Introduction to Operational
MATH2013 Simulation Assignment
The problem
The management of a call centre has hired your simulation consulting firm, SureSim, to provide decision support on call centre operations. They have provided the following problem definition and data.
The call centre serves two types of calls. There are three types of agents (servers). Agent types 1 and 2 are specialists for call types 1 and 2, respectively. Agent type 3 is a generalist that can serve either call type (not at once). The call centre opens at 8:00 empty (i.e., with no calls in the system) and stops accepting calls at 18:00. Calls already in the system at
18:00 do get processed on the same day; such calls are a negligible minority. Call service times are exponentially distributed with mean 5 minutes.
Call arrival rates vary across days. 50% of days are “heavy 1”, with per-minute arrival rates of 2 for type-1 calls and 1.6 for type-2 calls (NB: The mean inter-arrival time is the inverse of the arrival rate); and the other 50% of days are “heavy 2”, with arrival rates reversed (1.6 for type-1 calls and 2 for type-2 calls).
A customer abandons (hangs up) without receiving service as soon as his/her waiting time in queue is equal to his patience time. Customer patience times are independent and exponentially distributed with mean 5 minutes.
Management must fix a staffing for both types of day, as the type of day is unpredictable.
The staffing must satisfy the following constraints on performance:
1. The Quality of Service (QoS) is the fraction of calls whose waiting time in queue is no larger than 30 seconds. QoS should be no less than 70%.
2. The fraction of calls that abandon should not exceed 5%.
It is important that the constraints above refer to performance averaged across the two day types, but monitored separately for each call type.
A routing policy specifies which type of agent an arriving call is sent to (when there is a choice) and also how a generalist selects the next call to process
The problem
The management of a call centre has hired your simulation consulting firm, SureSim, to provide decision support on call centre operations. They have provided the following problem definition and data.
The call centre serves two types of calls. There are three types of agents (servers). Agent types 1 and 2 are specialists for call types 1 and 2, respectively. Agent type 3 is a generalist that can serve either call type (not at once). The call centre opens at 8:00 empty (i.e., with no calls in the system) and stops accepting calls at 18:00. Calls already in the system at
18:00 do get processed on the same day; such calls are a negligible minority. Call service times are exponentially distributed with mean 5 minutes.
Call arrival rates vary across days. 50% of days are “heavy 1”, with per-minute arrival rates of 2 for type-1 calls and 1.6 for type-2 calls (NB: The mean inter-arrival time is the inverse of the arrival rate); and the other 50% of days are “heavy 2”, with arrival rates reversed (1.6 for type-1 calls and 2 for type-2 calls).
A customer abandons (hangs up) without receiving service as soon as his/her waiting time in queue is equal to his patience time. Customer patience times are independent and exponentially distributed with mean 5 minutes.
Management must fix a staffing for both types of day, as the type of day is unpredictable.
The staffing must satisfy the following constraints on performance:
1. The Quality of Service (QoS) is the fraction of calls whose waiting time in queue is no larger than 30 seconds. QoS should be no less than 70%.
2. The fraction of calls that abandon should not exceed 5%.
It is important that the constraints above refer to performance averaged across the two day types, but monitored separately for each call type.
A routing policy specifies which type of agent an arriving call is sent to (when there is a choice) and also how a generalist selects the next call to process