Reference no: EM133047535

Wings Airlines flies international flights between Columbus and Quebec. The management must determine how to staff the ticket counters and the arrival/departure gates between the hours of 6:00am and 9:00pm at the Port Columbus International Airport. Wings Airlines is very aware of problems that can occur with international passengers so it hires both bilingual agents as well as agents who only speak English. The agents can work 3-hour shifts, 6-hour shifts, or 9-hour shifts. The table below indicates the minimum number of agents for each 3-hour time period throughout the day:

Time Agents Required
6:00am - 9:00am
15 at least workers
9:00am - 12:00pm
25 at least workers
12:00pm - 3:00pm
31 at least workers
3:00pm - 6:00pm
27 at least workers
6:00pm - 9:00pm
17 at least workers

Agents begin their shifts either at 6:00am, 9:00am, noon, 3:00pm, or 6:00pm. The English-speaking agents are paid $19.00 per hour and bilingual agents are paid $23.00 per hour. In addition, Wings Airlines provides outstanding benefits; the cost of these benefits is $50.00 per agent per day regardless of the length of their shift. No more than 40% of the agents must be on 9-hour shifts and at least 20% of the agents must be on 3-hour shifts. Wings Airlines' policy is that at least 30% the agents working during any 3-hour time period be bilingual.

Formulate an integer program to determine the staffing (the number of each type of agent, their starting time, and the number of hours worked) to minimize total staffing cost. Note that the general form must be used as the total number of agents working may be different from the total number of agents required.