Arrangement for scheduling tasks based on probability of availability of resources at a future point in time
A resource task-completion forecaster ( 122 ) of an ACD ( 104 ) determines a probability that an agent ( 156 ) will complete servicing a presently-assigned call by a specified time horizon h. The forecaster determines ( 202 ) the type of call that the agent is servicing, determines ( 204 ) the amount of time t that the agent has already been servicing the call, retrieves ( 206 ) the mean and the variance of time historically spent by agents on servicing this type of call to completion, fits ( 208 ) the mean and the variance to a lifetime closed-form cumulative-probability distribution F, such as a Weibull distribution, to determine parameters of dispersion and central tendency, evaluates ( 210, 212 ) the distribution for t and h+t, computes ( 216 ) the probability of the agent not having completed servicing the call by now as Q=1−F(t), and computes ( 218 ) the probability that the agent will have completed servicing the call by the time horizon as P = F ( t + h ) - F ( t ) Q . A resource scheduler ( 124 ) sums ( 302 ) the probabilities P for all agents to obtain the number of agents that are expected to be available at the time horizon, and schedules (304) for the time horizon no more than that number of new calls for servicing by the agents.
1. A work-management method comprising:
for a future point in time, determining a probability of availability of each resource of a plurality of resources at said future point in time, to obtain the probabilities of availability of the plurality of the resources, comprising
determining an amount of time that a resource has already spent servicing a task,
determining a first probability of completion of the servicing of the task by the resource by the future point in time without consideration of the amount of time that the resource has already spent servicing the task,
determining a second probability that the resource has not completed servicing the task within the amount of time that the resource has already spent servicing the task, and
determining from the first and the second probability a third probability of completion of the servicing of the task by the resource by the future point in time considering the amount of time that the resource has already spent servicing the task;
combining together the third determined probability of availability of each resource of the plurality of resources to obtain a number that is a result of the combining; and
using the number to schedule new tasks for the resources for the future point in time.
2. The method of claim 1 wherein:
using the number to schedule new tasks comprises
scheduling for the future point in time no more than the number of the new tasks to become available for servicing by the plurality of the resources.
3. The method of claim 2 wherein:
combining together the determined probabilities comprises
summing the probabilities to obtain the number.
4. A work-management method comprising:
for a future point in time, determining a probability of availability of each resource of a plurality of resources at said future point in time, to obtain the probabilities of availability of the plurality of the resources, comprising
determining an amount of time t that each resource of the plurality of resources has been servicing a task by now,
for each of the resources, determining a probability F(t+h) of the resource servicing its task to completion within a total amount of time t+h, where h is a selected time horizon,
for each of the resources, determining a probability F(t) of the resource completing servicing its task by now, and
for each of the resources, determining a probability P that the resource will complete servicing its task at the future point in time the amount of time h from now as
F
(
t
+
h
)
-
F
(
t
)
1
-
F
(
t
)
.
combining together the determined probabilities of availability of the plurality of resources to obtain a number that is a result of the combining; and
using the number to schedule new tasks for the resources for the future point in time.
5. The method of claim 4 in a call center wherein:
the new tasks comprise calls; and
using the number to schedule new tasks comprises
in response to P, determining whether or not to initiate or cancel an outbound call.
6. A work-management method comprising:
determining an amount of time t that a resource has been servicing a task by now;
determining a probability F(t+h) of the resource servicing the task to completion within a total amount of time t+h, where h is a selected time horizon;
determining a probability F(t) of the resource completing servicing the task by now;
determining a probability P that the resource will complete servicing the task within the amount of time h from now as
F
(
t
+
h
)
-
F
(
t
)
1
-
F
(
t
)
;
and
in response to P, scheduling another task for servicing.
7. The method of claim 6 wherein:
scheduling comprises
in response to P, determining whether or not to initiate said another task.
8. The method of claim 6 in a call center wherein:
the new tasks comprise calls; and
scheduling comprises
in response to P, determining whether or not to initiate an outbound call.
9. The method of claim 6 further comprising:
performing the determining steps for a plurality of resources, and
determining a number of the resources that will likely have completed servicing their respective tasks within the amount of time h from now as a sum of the probabilities P determined for individual ones of the plurality of resources; wherein
scheduling comprises
in response to determining the number of the resources, scheduling new tasks for servicing.
10. The method of claim 9 wherein:
scheduling tasks for servicing comprises scheduling no more than the number of the tasks for servicing.
11. The method of claim 6 wherein:
determining a probability F(t+h) comprises
obtaining historical task-completion statistics, and
from the obtained statistics determining the probability F(t+h); and
determining a probability F(t) comprises
from the obtained statistics determining the probability F(t).
