A service centre has 60 staff to be scheduled in six time periods in one day...

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A service centre has 60 staff to be scheduled in six time periods in one day (24 hours). One staff works continuously for 8 hours per day, that is, a staff can start from any time period. For example, if one staff starts at 4:00 pm, he or she will finish at 12:00 midnight. However, the number of incoming calls varies significantly according to the time of day. The slowest period is between midnight and 4:00 am. It is estimated that the average number of calls served by a staff is 8 during that period. The average number of calls served by a staff in different time period of day is shown in the following table: Time period 1 2 3 Duration 0:00 am to 4:00 am 4:00 am to 8:00 am 8:00 am to 12:00 noon Average number of calls served 8 15 30 4 5 6 12:00 noon to 4:00 pm 4:00 pm to 8:00 pm 8:00 pm to 12:00 midnight 35 32 25 To retain customers and acquire new ones, the service centre must maintain a high customer service level. To do so, it has determined the minimum number of staff it needs to work during every 4-hour time segment is as follows: 8 from midnight to 4:00 am, 14 from 4:00 to 8:00 am, 24 from 8:00 am to noon, 28 from noon to 4:00 pm, 20 from 4:00 to 8:00 pm, and 15 from 8:00 pm to midnight. Tasks: 1) Formulate and solve an integer programming model to help the service centre schedule its staff. (10 marks) 2) If the service centre has a maximum of only 10 staff who will work the late shift from midnight to 8:00 am, reformulate the model to reflect this complication and solve it. Take note that you are required to present the whole model again with all constraints added. (10 marks) 3) All staff like to work the day shift from 8:00 am to 4:00 pm, so the service centre has decided to limit the number of staff who work from 8:00 am to 4:00 pm to maximum 16. Reformulate the model in 2) to reflect this restriction and solve it. Take note that you are required to present the whole model again with all constraints added. (5 marks) A service centre has 60 staff to be scheduled in six time periods in one day (24 hours). One staff works continuously for 8 hours per day, that is, a staff can start from any time period. For example, if one staff starts at 4:00 pm, he or she will finish at 12:00 midnight. However, the number of incoming calls varies significantly according to the time of day. The slowest period is between midnight and 4:00 am. It is estimated that the average number of calls served by a staff is 8 during that period. The average number of calls served by a staff in different time period of day is shown in the following table: Time period 1 2 3 Duration 0:00 am to 4:00 am 4:00 am to 8:00 am 8:00 am to 12:00 noon Average number of calls served 8 15 30 4 5 6 12:00 noon to 4:00 pm 4:00 pm to 8:00 pm 8:00 pm to 12:00 midnight 35 32 25 To retain customers and acquire new ones, the service centre must maintain a high customer service level. To do so, it has determined the minimum number of staff it needs to work during every 4-hour time segment is as follows: 8 from midnight to 4:00 am, 14 from 4:00 to 8:00 am, 24 from 8:00 am to noon, 28 from noon to 4:00 pm, 20 from 4:00 to 8:00 pm, and 15 from 8:00 pm to midnight. Tasks: 1) Formulate and solve an integer programming model to help the service centre schedule its staff. (10 marks) 2) If the service centre has a maximum of only 10 staff who will work the late shift from midnight to 8:00 am, reformulate the model to reflect this complication and solve it. Take note that you are required to present the whole model again with all constraints added. (10 marks) 3) All staff like to work the day shift from 8:00 am to 4:00 pm, so the service centre has decided to limit the number of staff who work from 8:00 am to 4:00 pm to maximum 16. Reformulate the model in 2) to reflect this restriction and solve it. Take note that you are required to present the whole model again with all constraints added. (5 marks) A service centre has 60 staff to be scheduled in six time periods in one day (24 hours). One staff works continuously for 8 hours per day, that is, a staff can start from any time period. For example, if one staff starts at 4:00 pm, he or she will finish at 12:00 midnight. However, the number of incoming calls varies significantly according to the time of day. The slowest period is between midnight and 4:00 am. It is estimated that the average number of calls served by a staff is 8 during that period. The average number of calls served by a staff in different time period of day is shown in the following table: Time period 1 2 3 Duration 0:00 am to 4:00 am 4:00 am to 8:00 am 8:00 am to 12:00 noon Average number of calls served 8 15 30 4 5 6 12:00 noon to 4:00 pm 4:00 pm to 8:00 pm 8:00 pm to 12:00 midnight 35 32 25 To retain customers and acquire new ones, the service centre must maintain a high customer service level. To do so, it has determined the minimum number of staff it needs to work during every 4-hour time segment is as follows: 8 from midnight to 4:00 am, 14 from 4:00 to 8:00 am, 24 from 8:00 am to noon, 28 from noon to 4:00 pm, 20 from 4:00 to 8:00 pm, and 15 from 8:00 pm to midnight. Tasks: 1) Formulate and solve an integer programming model to help the service centre schedule its staff. (10 marks) 2) If the service centre has a maximum of only 10 staff who will work the late shift from midnight to 8:00 am, reformulate the model to reflect this complication and solve it. Take note that you are required to present the whole model again with all constraints added. (10 marks) 3) All staff like to work the day shift from 8:00 am to 4:00 pm, so the service centre has decided to limit the number of staff who work from 8:00 am to 4:00 pm to maximum 16. Reformulate the model in 2) to reflect this restriction and solve it. Take note that you are required to present the whole model again with all constraints added. (5 marks) A service centre has 60 staff to be scheduled in six time periods in one day (24 hours). One staff works continuously for 8 hours per day, that is, a staff can start from any time period. For example, if one staff starts at 4:00 pm, he or she will finish at 12:00 midnight. However, the number of incoming calls varies significantly according to the time of day. The slowest period is between midnight and 4:00 am. It is estimated that the average number of calls served by a staff is 8 during that period. The average number of calls served by a staff in different time period of day is shown in the following table: Time period 1 2 3 Duration 0:00 am to 4:00 am 4:00 am to 8:00 am 8:00 am to 12:00 noon Average number of calls served 8 15 30 4 5 6 12:00 noon to 4:00 pm 4:00 pm to 8:00 pm 8:00 pm to 12:00 midnight 35 32 25 To retain customers and acquire new ones, the service centre must maintain a high customer service level. To do so, it has determined the minimum number of staff it needs to work during every 4-hour time segment is as follows: 8 from midnight to 4:00 am, 14 from 4:00 to 8:00 am, 24 from 8:00 am to noon, 28 from noon to 4:00 pm, 20 from 4:00 to 8:00 pm, and 15 from 8:00 pm to midnight. Tasks: 1) Formulate and solve an integer programming model to help the service centre schedule its staff. (10 marks) 2) If the service centre has a maximum of only 10 staff who will work the late shift from midnight to 8:00 am, reformulate the model to reflect this complication and solve it. Take note that you are required to present the whole model again with all constraints added. (10 marks) 3) All staff like to work the day shift from 8:00 am to 4:00 pm, so the service centre has decided to limit the number of staff who work from 8:00 am to 4:00 pm to maximum 16. Reformulate the model in 2) to reflect this restriction and solve it. Take note that you are required to present the whole model again with all constraints added. (5 marks)

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