Basic Employee Scheduling

Generic Situation:

One of the most difficult tasks confronting any business owner with a large employee base is scheduling employees.

Example:

Controlled Environment Inc. is a large discount web-based seller of climate control components. The company has various operation centers across the US and receives a large number of orders each day. The warehouse operation is very labor intensive in terms of packing and shipping and the business runs seven days a week. The owner, Russ Harper, is particularly concerned about the labor costs at the central warehouse in Fall Village, CT. The number of packages handled at this location varies from day to day, sometimes greatly. Based upon averaged data for the past two years, Russ estimates that the number of workers needed to take care of business is:

Day Of The WeekWorkers Required
Sunday18
Monday27
Tuesday22
Wednesday26
Thursday25
Friday21
Saturday19
MANPOWER REQUIREMENTS

The workers are unionized and are guaranteed a five day work week with two consecutive days off. Base wage is $655/week. Because most workers prefer to have Saturday and Sunday off, the union has negotiated bonuses of $25 per day for its members who choose to work on the weekend. The possible shifts and salaries for the workers are:


ShiftDays OffWage
1Sunday and Monday$680
2Monday and Tuesday$705
3Tuesday and Wednesday$705
4Wednesday and Thursday$705
5Thursday and Friday$705
6Friday and Saturday$680
7Saturday and Sunday$655
SHIFT v. WAGE REQUIREMENTS


In order to keep the total wage expenses as low as possible, Russ must determine how many employees should be assigned to each shift if he wants to have a sufficient number of workers available each day.

Profit Maximizing Solution:

ShiftSunMonTuesWedThursFriSatWorkers
Scheduled
Wages Per
Worker
1OOWWWWW6$680
2WOOWWWW0$705
3WWOOWWW6$705
4WWWOOWW1$705
5WWWWOOW6$705
6WWWWWOO5$680
7OWWWWWO9$665
W=Days On, O= Days Off

This solution ensures that the available number of employees is at least as great as the required number of employees for each day. The minimal total wage expense associated with this solution is $22,450