12. The method of claim 11 wherein:
obtaining historical task-completion statistics comprises
obtaining a mean and a variance of time historically spent by resources on servicing tasks to completion.
13. The method of claim 6 wherein:
determining a probability F(t+h) comprises
obtaining historical task-completion statistics,
fitting the task-completion statistics into a lifetime closed-form cumulative-probability distribution to determine parameters of the distribution, and
evaluating the distribution with the determined parameters and the total amount of time t+h to obtain F(t+h); and
determining a probability F(t) comprises
evaluating the distribution with the determined parameters and the amount of time t to obtain F(t).
14. The method of claim 13 wherein:
obtaining historical task-completion statistics comprises
obtaining a mean and a variance of time historically spent by resources on servicing tasks to completion;
the cumulative-probability distribution F comprises a Weibull distribution; and
the parameters comprise a dispersion parameter and a parameter of central tendency.
15. The method of claim 6 wherein:
determining an amount of time t comprises
determining the amount of time t that the resource has been servicing a task of one of a plurality of different types of tasks; and
determining historical task-completion statistics comprises
determining the historical task-completion statistics for the one type of tasks.
16. The method of claim 6 wherein:
scheduling another task comprises
in response to P initiating preparation of a task that may require servicing by an agent at a later time.
17. The method of claim 6 wherein:
determining a probability F(t+h) comprises
obtaining a historical histogram for task completion, and
evaluating a cumulative said probability with the obtained histogram for the total amount of time t+h to obtain F(t+h); and
determining a probability F(t) comprises
evaluating the cumulative probability with the obtained histogram for the amount of time t to obtain F(t).
18. The method of claim 6 wherein:
scheduling comprises
in response to P, canceling preparation of a task that could require servicing by a resource.
19. A computer-readable medium containing instructions which, when executed in a computer, cause the computer to perform the steps of:
for a future point in time, determining a probability of availability of each resource of a plurality of resources at said future point in time, to obtain the probabilities of availability of the plurality of the resources, comprising
determining an amount of time that a resource has already spent servicing a task,
determining a first probability of completion of the servicing of the task by the resource by the future point in time without consideration of the amount of time that the resource has already spent servicing the task,
determining a second probability that the resource has not completed servicing the task within the amount of time that the resource has already spent servicing the task, and
determining from the first and the second probability a third probability of completion of the servicing of the task by the resource by the future point in time considering the amount of time that the resource has already spent servicing the task;
combining together the third determined probability of availability of each resource of the plurality of resources to obtain a number that is a result of the combining; and
using the number to schedule new tasks for the resources for the future point in time.
20. The medium of claim 19 wherein:
using the number to schedule new tasks comprises
scheduling for the future point in time no more than the number of the new tasks to become available for servicing by the plurality of the resources.
21. The medium of claim 20 wherein:
combining together the determined probabilities comprises
summing the probabilities to obtain the number.
22. A work-management apparatus comprising:
a storage medium for storing instructions, and
a processor for executing the instructions, the medium and the processor together comprising:
means for determining, for a future point in time, a probability of availability of each resource of a plurality of resources at said future point in time, to obtain the probabilities of availability of the plurality of the resources, including
determining an amount of time that a resource has already spent servicing a task,
determining a first probability of completion of the servicing of the task by the resource by the future point in time without consideration of the amount of time that the resource has already spent servicing the task,
determining a second probability that the resource has not completed servicing the task within the amount of time that the resource has already spent servicing the task, and
determining from the first and the second probability a third probability of completion of the servicing of the task by the resource by the future point in time considering the amount of time that the resource has already spent servicing the task;
means cooperative with the determining means for combining together the third probability of availability of each resource of the plurality of resources to obtain a number that is a result of the combining; and
means cooperative with the means for combining the determined probabilities, for scheduling no more than the obtained number of new tasks to be serviced by the plurality of the resources at the future point in time.
23. The apparatus of claim 22 wherein:
the means for combining together the determined probabilities comprise
means for summing the probabilities to obtain the number.
24. The apparatus of claim 22 in a call center wherein:
the new tasks comprise calls; and
the means for scheduling comprise
means responsive to P, for determining whether or not to initiate or cancel an outbound call.
25. A work-management apparatus comprising:
a storage medium for storing instructions, and
a processor for executing the instructions, the medium and the processor together comprising:
means for determining an amount of time t that a resource has been servicing a task by now;
means cooperative with the time-determining means for determining a probability F(t+h) of the resource servicing the task to completion within a total amount of time t+h, where h is a selected time horizon;
means cooperative with the time-determining means for determining a probability F(t) of the resource completing servicing the task by now;
means cooperative with both of the probability-determining means for determining a probability P that the resource will complete servicing the task within the amount of time h from now as
F
(
t
+
h
)
-
F
(
t
)
1
-
F
(
t
)
;
and
means cooperative with the P-determining means and responsive to P for scheduling another task for servicing.
