Mexico City that includes the following:
1. An executive summary with key results
2. An employee assignment schedule for a typical day that minimizes personnel costs using the operations analysts' schedule modified as by the qualitative factors, if any, that you determine are relevant
3. A discussion of underlying assumptions and of your selected qualitative factors
4. A further discussion of how non-typical days might affect the schedule
5. Optionally, and for extra points to be determined by your section professor, a sensitivity analysis that shows how relaxation of the 50% constraint on the hours worked by part-time customer service employees might affect the daily personnel costs