Getchathere Airlines must staff it ticket counters between the hours of 6am and
ID: 358677 • Letter: G
Question
Getchathere Airlines must staff it ticket counters between the hours of 6am and 9pm daily inside Columbus International Airport. Ticket attendants work six-hour shifts at the counter. Due to the large international population of Columbus, Getchather employs two types of agents – those who speak English as the first language and those who are bilingual (English and Polish). The requirements for the number of agents are a function of the numbers of people expected to pass through the ticket counter during various hours. Getchathere’s management believes that the need for agents between the hours of 6am and 9 pm are as in the table below:
Agents begin their shifts either at 6am, 9am, noon, or 3pm. The shifts are designated A, B, C, and D, respectively. Getchathere Airlines policy is that at least half the attendants on any shift speak English as their first language and that at least one-quarter of the attendants be bilingual. The English-speaking agents are paid $19/hour and bilingual agents are paid $23/hour.
Formulate as an integer program to determine the number of English-speaking and bilingual attendants that minimizes the total cost without violating any constraints.
Period Time Agents Required 1 6am - Noon 24 2 9am - Noon 40 3 Noon - 3pm 32 4 3pm - 6pm 48 5 6pm - 9pm 24Explanation / Answer
Formulate ILP
Decision variablaes:
A1, B1, C1, D1 = Number of English speaking agents employed to work in shift A,B,C,D respectively
A2, B2, C2, D2 = Number of Bilingual agents employed to work in shift A,B,C,D respectively
Objective: Minimize Z = 19*(A1+B1+C1+D1)+23*(A2+B2+C2+D2)
Constraints:
A1+B1 >= 24
A1+A2+B1+B2 >= 40
A2+A3+B2+B3 >= 32
A3+A4+B3+B4 >= 48
A4+B4 >= 24
A1 >= 0.5(A1+B1)
A1+A2 >= 0.5(A1+A2+B1+B2)
A2+A3 >= 0.5(A2+A3+B2+B3)
A3+A4 >= 0.5(A3+A4+B3+B4)
A4 >= 0.5(A4+B4)
B1 >= 0.25(A1+B1)
B1+B2 >= 0.25(A1+A2+B1+B2)
B2+B3 >= 0.25(A2+A3+B2+B3)
B3+B4 >= 0.25(A3+A4+B3+B4)
B4 >= 0.25(A4+B4)
A1,B1,C1,D1,A2,B2,C2,D2 >= 0, Integer
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