26. The apparatus of claim 25 wherein:
the means for scheduling comprise
means responsive to P, for determining whether or not to initiate said another task.
27. The apparatus of claim 25 in a call center wherein:
the new tasks comprise calls; and
the means for scheduling comprise
means responsive to P, for determining whether or not to initiate an outbound call.
28. The apparatus of claim 25 wherein:
the means for determining an amount of time t comprise
means for determining the amount of time t for each of a plurality of resources;
the means for determining a probability F(t+h) comprise
means for determining the probability F(t+h) for each of the plurality of resources;
the means for determining a probability F(t) comprise
means for determining the probability F(t) for each of the plurality of resources, and
means for determining a number of the plurality of resources that will likely have completed servicing their respective tasks within the amount of time h from now as a sum of the probabilities P determined for individual ones of the plurality of resources; and
the means for scheduling comprise
means responsive to determining the number of the resources, for scheduling new tasks for servicing.
29. The apparatus of claim 28 wherein:
the means for scheduling comprise
means for scheduling no more than the number of the tasks for servicing.
30. The apparatus of claim 25 wherein:
the means for determining a probability F(t+h) comprise
means for obtaining historical task-completion statistics, and
means for determining the probability F(t+h) from the obtained statistics; and
the means for determining a probability F(t) comprise
means for determining the probability F(t) from the obtained statistics.
31. The apparatus of claim 30 wherein:
the means for obtaining historical task-completion statistics comprise
means for obtaining a mean and a variance of time historically spent by resources on servicing tasks to completion.
32. The apparatus of claim 25 wherein:
the means for determining a probability F(t+h) comprise
means for obtaining historical task-completion statistics,
means for fitting the task-completion statistics into a lifetime closed-form cumulative-probability distribution to determine parameters of the distribution, and
means for evaluating the distribution with the determined parameters and the total amount of time t+h to obtain F(t+h); and
the means for determining a probability F(t) comprise
means for evaluating the distribution with the determined parameters and the amount of time t to obtain F(t).
33. The apparatus of claim 32 wherein:
the means for obtaining historical task-completion statistics comprise
means for obtaining a mean and a variance of time historically spent by resources on servicing tasks to completion;
the cumulative-probability distribution F comprises a Weibull distribution; and
the parameters comprise a dispersion parameter and a parameter of central tendency.
34. The apparatus of claim 25 wherein:
the means for determining an amount of time t comprise
means for determining the amount of time t that the resource has been servicing a task of one of a plurality of different types of tasks; and
the means for determining historical task-completion statistics comprise
means for determining the historical task-completion statistics for the one type of tasks.
35. The apparatus of claim 25 wherein:
the means for scheduling another task comprise
means responsive to P for initiating preparation of a task that may require servicing by an agent at a later time.
36. The apparatus of claim 25 wherein:
the means for determining a probability F(t+h) comprise
means for obtaining a historical histogram for task completion, and
means for evaluating a cumulative said probability with the obtained histogram for the total amount of time t+h to obtain F(t+h); and
the means for determining a probability F(t) comprise
means for evaluating the cumulative probability with the obtained histogram for the amount of time t to obtain F(t).
37. The apparatus of claim 25 wherein:
the means for scheduling comprise
means responsive to P, for canceling preparation of a task that could require servicing by a resource.
38. A work-management apparatus comprising:
a storage medium for storing instructions, and
a processor for executing the instructions, the medium and the processor together comprising:
means for determining, for a future point in time, a probability of availability of each resource of a plurality of resources at said future point in time, to obtain the probabilities of availability of the plurality of the resources;
means for determining, for each resource of the plurality of resources, an amount of time t that the resource has been servicing a task by now,
means for determining, for each resource of the plurality of resources, a probability F(t+h) of the resource servicing its task to completion within a total amount of time t+h, where h is a selected time horizon,
means for determining, for each resource of the plurality of resources, a probability F(t) of the resource completing servicing its task by now, and
means for determining, for each resource of the plurality of resources, a probability P that the resource will complete servicing its task at the future point in time the amount of time h from now as
F
(
t
+
h
)
-
F
(
t
)
1
-
F
(
t
)
;
means cooperative with the determining means for combining together the probabilities of availability of the plurality of resources to obtain a number that is a result of the combining; and
means cooperative with the means for combining the determined probabilities, for scheduling no more than the obtained number of new tasks to be serviced by the plurality of the resources at the future point in time.
39. A computer-readable medium containing instructions which, when executed in a computer, cause the computer to perform the steps of:
for a future point in time, determining a probability of availability of each resource of a plurality of resources at said future point in time, to obtain the probabilities of availability of the plurality of the resources, comprising
for each resource of the plurality of resources, determining an amount of time t that the resource has been servicing a task by now,
for each resource of the plurality of resources, determining a probability F(t+h) of the resource servicing its task to completion within a total amount of time t+h, where h is a selected time horizon,
for each resource of the plurality of resources, determining a probability F(t) of the resource completing servicing its task by now, and
for each resource of the plurality of resources, determining a probability P that the resource will complete servicing its task at the future point in time the amount of time h from now as
F
(
t
+
h
)
-
F
(
t
)
1
-
F
(
t
)
;
combining together the determined probabilities of availability of the plurality of resources to obtain a number that is a result of the combining; and
using the number to schedule new tasks for the resources for the future point in time.
40. The method of claim 39 for a call center wherein:
the new tasks comprise calls; and
using the number to schedule new tasks comprises
in response to P, determining whether or not to initiate or cancel an outbound call.
41. A computer-readable medium containing instructions which, when executed in a computer, cause the computer to perform the steps of:
determining an amount of time t that a resource has been servicing a task by now;
determining a probability F(t+h) of the resource servicing the task to completion within a total amount of time t+h, where h is a selected time horizon;
determining a probability F(t) of the resource completing servicing the task by now;
determining a probability P that the resource will complete servicing the task within the amount of time h from now as
F
(
t
+
h
)
-
F
(
t
)
1
-
F
(
t
)
;
and
in response to P, scheduling another task for servicing.
42. The method of claim 41 wherein:
scheduling comprises
in response to P, determining whether or not to initiate said another task.
43. The medium of claim 41 for a call center wherein:
the new tasks comprise calls; and
scheduling comprises
in response to P, determining whether or not to initiate an outbound call.
44. The medium of claim 41 further comprising instructions which, when executed in the computer, cause the computer to perform the steps of:
performing the determining steps for a plurality of resources, and
determining a number of the resources that will likely have completed servicing their respective tasks within the amount of time h from now as a sum of the probabilities P determined for individual ones of the plurality of resources; wherein
scheduling comprises
in response to determining the number of the resources, scheduling new tasks for servicing.
45. The medium of claim 44 wherein:
scheduling tasks for servicing comprises scheduling no more than the number of the tasks for servicing.
46. The medium of claim 41 wherein:
determining a probability F(t+h) comprises
obtaining historical task-completion statistics, and
from the obtained statistics determining the probability F(t+h); and
determining a probability F(t) comprises
from the obtained statistics determining the probability F(t).
47. The medium of claim 46 wherein:
obtaining historical task-completion statistics comprises
obtaining a mean and a variance of time historically spent by resources on servicing tasks to completion.
48. The medium of claim 41 wherein:
determining a probability F(t+h) comprises
obtaining historical task-completion statistics,
fitting the task-completion statistics into a lifetime closed-form cumulative-probability distribution to determine parameters of the distribution, and
evaluating the distribution with the determined parameters and the total amount of time t+h to obtain F(t+h); and
determining a probability F(t) comprises
evaluating the distribution with the determined parameters and the amount of time t to obtain F(t).
49. The medium of claim 48 wherein:
obtaining historical task-completion statistics comprises
obtaining a mean and a variance of time historically spent by resources on servicing tasks to completion;
the cumulative-probability distribution F comprises a Weibull distribution; and
the parameters comprise a dispersion parameter and a parameter of central tendency.
50. The method of claim 41 wherein:
determining an amount of time t comprises
determining the amount of time t that the resource has been servicing a task of one of a plurality of different types of tasks; and
determining historical task-completion statistics comprises
determining the historical task-completion statistics for the one type of tasks.
51. The medium of claim 41 wherein:
scheduling another task comprises
in response to P initiating preparation of a task that may require servicing by an agent at a later time.
52. The medium of claim 41 wherein:
determining a probability F(t+h) comprises
obtaining a historical histogram for task completion, and
evaluating a cumulative said probability with the obtained histogram for the total amount of time t+h to obtain F(t+h); and
determining a probability F(t) comprises
evaluating the cumulative probability with the obtained histogram for the amount of time t to obtain F(t).
53. The medium of claim 41 wherein:
scheduling comprises in response to P, canceling preparation of a task that could require servicing by a resource.